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 | . _, COST EFFECTIVE ANALYSIS OF NETWORK COMPUTERS 
 
 i 
 
 August 1972 
 
 BY 
 WILLIAM J. BARR 
 
 IHE UiRARjr Q£ IHe 
 
 ; 1 9 1972 
 
 UNIVERSITY OF ILLINOIS 
 AIiilRP>ANA^HAMPAIGN 
 
UIUCDCS-R-72-538 
 
 COST EFFECTIVE ANALYSIS OF NETWORK COMPUTERS 
 
 BY 
 
 WILLIAM J. BARR 
 
 August 1972 
 
 Department of Computer Science 
 University of Illinois at Urbana-Champaign 
 Urbana, Illinois 6l801 
 
 *This work was supported in part by Contract No. NSF GJ 28289 and was 
 was submitted in partial fulfillment of the requirements for the Master 
 of Science degree in Computer Science, August 1972 • 
 
Digitized by the Internet Archive 
 in 2013 
 
 http://archive.org/details/costeffectiveana538barr 
 
ABSTRACT 
 
 With the advent of network computers , a new area of computer systems 
 analysis has evolved. Unfortunately, most of the work to date merely extends 
 the previously existing theory of communications. Our analysis is predicated 
 on the assumption that a geographically distributed network computer is quite 
 different from telephone networks and individual computing centers. The 
 potential advantages, from a businessman's point of view, of network computers 
 are discussed and some of the more important problems which arise are 
 presented. We take a look at several existing networks and examine their 
 goals and solutions to these kinds of problems. We develop a priority 
 assignment technique for the individual centers that comprise the network 
 and determine load leveling rules for the entire network. In addition, we 
 analyze this system using classical queueing theory techniques. 
 
Ill 
 
 ACKNOWLEDGEMENT 
 
 The author would like to express his most sincere gratitude to his 
 advisor, Professor E. K. Bowdon, Sr., for his advice and criticisms. 
 Without his help and encouragement, this paper would not exist. 
 
 Thanks also goes to my wife, Rhoda, for her aid in proofreading 
 and encouraging me to write in the English language. 
 
 Special thanks go to Phyllis Sloat for her "beautiful typing. 
 
IV 
 
 TABLE OF CONTENTS 
 
 Page 
 
 1 . INTRODUCTION 1 
 
 2 . THE ECONOMIES AND ECONOMICS OF NETWORK COMPUTERS 6 
 
 2.1. Money — The Root of all Research 6 
 
 2.2. The ARPA Network 13 
 
 2.3. The TUCC Network 18 
 
 2.k. The Distributed Computer System 20 
 
 2.5. The ALOHA System and the Problem of Communication Media 25 
 
 3. COST EFFECTIVE PRIORITY ASSIGNMENT 30 
 
 3.1. A Scenario of Cost Effectiveness 30 
 
 3.2. Priority Assignment 35 
 
 3.3. Load Leveling in a Network of Centers ^5 
 
 3 . h . Summary hQ 
 
 k. QUEUEING THEORY ANALYSIS OF THE SINGLE SERVER PRIORITY CASE WITH 
 
 BRIBING AND RENEGING 52 
 
 5 . CONCLUSION 63 
 
 LIST OF REFERENCES 65 
 
1. INTRODUCTION 
 
 Communication systems have long been recognized as being of great 
 importance to all facets of human society. Dating from Greek mythology and 
 Pheidippides' historic run, praises have been heaped upon those who succeeded 
 in delivering important messages before the messages became unimportant. Paul 
 Revere was immortalized for his success in this field as were the riders of 
 the Pony Express. However, all of these legendary and romantic figures were 
 residents of an earlier age when information could be important even when 
 several days old. The invention of the telegraph, the telephone, and, later, 
 the radio changed the nature of the communications industry. The excitement 
 of crawling through the enemy camp with critical information which had been 
 carefully memorized (and the paper it was written on eaten) has been replaced 
 by the thrill of watching a maze of wires and lights spit forth the unscrambled 
 transmission from the guy down the road. The fastest runner with the swiftest 
 horse has been replaced by majestic telephone lines as the dominant hero of the 
 industry. Seconds have replaced days as the critical time units in which 
 transmissions must occur and ulcers have replaced sore muscles as the physical 
 characteristics of the hard working messenger. The communication industry has 
 grown up ! 
 
 By the middle of the twentieth century the phone company had grown to 
 be perhaps the single most important component of industry. The United States 
 had become a nation filled with telephones and all of them were interconnected. 
 In short, the phone company had built a very large network. During the 1960's 
 most of the components of the network became electronic. It was no longer 
 necessary to argue with an operator to place a long distance call, it was 
 sufficient, and cheaper, to simply dial the proper sequence of numbers and it 
 was possible to reach almost anyone in the country. 
 
The 60 's were also the glory years for the electronic digital computer. 
 The computer left the day to day drudgery of number crunching behind-usually 
 as a background job-and moved into the business world. Information storage, 
 retrieval, and processing became the primary occupation of the computer. To 
 the frustration of many an information systems manager, the information he 
 wanted typically took days to arrive at the computing center but only fraction* 
 of a second to process. Thus the information which was available to manage- 
 ment, though available at the push of a button, was usually days old. The 
 stage was now set for the merger of the two entities, the telephone network 
 and the computer, into one which we call the NETWORK COMPUTER.* 
 
 Two definitions are required before we proceed. We define a computing 
 center to be either a single processor or a geographically local and indepen- 
 dent group of interconnected processors. We now define a network computer to 
 be any interconnected group of computing centers. Thus a multiprocessor 
 computing center is also a network computer (frequently called a subnetwork). 
 The apparent ambiguity in this definition is important since the statements 
 we shall make in this paper will apply to all multicenter network computers 
 without regard to whether the centers are comprised of a single processor or 
 a subnetwork. Furthermore, we note that there is no requirement that the 
 interconnections be provided by the phone company. We specifically wish to 
 allow microwave, radio, and light to be possible media for communication 
 between centers. 
 
 -We use the term network computer as opposed to computer network for many 
 reasons the most immediate of which is to avoid confusion with the logic 
 n tw rks which are used in computers and are frequently called comput r 
 networks. Furthermore, the analysis of electrical networks by computers 
 is well known as "computer network analysis. 
 
Since the initial conception of the idea, many network computers have 
 been designed and some have reached the working stage. Until recently, these 
 have all "been constructed primarily as experiments — investigations into the 
 unknown. With support from several organizations — primarily the Advanced 
 Research Projects Agency (ARPA) and the National Science Foundation (NSF) — 
 the goal of these networks has been to advance technology to make it possible 
 to build network computers which can aid society or at least make some money. 
 These experiments have succeeded in advancing technology, but they have also 
 succeeded in opening a veritable Pandora's box of problems, both economic 
 and political in nature, which appear to be much more difficult to solve than 
 the remaining technological problems. We propose to concern ourselves here 
 with some of the miriad of problems which are economic in nature. Our primary 
 motivation for this choice is that computers tend to be very expensive guinea 
 pigs and unless techniques can be found to solve these problems, the political 
 problems may become irrelevent. The continued existence of network computers 
 is predicated upon the ability of designers and managers to show them to be 
 economically viable. 
 
 Network computers offer one significant advantage that is not offered 
 by single processor installations: the availability of large quantities of 
 resources at a cost which is significantly less than would be required if 
 each center purchased these resources individually. These resources are 
 basically of two types: unique resources and common resources. Unique 
 resources are those resources which, for whatever reason, can be made avail- 
 able only at a small number of locations. Examples of unique resources would 
 include the array processing capabilities of the ILLIAC IV or the CDC STAR or 
 specially developed software systems and proprietary programs. Common resources 
 
h 
 
 are those resources which are available at many centers. Increasing the 
 common resources of a center has two distinct advantages. First of all, the 
 computing services become a more reliable commodity. If a processor goes 
 down in a single processor installation, computing services are lost for the 
 duration of the down time. However, if the installation is part of a network 
 computer, some of its tasks can be sent to other installations within the 
 network for processing with a minimum loss of service. The second advantage 
 to increasing the amount of common resources is that the network achieves 
 load leveling capabilities. By load leveling, we mean the capability to trans 
 mit tasks between centers for the purpose of improving the overall through- 
 put of the network. What load leveling does, from a user's point of view, 
 is improve the stability of the computing services which he uses since the 
 peak demand periods at his home center can be smoothed into the slack periods 
 at another center. 
 
 These advantages, while enticing, remain advantages only if they can 
 by achieved in a cost effective manner. In this paper we shall direct our 
 analysis towards developing cost effective tools for use in network computers. 
 
 In Chapter II we briefly discuss some of the problems which arise in 
 network computers from making available increased amounts of each type of 
 resource through a network. We primarily take the businessman's point of 
 view in the analysis with the goal of developing concepts to make network 
 computers attractive to the people who have money to spend in exchange for 
 services. (For insight into these problems we are deeply grateful to Einar 
 Stefferud of Einar Stefferud and Associates, Santa Monica, California.) In 
 this chapter we also examine several networks, both existing and planned, to 
 see how the businessman's problems have affected or might affect policies 
 
and operations. Additionally, we take a look at the communications problem 
 and see what types of communications media are most cost effective in 
 different types of environments. 
 
 In Chapter III we develop priority assignment and scheduling algo- 
 rithms designed to simplify load leveling in a network computer. The system 
 which evolves from this algorithm is analyzed using queueing theory techniques 
 in Chapter IV. 
 
 Finally, in Chapter V, we take time to get a perspective of the results 
 obtained in this paper. We also take a brief look at the road ahead for 
 network computers and indicate some of the roadblocks which remain. 
 
2. THE ECONOMIES AND ECONOMICS OF NETWORK COMPUTERS 
 
 '"The time has come,' the Walrus said, 'to talk of many things'..." 
 Of research done, and networks built, and money making things. 
 
 With apologies to Lewis Carroll 
 
 In this chaper we are concerned with defining and discussing consider- 
 ations which must be taken into account in order for network computers to 
 become viable commodities in the computer marketplace. The potential 
 advantages, from a businessman's point of view, of network computers are 
 discussed and some of the more important business problems which arise are 
 presented. Finally, we take a look at several existing networks and examine 
 their goals and solutions to these kinds of problems. 
 
 2.1 Money — the Root of all Research 
 
 Until recently little justification was needed for the construction 
 and maintenance of network computers. Each project was viewed as a novel 
 and noble investigation into the unknown. During such investigations, 
 inefficiencies could be tolerated and practicality certainly was not an 
 immediate goal. Computers, however, tend to be very expensive guinea pigs 
 and the continued existence of network computers is predicated upon the 
 ability of designers and managers to demonstrate their economic viability. 
 
 With the technological problems virtually solved, it is becoming 
 apparent that no matter whose point of view one takes, the only economically 
 justifiable motivation for building a network computer is resource sharing. 
 However, the businessmen, the users, the people with money to spend, could 
 not care less whose resources they are using for their computer runs. They 
 
7 
 care only that they receive the test possible service at the lowest possible 
 price. The computing center manager who cannot fill this order will soon 
 find himself out of customers. Let us place ourselves in the shoes of a 
 computing center manager, attempt to define some of his problems, and then 
 see how a network computer might help to solve them. 
 
 "The best possible service..." is, in itself, a tall order to fill. 
 The computing center manager finds himself in a position to offer basically 
 two kinds of computing services: contract services and demand services. 
 Contract services are those services which the manager agrees to furnish, 
 at a predetermined price, within specified time periods. Examples of this 
 type of service include payroll runs, billings, and inventory updates. Each 
 of these is run periodically and the value placed by the businessman on the 
 timely completion of the task is large. Demand services are those services 
 which, though defined in advance, may be required at any time and at a 
 possibly unknown price. Frequently the only previous agreements made refer 
 to the type of service to be delivered and limits on how much will be 
 demanded. Examples of tasks which are run on a demand basis include research, 
 information requests, and program debugging runs. University computing 
 centers generally find that most of the services which they offer are of this 
 type. 
 
 Though the classification of computing tasks into one of these pidgeon 
 holes may sometimes be difficult, the distinction is important because of 
 the differing nature of the problems which arise in the successful delivery 
 of services. We will make no attempt to classify computing tasks as belonging 
 to either class but the division is convenient in terms of problem definition. 
 Each type of service generates its own set of problems. For clarity we will 
 discuss them separately and then return to tie them together. 
 
8 
 
 The major problem which arises when a computing center offers contract 
 services is how to be certain that any guarantees made can be kept. 
 Computer down time is an unfortunate but all too real fact of life. Ensuring 
 that equipment does not go down during critical production periods is one of 
 the most difficult tasks in the computing business. Murphy's law (a well 
 known heuristic which states, among other things, that if anything can 
 possibly go wrong, it will, and at the worst possible time) warns us to 
 beware of putting all of our eggs in one basket. Every computing center 
 manager who offers contract services should have a solid and acceptable 
 answer to the critical question, "What do I do when my computer breaks down?" 
 If he wishes to ensure that he can meet all commitments the only answer is 
 to transfer contract tasks to another processor. This is where network 
 computers enter the picture. If the center is part of a network computer, 
 tasks can easily and quickly be transferred to another center (presumably 
 one with resources compatable with the center in question) for processing. 
 The user is happy because his work got done, the manager of the recipient 
 center is happy because he got extra work, and the manager of the stricken 
 center is happy (or at least relieved) because he was able to meet his 
 commitments . 
 
 Associated with the advantage of the manager's being able to offer a 
 more reliable guarantee is the increased expansion capabilities associated 
 with being part of a network computer. Should a center become so busy that 
 its existing computing capabilities are strained, he would clearly like to 
 expand. However, if he has only a single processor, me may find it 
 difficult to continue expanding until another, or larger, processor is 
 working. If he is part of a network computer it would be possible for 
 him to use someone else's resources to process his overflow work until his 
 

 new resources are available. Furthermore, if the increased work is not 
 sufficient to justify expansion of his own facilities, it is possible for 
 him to act as a "broker for resources at other centers. 
 
 The broker concept is also a valid one when talking about the 
 availability of unique resources. The existance, for example, of a CDC 
 STAE on the network offers the manager extensive array processing capabil- 
 ities which he can provide to his customers with little additional effort 
 on his own part. Similar services, of less dramatic impact, can likewise 
 be provided through the network. The user is happy because he can get 
 
 this increased service through his own broker (again with little additional 
 effort) and the manager of the center with the unique resources is happy 
 for the increased business. The broker concept has been widely discussed 
 in the literature and details will not be included here (see especially [29] 
 and [Ij-O]). (As an aside, we feel that network computers provide the only 
 feasible means for such super computers to become viable. They are so 
 fast and so powerful that only an extremely large customer base will suffice 
 to keep them in business. Only through a network computer can this base 
 be economically provided and maintained.) 
 
 Offering computing services on a contract basis can be an ulcer- 
 producing job. However, with the potential for stability which the network 
 computer offers, the problem of guarantees is somewhat alleviated. It 
 should be noted that the word is "alleviated" — not eliminated. Network 
 computers do not completely satisfy Murphy's law. It is possible for the 
 communications equipment, like all other machines, to break down. However, 
 the probability that both the processor and the communications equipment 
 will be down at the same time is considerably less than that for the 
 processor alone. Thus we feel that network computers can be of signifi- 
 cant service in the business of offering contract computing services. 
 
10 
 The second type of service which is offered by computing centers is 
 called demand service. The expectations of the user of demand services 
 are less clearly defined than those of the user of contract services. The 
 traditional viewpoint associated with this type of user is that he simply 
 wishes to get his tasks processed as quickly as possible. Discrimination 
 is frowned upon and, apart from partitioning tasks by size, a first come- 
 first served policy is generally used for resource allocation. We feel 
 that this is an outdated policy. The basic assumption upon which it is 
 predicated is that all tasks are of equal value to the user and hence should 
 be treated as equal by the computing system. We do not doubt that this 
 assumption was valid, even a few years ago, when no task was given to the 
 computer unless it was reasonably important. This, however, is no longer 
 the case. Computing centers handle a wide variety of tasks ranging from 
 urgent to trivial. Thus all tasks should not be treated equally. If the 
 user can somehow specify the value of a task, the computing system should 
 recognize this value and treat the task accordingly. In Chapter 3 we shall 
 develop a priority assignment system which allows the user to specify 
 not only the value of a task but also a deadline which represents the latest 
 moment at which the task has that value. We feel that this system comes 
 much closer to serving the needs of the user who requests demand services. 
 He has more control over the fate of his tasks and the system respects his 
 requests and accords the privileges due them. 
 
 Given the system sketched above, the job of the task scheduler 
 becomes much more difficult. The scheduler now has the additional task of 
 keeping track of and meeting deadlines. This need not be as difficult as 
 it seems. If the scheduler can have enough foresight to know when tasks 
 are in danger of missing a deadline, it will be able to send some of these 
 tasks to other centers who can meet the deadline. Again, network computers 
 
11 
 
 are a tremendous help in solving the problem. This idea is similar to that 
 presented in the discussion of contract services. However, it is much more 
 dynamic in nature and requires more careful supervision. A system which 
 develops from attending to these concerns is generally called a load leveling 
 system. Our version of a load leveling system is described in Chapter 3. 
 
 We have seen that a network computer can offer many advantages to 
 managers of computing centers. However, building a network computer is not 
 cheap. The problem now facing the industry is how to make these advantages 
 available at a price we can afford. This is again the problem of cost 
 
 (effectiveness. Different networks take different approaches in presenting 
 a cost effective facade to the businessman. Whether or not this facade 
 will withstand the pressures of adversity will decide the fate of the networks. 
 
 There are still problems which remain unsolved. Especially sticky 
 are those problems which arise in a network made up of competitive centers. 
 The manager of a computing center is not pleased by the prospect of sending 
 business to a competitor. Yet this is exactly the method we have proposed. 
 Billing is another problem which arises in this open market situation. How 
 does the manager of the recipient center determine the price to charge for 
 services rendered? These are very difficult management problems. One 
 feasible solution is to construct networks made up of centers working for 
 the common good. Another is to have one center which is impartial — an 
 overflow center — which does not compete for outside business. This approach 
 is probably impractical, although a policy of mutually exclusive clientele 
 may be feasible. 
 
12 
 
 In the following sections we shall examine the approaches taken by- 
 several networks. These networks were selected for study because we feel 
 they are representative of the wide variety of philosophies and ideas which 
 enter into the design of network computers. Though our prejudices may be 
 reflected, we do not intend to imply that ony one network is better than 
 any other . 
 
 There are three basic multiprocessor (or network) topologies. Type 1, 
 the distributed network (Figure 2.1a), is unique because it offers more than 
 one path between any two centers. This topology was chosen for the ARPA 
 network which is discussed in section 2.2. Type 2, the star network 
 (Figure 2.1b), is distinguished by a central message switch. All center to 
 center communication must pass through this switch. The TUCC network 
 (section 2.3) utilizes a modified version of the star network. In the third 
 type, the ring structure (Figure 2.1c), all communication is along the same 
 path and there is only one path between any two centers. This topology is 
 being investigated for the Distributed Computer System (section 2.U). As 
 we shall see, each of these topologies has some advantages and disadvantages 
 and each can be cost effective in some setting. 
 
 Nk 
 
 /1\ 
 
 a) A Distributed b) A Star Network c) Ring Structure 
 
 Network 
 
 Figure 2.1 Possible Network Topologies 
 
13 
 
 2.2 The ARPA Network 
 
 We begin our survey of network computers with the ARPA (Advanced 
 Research Projects Agency) network. We do this for several reasons. It 
 is the most widely discussed network computer (see especially [15], [1T]» 
 [2U], [28], [31], and [38]) and has probably provided the single most 
 important impetus in the advance of network computer technology. It is 
 also the largest fully automatic network computer in operation (with 
 the possible exception of defense networks about which little information 
 is available) both in terms of geographic distribution and number of centers. 
 (We do not include Cybernet since human intervention is generally required 
 for its successful operation. ) The initial topology for the ARPA network 
 is shown in Figure 2.1 (diagram taken from [38]). 
 
 The ARPA network has provided most of the current widely used 
 terminology in the field, some of which will be used in the discussions 
 that follow. The most widely used term is "node", the name given to a center 
 and its communications computer. The center has been dubbed the "Host" 
 (initially only one processor though there is no necessary restriction on 
 tthe number of processors in a host) while the communications computer has 
 been named "IMP" for Interface Message Processor. 
 
 SRI 
 
 UTAH NCAR 
 
 AWS 
 
 CASE 
 
 UCSB 
 
 RAND BBN HARVARD BTL 
 Figure 2.2 The ARPA Network 
 
 MITRE 
 
 CMU 
 
Ill 
 
 The design of the ARPA network was influenced by two major consider- 
 ations. Since this was the first widely funded fully computer run network, 
 a primary goal was to explore network computer technology. This work has 
 progressed well enough for us to remove it from further consideration. A 
 second, and more relevent, goal was to interconnect those research centers 
 across the country to which ARPA contributed substantial financing. This 
 interconnection would allow the sharing of unique resources and, hopefully, 
 eliminate some duplication of effort. 
 
 One of the primary elements of cost in any network computer is topology. 
 The topology of the ARPA network as shown in Figure 2.2 can be called 
 distributed. It is not a fully interconnected distributed network since 
 this would imply direct paths between any two nodes. The most important 
 consideration which led to the choice of a distributed network was reliability 
 The central switch network is unreliable since there is only one path between 
 any two nodes — through the central switch. The central switch should not be 
 dismissed lightly (see section 2.3 on the TUCC network) but it does not fulfi] 
 the needs of the ARPA network. The consideration of reliability also leads 
 to difficulty in the ring network. However, the ring structure has been 
 modified for the Distributed Computer System (see section 2.5) and the 
 reliability of this type of network has been improved. The geographical 
 distribution of the ARPA network and its traffic considerations rule out the 
 use of a ring structure. 
 
 Once it had been decided that the ARPA network was to be a distributed 
 network, much effort was spent in optimizing the final topology. This work 
 has been well referenced in the literature (see especially [2U]) and will 
 not be discussed here. 
 
 
 
15 
 
 One of the most important side effects which resulted from the 
 choice of a distributed network was the sophistication which is required 
 in the IMP. Due to technological considerations, a distributed network 
 which is not fully interconnected must use store and forward message 
 switching. This requires considerable error checking and decision making 
 capabilities in the IMP. For these reasons the ARPA network communications 
 computer is significantly more expensive than that required for some other 
 networks. Available figures indicate that the basic IMP will run in the 
 neighborhood of $U0,000 to $50,000 [hk] . However, the IMP by itself is not 
 of much value, and from the beginning, work has continued on developing 
 an intelligent terminal which can be connected to a Host. The initial work 
 in this area resulted in a Terminal Information Processor (or TIP) which 
 included the HP 3l6 IMP in its cost of about $92,000. However, the TIP has 
 proved unsatisfactory for some applications and further work has resulted 
 in the ARPA Network Terminal System (ANTS) which includes the HP 3l6 and 
 a PDP 11. Work is now progressing to connect the $120,000 ANTS system to 
 a CDC 6600 at Ft. Belvoire. If successful, this work would make the entire 
 ARPA network to look like simply an intelligent terminal (obviously one 
 with large resources) to each Host [^]. 
 
 We have seen that membership in the ARPA network will require a 
 minimum initial investment of at least $90,000. In addition, $20,000 to 
 $35,000 in annual maintenance and ARPA priviledges can be anticipated [UU], 
 What then are the motivations which justify the high cost of membership in 
 ARPA? To the research oriented nodes the primary motivation is obviously 
 
L6 
 
 the capability of using a wide variety of unique resources. Anyone doing 
 work which requires large amounts of matrix arithmetic and array processing 
 would clearly prefer to have the ILLIAC IV (in a working version) available 
 than any of the currently popular general purpose processors. For many of 
 the major universities, access to the ILLIAC IV alone may justify the 
 expense of ARPA network membership. Another valuable unique resource is 
 the University of Utah interactive graphics system. This likewise provides 
 a significant amount of justification for membership. As was previously 
 mentioned, a network computer is a virtual necessity for these specialized 
 and very expensive unique resources and we have just seen that these 
 resources can be very important to the network. 
 
 However useful the availability of these unique resources may be, 
 we feel that, for the ARPA network to become a viable commodity without 
 being subsidized, a wider variety of advantages must be offered. As ARPA 
 becomes more commercial, we feel that we shall see significant use of the 
 common resources of the network. Since communication costs are expected 
 to be low (about $.30 per megabit after the first U000 megabits) it would 
 be quite feasible to shop around for the node with the quickest turn-around 
 time before submitting a task or, perhaps more interestingly, do some load 
 leveling on a network-wide basis. If this is the case, any computing center 
 with either unused or excess capacity could become a candidate for membership 
 in the ARPA network. Assuming it is possible to solve the political 
 problems which would obviously arise in such an association (definitely a 
 non-trivial assumption), this approach could be the key to cost effective 
 operation of the ARPA network. 
 
17 
 
 Perhaps the most radical possibility opened by the ARPA network is 
 that its successful implementation could lead to the elimination of most 
 medium and large scale machines. The ANTS system clearly has the potential 
 to operate as a remote job entry station for all kinds of tasks — including 
 interactive procedures. Given this capability and assuming that the ARPA 
 network traffic capacity is great enough, we can envision a time when, 
 instead of purchasing a medium or large scale computing system, the most 
 economical action would be to purchase an ANTS type system and use already 
 existing resources. This approach would probably require the use of brokers 
 and would undoubtedly lead to the development of more specialized machines 
 which could do certain types of tasks more cost effectively than general 
 purpose machines. One factor that will hinder the development of this type 
 of system is the well known "blame it on the computer" syndrome. When 
 errors are made, top management does not like to blame things on a machine. 
 They instead would like to have someone close by who is responsible for the 
 success and failure of the computing system. It is this tendency which leads 
 those responsible to want their own machines. If a person is responsible 
 for a product he would at least like to have control over the development 
 of the product. Far from demeaning this tendency, we encourage it. This 
 reluctance is well justified and its existence will help to encourage 
 responsible development of computing systems. The idea is to solve as many 
 problems as possible before they arise. Responsible development, along 
 with open ears, are the keys to developing cost effective computing systems. 
 
18 
 
 2.3 The TUCC Network 
 
 The TUCC (Triangle Universities Computation Center) network is a 
 system which is entirely different from the ARPA network. In the first 
 place it is contained entirely within the state of North Carolina, thus 
 serving a much smaller area than the nationally distributed ARPA network. 
 Just as significant, it is currently operational and working in a cost 
 effective manner, while ARPA is still getting the bugs out. For these 
 reasons, and others, it is an interesting network to examine. 
 
 The TUCC network is a regional homogeneous network consisting of an 
 IBM 370/165 (at Research Triangle Park), and IBM 360/75 (at the University 
 of North Carolina/Chapel Hill), and two IBM 36oAO's (at Duke University/ 
 Durham and North Carolina State University at Raleigh). (Also connected to 
 the 370/165 are several secondary terminals at state educational institutions 
 Dub we will not concern ourselves with these in this discussion.) These 
 four processors are connected in a central switch topology as shown 
 in Figure 2.3. This topology was chosen for primarily one reason: Communica- 
 tion from the three universities is expected to be mainly to Research Triangle 
 
 [37] 
 Park, and direct university to university communication rare. Thus extra 
 
 links would be economically unjustifiable. Total cost to the universities 
 
 for belonging to the TUCC network is in the range of $13,000 to $lU,000 per 
 
 360/UO 
 DUKE 
 
 360/75 
 UMC 
 
 RESEARCH 
 TRIANGIE 
 
 BfcRK 
 370/165 
 
 OTHER 
 INSTITUTES 
 
 Figure 2.3 The TUCC Network 
 
19 
 
 month [U3]. Though this may seem high at first glance, one should realize that 
 this fee includes approximately 25% of the computing capacity of the 370/165. 
 Adding this amount of capability to any of the centers individually would 
 cost around $19,000 per month [43] . Thus, if the capacity can be used, member- 
 ship in the TUCC network is certainly economically justified. 
 
 The primary motivation in developing the TUCC network was economics. 
 Thus far, the performance of the network seems to justify most of the grossly 
 general statements which have been made earlier in this paper. The 370/165 
 is primarily available to provide remote job entry and interactive services 
 to the three universities. It should be noted that most of the tasks 
 processed at Research Triangle Park represent excess capacity demanded by 
 users at the three universities. That this demand is significant can be 
 seen from the fact that it was necessary to install an IBM 370 since the 
 360/75 which it replaced in September, 1971 was frequently saturated. This 
 clearly supports the argument which we made earlier for increasing the 
 availability of common resources. 
 
 The increase in the availability and utilization of unique resources 
 has not been nearly as dramatic. A few proprietary programs exist and are 
 utilized. However, the existence of these does not, alone, justify the cost 
 of the network. Two fairly unique advantages were obtained, however, with 
 the formation of the network. First, the universities became better able 
 to attract faculty and staff who require large scale computing services for 
 research and teaching. As any educator can tell you, this attraction can 
 be an important help to the relevent university departments. A second 
 important consideration was that TUCC was able to attract outstanding 
 systems programmers which the individual universities could neither afford 
 
20 
 
 nor keep busy. Attracting the top men in the field always helps a 
 university — or a network of universities. 
 
 Though currently operating in a cost effective manner, the TUCC 
 network is far from becoming sedentary. Plans are currently under way to 
 enable the 360's at the various universities to handle overflow from the 
 370. Obtaining this capability is especially important in a university 
 environment where vacations, and hence due dates for term projects, can be 
 staggered. Although other services are provided by the TUCC network 
 perhaps deserving more attention in this discussion) the load sharing 
 capabilities which are made available are sufficient to provide significant 
 monetary savings, as well as improvements in service, to the three univer- 
 sities involved. 
 
 We saw earlier that the ARPA network was designed to share unique 
 resources and that there was at least some justification for feeling that 
 these alone could support a network computer. We have just seen that it 
 is possible to maintain a network computer built to share common resources. 
 One wonders how a network computer might fare if both types of resources 
 were made available. 
 
 2.k The Distributed Computer System 
 
 We have already looked at the ARPA network, which is nationally 
 distributed, and the regional TUCC network. The logical third type of 
 network to discuss is a local network. The Distributed Computer System 
 (DCS) fills this bill with a great many ingenious ideas which deserve 
 discussion. In addition, DCS, is an example of the third type of network 
 topology, the ring network. 
 
21 
 
 The Distributed Computer System is an experimental computer network 
 which is being designed and built at the University of California at Irvine 
 under the direction of David J. Farber. When completed, DCS is expected 
 to provide medium and small scale computing services to the users at UCI. 
 Providing complete computing services is never an easy thing to do. To 
 make the development of DCS even more interesting, a number of restrictive 
 design objectives were imposed on the system. The following were the 
 design objectives proposed for DCS [21]: 
 
 1) Reliability : The system should be invulnerable to total failure. 
 It is a fact of life that individual compoents will fail, but the 
 failure of any individual component should have minimal effect on 
 the operation of the rest of the system. This capability is called 
 "soft fail". 
 
 2) Low initial cost : Like most institutions, UCI is short of money. 
 The initial hardware cost of the system was restricted to less than 
 $250,000. This effectively ruled out the medium scale systems used 
 by most universities of this size, such as IBM's 360/50, DEC's PDP-10, 
 or XDS's Sigma 7. 
 
 3) Incremental expansion ability : The system should be capable of 
 expansion of virtually any type, at a relatively low expansion cost. 
 
 h) Variety of language systems : Since this is to be a university 
 
 computing system, a wide variety of computer languages and resources 
 should be available. 
 
 5) Modest system programming requirements : It would be nice to keep the 
 system as simple as possible. 
 
22 
 
 We now examine the ways in which these design objectives affected 
 the final system design. The most important objective is that the system 
 be capable of soft fail. In a single processor system, if that processor 
 goes down the whole system is down. This violates the soft fail objective, 
 so we are forced to consider multiprocessor possibilities. 
 
 As we have seen before, there are three basic multiprocessor (or 
 network) topologies. All others degenerate to one of these. Type one, 
 the distributed network, solves this problem since between any two processors 
 in the net there exist at least two possible communication paths. (This 
 is not true in general, but if it weren't true for our system we wouldn't 
 consider it at all. ) Another property, however, makes this configuration 
 undesirable for DCS. The interface between the processor and the net 
 must be capable of store-and-forward message switching and intelligent 
 enough to perform all message routing functions, which might be quite 
 complex. As is usually the case, this increased interface sophistication 
 leads to increased cost. It turns out that if we wished to start with 
 a modest network of five or six processors, the interfaces alone would 
 account for at least half, if not all, of the allotted initial funding. 
 Type two, a network with central message switch, has the same problem as 
 the single processor system. If the switch dies, all interprocessor communi- 
 cation dies, too. 
 
 By using type 3, the ring structure, we can at least avoid these 
 problems. In the maintenance of the communications ring, two things can go 
 wrong: the ring itself can fail or some interface between the ring and a 
 processor can fail. About the only way the ring can fail is if it is 
 broken. Although the probability of a cable being broken is near zero, 
 we can guard against this failure by placing secondary alternatives to the 
 primary ring path which can be invoked by a hardware mechanism. One method 
 
23 
 
 considered to accomplish this objective was to force the ring to have an 
 even number of ring interfaces (nodes) by inserting an extra dummy node if 
 necessary, and connecting node N to node N+2, node N+l to node N+3, etc., 
 as well as to their immediate neighbors. This "daisy chain" scheme has the 
 drawback of making it more difficult to include new nodes in the network. 
 Early literature indicated that a simpler alternative, buying two rings 
 initially and installing both at the same time was feasible [2l]. With 
 synchronization problems taken care of, it might also be possible to use 
 both at the same time when both are operational, but at worst we are left 
 with a complete backup system for the ring cable. More recently, however, 
 the designers seem to be seriously investigating the daisy chain scheme [26]. 
 
 The other possible problem arises if one of the nodes goes down and 
 interferes with messages in a roadblock fashion. This problem can be avoided 
 by building a hardwired "short-circuit" device which can be engaged by the 
 node itself or by an outside source. This short-circuit device logically 
 disconnects the processor from the ring. In addition, the ring interface 
 is constructed in such a way that store-and-forward message switching 
 techniques are required only between a processor and its own ring interface. 
 This allows a substantial decrease in transmission time of messages and 
 simplifies the ring interface. The result is that the node can be built far 
 more inexpensively than any other type of communications processor (perhaps 
 $500) [21]. The initial planned structure of DCS is shown in figure 2.k. 
 
 So much for the objectives of reliability and cost. The other objec- 
 tives can also be easily met with a ring structure. Incremental expansion 
 presents no problem. Expansion of the system requires only hooking up an 
 additional ring interface and attaching it to the new processor. There is 
 
2k 
 
 no theoretical limit to the expansion of the system, although in practice the 
 number of processors the ring can efficiently handle is limited to a number 
 currently unknown. Expansion is economical because of the low cost of the 
 ring interface. A variety of language systems can be obtained by attaching 
 small language-oriented processors to the ring. It is well known that this 
 approach can be very cost-effective. The system programming objective may 
 be violated by building a distributed operating system but we adopt this 
 approach anyway to maintain the soft fail capability of the ring. 
 
 We note that the critical design objectives for DCS are reliability 
 and low initial cost. We have seen that a ring structure is the most 
 feasible way to meet these objectives, and that the others can also be met 
 using this approach. 
 
 Figure 2.U. The Distributed Computer System 
 
 This relatively detailed discussion was provided in order to give a 
 feeling for the real goals of the system and some of the problems encountered. 
 Other important aspects of the system, especially the distributed operating 
 system, are deserving of discussion. To do so, however, would be to deviate 
 from the purpose of this paper. The reader is referred to references 
 [21] and [22] for more complete discussions. 
 
25 
 
 We now have a pretty good idea of the cost of DCS. How effectively 
 it will operate remains an unanswered question. It is, after all, an 
 experimental network which is not even operational at this time. It is 
 important to note that speed was not a major design objective. Some of the 
 decisions that were made to ensure reliability were undoubtedly made at the 
 cost of reduced speed. The degree to which this tradeoff will affect the 
 system is yet undetermined. 
 
 We are encouraged by the development of DCS. If all of the remaining 
 hurdles can be negotiated, we feel that the flexibility provided in the 
 design and the services which can be offered by the system are a real bargain 
 for the price. 
 
 2.5 The ALOHA System and the Problem of Communication Media 
 
 In each of the networks studied so far, the communication media used 
 has been wire. In the continental United States, where telephone networks 
 already exist, or in local networks, wire is currently the most cost effective 
 communications media and is well documented in the literature [1T» 21, 23, 
 32, 38, U3]. That this situation exists is not, however, due to any inherent 
 qualities in the wire but is due primarily to convenience. One proposed 
 system which has selected an alternate medium is the ALOHA System. As we 
 shall see, of the many feasible media, wire is perhaps the least cost effective 
 choice for the ALOHA System. 
 
 The ALOHA System is being built by the University of Hawaii and is 
 intended to provide computing services to users at the University's main 
 campus in the Manoa Valley on Oahu, a four -year college at Hilo, Hawaii, 
 two-year community colleges on the islands of Oahu, Kauai, Maui, and Hawaii, 
 and associated research institutes within a 200-mile radius of the 
 
26 
 
 University. Long-range plans include extending the communications system 
 throughout the Pacific area, possibly even for ship to shore use. Some 
 fast, inexpensive method is needed to connect an IBM 36O/65 computer at the 
 University's main campus, called the Kahuna, with remote access terminals 
 (Keikis) at all of the above-mentioned locations [l,2]. 
 
 It is expected that ALOHA will eventually have a very large number 
 of Keikis, but that relatively few of them will be in use at any given time. 
 The expected usage pattern of a single active Keiki is that a user will 
 type in some message to be sent to the Kahuna and await a response. It is 
 important to note that the action of typing a message takes a few seconds, 
 
 and it takes the user at least a second or so to realize he has received a 
 response and react to it, but the Kahuna's results are available in milli- 
 seconds. This motivates the requirement that the communications process 
 should take a maximum of a few seconds, but it also means that a minimum 
 communication time of as much as half a second is not unreasonable from the 
 user's point of view. 
 
 The usual method of remote access communication is by wire, most 
 often over leased telephone lines. This approach can be cost-effective when 
 the distances involved are not too great, the wires already exist, or they 
 would be in use much of the time. It is not appropriate for ALOHA because 
 new wires would be needed to some of the islands (existing wires in many 
 places provide only low-quality voice-grade communication and are, therefore, 
 not sufficiently reliable for data transmission), many Keikis are located at 
 relatively large distances from the Kahuna, and each Keiki is expected to 
 be used only a few hours a day. To make matters worse, extending ALOHA 
 throughout the Pacific would make the cost of wire communication prohibitive 
 because of the distances involved, and its use by ships at sea would be quite 
 impossible. 
 
27 
 
 Among the alternatives to wire communication are radio, light waves, 
 
 and an amphibious marine troop transporting reels of magnetic tapes. The 
 
 latter must be rejected immediately because it is too expensive and too slow. 
 
 At present ALOHA is being built using radio communication, but research on 
 
 the feasibility of light wave communication using light emitting diodes is 
 
 also under way. Radio communication was chosen because it is inexpensive 
 
 to use over large distances (in fact, radio messages could be beamed in 
 
 by satellite from all over the world), the Keikis can be mobile, and a 
 
 communications protocol can be established which takes advantage of the 
 
 burst nature of messages from a single Keiki while ignoring all the 
 
 inactive Keikis. It is this protocol which makes ALOHA so interesting. 
 
 While the Kahuna is kept busy with computing tasks, an HP2115A named 
 
 Menehune (after a legendary Hawaiin elf) serves as its link to the radio 
 
 communication channel. It is Menehune' s job to multiplex messages between 
 
 Kahuna and a large, indeterminate number of users. Menehune uses two 100KHZ 
 
 channels, one for receiving messages from the Keikis, and the other for 
 
 sending messages to the Keikis. The complete makeup of the ALOHA System 
 
 is shown in Figure 2.5. 
 
 Multiplexing messages from Menehune to the Keikis is relatively easy. 
 For traffic in this direction there is only one sender and messages can be 
 queued and transmitted sequentially. Transmission from the Keikis to 
 Menehune is quite another story, however, and the reader is enthusiastically 
 referred to the literature for a complete discussion [l,2]. We will concern 
 ourselves, in this paper, only with the results of the investigation. 
 
 Because of the anticipated usage pattern of the Keikis, the designers 
 of the ALOHA System have chosen to allow communication in burst mode only. 
 Under this constraint, Menehune can be said to have a capacity of about 
 2^,000 bits per second. In practice, since message arrivals are virtually 
 
28 
 random, the capacity will be much less. Studies by the author agree, within 
 reason, with the results of Bortels [8] and the theoretical results [1,2] 
 that for message packets of about 700 bits, the system can support between 
 lUO and 160 active users if the transmission rate is about two packets per 
 
 KAHUNA 
 
 IBM 
 360/65 
 
 MENEKUNE 
 * — *HT 2115 A 
 
 *-a 
 
 TRANSMIT 
 DATA 
 MODEM 
 
 TRANS - 
 £— ^1 MITTER 
 
 L 
 
 RECEIVE 
 DATA fc—a 
 MODEM 
 
 4 
 
 KEIKI # 1 
 
 RECEIVER 
 
 
 KEIKI # 2 
 
 KEIKI # K 
 
 ] 
 
 Figure 2.5 The AL0HA System 
 
 Keiki per minute. (Bortels actually indicates that this number may be a bit 
 high but we will stick by these numbers). This is obviously a significant 
 number of users especially when one realizes that they are all using the 
 same channel. 
 
 The investment needed to become part of the ALOHA system is anticipated 
 to be one teletype and the $3,000 Keiki (a one-time cost) [l]. We feel that 
 this is a very reasonable amount since it allows the user access to the 
 complete computing capabilities of the University of Hawaii. And, should 
 the user keep the Keiki. long enough, the average monthly cost will be low 
 enough to allow almost anyone, regardless of location, to join the system. 
 
 According to the definitions presented earlier, the ALOHA System is 
 not really a network computer. The Keiki s, after all, support only terminals, 
 not processors. The potential remains, however, to utilize the methods 
 proposed for the ALOHA System in computer to computer communication. 
 Obviously, the number of computers which could be connected in this way is 
 less than the number of Keikis which can be connected because of the nature 
 
29 
 
 of the traffic, but the potential remains. Perhaps radio communication would 
 not be feasible in the more densely populated areas of the world because of 
 interference. However, in at least one instance, the ALOHA System, radio 
 has been shown to be a cost effective alternative to wire for communication 
 in network computers. 
 
30 
 
 3. COST EFFECTIVE PRIORITY ASSIGNMENT 
 
 3.1 A Scenario of Cost Effectiveness 
 
 Until recently, efforts to measure computer efficiency have centered 
 on the measurement of resource (including processor) idle time. A major 
 problem with this philosophy is that it assumes that all tasks are of roughly 
 equal value to the user and hence the operation of the system. 
 
 As an alternative to the methods used in the past, ve propose a 
 priority assignment technique designed to represent the worth of tasks in 
 the system. We present the hypothesis that tasks requiring equivalent use 
 of resources are not necessarily of equivalent worth to the user with respect 
 to time. We would allow the option for the user to specify a "deadline" 
 after which the value of his task would decrease, at a rate which he can 
 specify, to a system determined minimum. With this in mind, we propose a 
 measure of cost effectiveness with which we can evaluate the performance of 
 a network with an arbitrary number of interconnected systems, as well as each 
 system individually. 
 
 We define our measure of cost effectiveness y» as follows: 
 
 R-l 
 y = (Lq/M) °U-(M-Lq)/j? 0(i)) 
 
 i=o 
 where 
 
 L is the number of tasks in the queue, 
 
 q 
 
 M is the maximum length queue, 
 R is the number of priority classes, 
 
 a is a measure (system-determined) of the "dedicatedness" of the 
 CPU to the processing of tasks in the queue, 
 
31 
 
 and g(i) = (R-i) I (g(j)/f(j)) 
 
 j=l 
 
 where g(j) is the reward for completing task j (a user specified 
 
 function of time), 
 and f(j) is the cost (system determined) to complete task j. 
 
 The term (Lq/M) is a measure of the relevance of the queue to processing 
 activities. Similarly, we can look at 3(i) as a measure of resource 
 utilization. Note that 3(i) indicates a ratio of reward to cost for a given 
 priority class and is sensitive to the needs of the user and the requirements 
 imposed on the installation. It is user sensitive because the user specifies 
 the reward and is installation sensitive because the cost for processing a 
 task is determined by the system. The measure of CPU dedicatedness ( a ), 
 on the other hand, is an entirely installation sensitive parameter. 
 
 The first problem which becomes apparent is that which arises if 
 
 R-l 
 I 3(i) =0. This occurs only in the situation where there is exactly one 
 i=o 
 
 priority class (i.e., the non-priority case). We will finesse away this 
 
 problem by defining 
 
 R-l 
 (M-Lq)/£ 3(i) = 
 i=0 
 
 for this case. Intuitively, this is obvious, since the smaller this term 
 
 gets, the more efficiently (in terms of reward) a system is using its 
 
 resources. Furthermore, in the absence of priorities, the order in which 
 
 tasks are executed is fixed, so this term becomes irrelevant to our measure 
 
 of cost effectiveness. Thus, for the non-priority case, we have 
 
 Y = (Lq/M) a 
 
32 
 
 which is simply the measure of the relevance of the queue to processing 
 
 activities. This is precisely what we want if we are going to consider 
 only load-leveling in non-priority systems. However, we are interested in 
 the more general case in which we can assign priorities. 
 
 An estimate of the cost to complete task j , f(j) is readily 
 determined from the user-supplied parameters requesting resources. 
 Frequently these estimated parameters are used as upper limits in resource 
 allocation and the operating system will not allow the program to exceed 
 them. As a result, the estimates tend to he high. On the other hand, 
 lower priorities are usually assigned to tasks requiring a large amount of 
 resources. So the net effect is that the user's parameters reflect his 
 best estimate and we may be reasonably confident that they truly reflect 
 his needs. 
 
 At the University of Illinois computing center, for example, as of 
 July 26, 1971, program charges are estimated by the following formula: 
 
 cents = a(X + Y)(bZ + c) + d 
 where X = CPU time in centi seconds, 
 
 Y = number of 1/0 requests, 
 Z = core size in kilobytes, 
 
 a, b, c are weighting factors currently having the values 
 0.0U, 0.00^5, and 0.5, respectively, 
 and d is an extra charge factor including $1.00 cover charge 
 
 plus any special resources used (tape/disk storage, 
 card read, cards punched, plotter, etc.). 
 The main significance of the reward function g(j) specified by the 
 user is that it allows us to determine a deadline or deadlines for the task. 
 
33 
 
 Typically we might expect g(j) to be a polynomial in t, where t is the time 
 in the system. For example, the following thoughts might run thorugh the 
 user's head: "Let's see, its 10:00 a.m. now and I don't really need immediate 
 results since I have other things to do. However, I do need the output before 
 the U: 00 p.m. meeting. Therefore, I will make 3:30 p.m. a primary deadline. 
 If it isn't done before the meeting, I can't use the results before tomorrow 
 morning, so I will make 8:00 a.m. a secondary deadline. If it isn't done by 
 then I can't use the results, so after 8:00 a.m. I don't care." 
 
 The function g(,j) this user is thinking about would probably look some- 
 thing like Figure 3.1a. Now, this type of function poses a problem in that 
 it is difficult for the user to specify accurately and would require an 
 appreciable amount of overhead to remember and compute. Notice, however, 
 that even if turnaround time is immediate, the profit oriented installation 
 manager would put the completed task on a shelf (presumably an inexpensive 
 storage device) and not give it to the user until just before the deadline — 
 
 3:30 pm 
 
 (a) 
 
 8:00 am 
 
 g(j) 
 
 9l t 
 
 
 
 
 \ 
 
 
 
 \ m, 
 
 
 
 
 \ 
 
 g 2 
 
 u 
 
 
 1 "^Ny 
 
 
 I 
 
 »-» 
 
 
 — i — 
 
 3*. 30 pm 
 
 ft 
 
 m 2 
 
 8:00 am 
 
 time time 
 
 Ideal Function (b) Approximate Function 
 
 Figure 3.1 Example of a User's Reward Function 
 
3% 
 
 thus collecting the maximum reward. As a result, there is little reason 
 to specifying anything more than the deadlines, the rewards associated 
 with meeting the deadlines, and the rate of decrease of the reward between 
 deadlines, if any. Applying this reasoning to Figure 3.1a we obtain Figure 
 3.1b. Note that this function is completely specified with only six para- 
 meters (deadlines t , t ; rewards g , g ; and rates of decrease m , m ). 
 
 In general, we may assume that g(j) is a monotonically non-increasing, 
 piecewise linear, reward function consisting of n distinct sets of deadlines, 
 rewards, and rates of decrease. Thus we can simple specify g(j) with 3n 
 parameters where n is the number of deadlines specified. 
 
 Note that, in effect, the user specifies an abort time when the g(j) 
 he specifies becomes less than f(j). If the installation happens to provide 
 a "lower cost" service, f(j) and if g(j) > f(j), this task would be processed, 
 but only when all the tasks with higher g(j) had been processed . 
 
 Now , what we are really interested in, is not so much an absolute 
 reward, but a ratio of reward to cost. Since f(j) is, at best, only an 
 estimate of cost, we cannot reasonably require a user to specify an absolute 
 reward. A more equitable arrangement would be to specify the rewards in 
 terms of a ratio g(j)/f(j) associated with each deadline. This ratio is 
 more indicative of the relative worth of a task, both to the system and to 
 the user, since it indicates the return on an investment. 
 
35 
 3.2 Priority Assignment 
 
 Let us now turn our attention to the development of a priority 
 assignment scheme which utilizes the reward/cost ratios described in the 
 previous section. We egin "by quantizing the continium of reward/cost 
 ratios into F distinct intervals. Each of these intervals is then assigned 
 to one of R priority classes 0, 1, 2, . .., R-l with priority being reserved 
 for tasks with highest reward/cost ratios and priority R-l for tasks with 
 reward/cost ratios of unity of less. A task entering the system will be 
 assigned a priority according to its associated reward/cost ratio. 
 
 We want to guarantee, if possible, that all priority tasks will meet 
 their deadlines. Furthermore, if all priority tasks can meet their dead- 
 lines, we want to guarantee, if possible, that all priority 1 tasks will 
 meet their deadlines and, in general, if all priority k tasks can meet their 
 deadlines, we want to guarantee that as many priority class k+1 tasks as 
 possible will meet their deadlines. To facilitate the priority assignment, 
 
 we introduce the following notation: 
 
 th 
 For priority k, let T. denote the i task. Then we assume for each 
 
 T. that we receive the following information vector: 
 
 (T., g/f, d., T., s.) 
 
 where 
 
 T. is an identifier, 
 
 l 
 
 g/f is the reward/cost ratio associated with meeting the task's 
 
 deadline , 
 
 d. is the task's deadline associated with g/f, 
 
 t. is the maximum processing time for the task, 
 
 and s. = d. - x., is the latest time at which the task may start 
 ill 
 
 processing and still be assured of meeting its deadline. 
 
36 
 Nov since each task has an associated deadline and maximum processing 
 
 time, we can us the resulting latest start time as the basis for assigning 
 
 positions to tasks within a priority class. A last come, first served rule 
 
 will be uused to break ties. Additionally, we will use a compacting scheme 
 
 to ensure that as many tasks as possible start processing before their latest 
 
 start times. More formally our algorithm may be stated as follows: 
 
 Priority Assignment Algorithm 
 
 First, we assign a new task a priority based on its g/f ratio, say 
 priority k. Then within class k, its position is determined as follows: 
 
 1. Beginning with the last priority k task (that is, the task with 
 
 latest deadline) search forward until two tasks, T. -, and T., are 
 
 J-l J 
 
 found such that d. . < d. < d.. Insert T. between the two tasks, 
 
 J-l i - J i 
 
 assign it a start time s. = d. - t. , and renumber the tasks behind 
 
 ill 
 
 T. accordingly (i.e., T. becomes T., T. becomes T. _, , etc.). 
 
 J i J J J+l 
 
 2. Now, if s. + t, < s, < s. - t, there is sufficient float 
 
 J-l J-l - J - J+l J 
 
 time between T. ., and T. _, for T. to be processed on time and the 
 J-l J+l J 
 
 priority assignment is complete. However, if either 
 
 s . ., + t. _, >s.ors.+ t. > s . _ , a deadline might be missed: 
 J-l J-l J J J J+l 
 
 so we proceed with Step 3. 
 3* Compacting Scheme . Let f . denote the float time between any two 
 
 J 
 
 tasks T. _, and T.., where f. is defined: 
 J-l JJ J 
 
 f . = s. - (s. + t ) 
 J J J-l J-l 
 
 Then, F., the total float time preceding T., is given by: 
 J J 
 
 F.= I f. = S.-T+ I T.. 
 
 J k=l J J k=l J 
 
 where t is the current time. 
 
37 
 
 Now, starting with task T., if s. + t > s and F > s + x - 
 
 J J J J+l J — j J 
 
 s. n we assign a new starting time to T. given by: 
 
 J J+l J 
 
 and we continue with T. , , T. ^, etc. until we encounter a 
 
 J-l J-2 
 
 task T, , k ^ j , such that s, < s, , - x . (Note that T . , 
 k k — k+1 k j+l 
 
 and all its predecessors are guaranteed to meet their deadlines.) 
 
 h. However, if s . + t. > s. , but F. < s. + t. - s . , , we do not 
 J J J+l J J J J+l 
 
 assign a new start time to T . . Instead we leave the start time 
 
 J 
 
 at its latest critical value, even though it may not start 
 
 processing at that time. We observe that many tasks may not 
 
 require all of the processing time specified by their maxima, 
 
 and as a result sufficient float time may be created later to 
 
 enable the task, T . , to meet its deadline. 
 
 J 
 
 Examples . 
 
 Several examples will now be given to illustrate the efficacy of the 
 algorithm. Suppose we have determined that a task, T. , should have priority 
 k and that at time t = 0, the state of priority class k is that shown in 
 Figure 3.2. (Note that since all priority class k tasks have similar g/f, 
 we need not show these ratios.) Notice that forming the float time 
 column is analogous to forming a forward difference table. In each of the 
 following examples we assume that Figure 3.2 is the initial state of 
 priority class k. 
 
 i) Suppose the information vector (with g/f omitted) for T. is 
 
 (T . ,6,1,5 ) . Beginning with T , we observe that d < d. : d_ < d, 
 < d . So we insert T. between T and T and renumber the tasks 
 accordingly. 
 
38 
 
 1 
 
 4 5 
 
 8 9 
 
 I 
 
 
 I I I 
 1 2 3 
 
 I 
 5 
 
 Ti 
 
 T 2 
 
 T 4 
 
 T 5 
 
 a) schedule of tasks, 
 
 Ti 
 
 d l = 2 
 
 n = i 
 
 Sl = l 
 
 T 2 
 
 d 2 = 4 
 r 2 * 2 
 s 2 = 2 
 
 T 3 
 
 d 3 - 10 
 T-3 = 3 
 
 s 3 = 7 
 
 T 4 
 
 d 4 = 14 
 r 4 = 2 
 S 4 = 12 
 
 T 5 
 
 d 5 = 15 
 S 5 s 14 
 
 INFORMATION VECTOR 
 
 FLOAT TIME/ fi 
 
 B) INFORMATION VECTORS. 
 
 FIGURE 3.2 ~ STATE OF PRIORITY CLASS K AT TIME t = 
 
39 
 
 Now s + x 2 <_ s < s^ - t since 2 + 2<_5<_7-l, so the priority 
 
 assignment is complete and all tasks are guaranteed to meet their 
 
 deadlines. The resulting state of priority class k is shown in 
 
 Figure 3.3. 
 
 ii) Suppose instead that the information vector for T. is (T.,9,2,7). 
 
 We find that d„ < d. < cL < di < d_, so we insert T. "between T 
 21—34 5' 1 2 
 
 and T_ and renumber the tasks accordingly. However, s„ + t„ > s, 
 3 '3 3 h 
 
 since 7 + 2 > 7 and a deadline could be missed. But F >_ s + t - s. 
 
 since h >_ 2, so we assign a new start time to T : s = s, - t_ = 
 
 7-2=5. Now s < s - t since 2 <_ 5 - 2, so the priority assignment 
 
 is complete and all tasks are guaranteed to meet their deadlines. 
 
 The resulting state of priority class k is shown in Figure 3.^-. 
 
 (Note the effect of the last in first out rule for breaking ties on 
 
 start times . ) 
 
 iii) Next suppose the information vector for T. is (T.,9»^»5). We find 
 
 11 
 
 that d < d. <_ d < d> < d , so we insert T. between T 9 and T and 
 renumber the tasks accordingly. However, s_ + t > s, since 5 + *+ 
 > 7 S and a deadline could be missed. But F >_ s + x - s, since 
 h >_ h so we assign a new start time to T : s = s, - t = 7 - ^ = 3. 
 Next s + t > s since 2 + 2 > 3, so we assign a new start time 
 to T : s = s - t = 3 - 2 = 1. Now s + x. > s since 1 + 1 > 1, 
 so we assign a new start time to T : s_ = s_ - x. = 0. The priority 
 assignment is complete and all tasks are guaranteed to meet their 
 deadlines. The resulting state of priority class k is shown in 
 Figure 3.5. 
 
^40 
 
 012345678901 
 
 1 I I 
 
 2 3 4 
 
 I 
 5 
 
 Ti 
 
 T 2 
 
 T 4 T 5 
 
 Ti 
 
 a) schedule of tasks before assignment, 
 
 I I I I I I 
 
 23456789012345 
 
 Tx 
 
 T 2 
 
 T, 
 
 T 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment. 
 
 
 
 t 
 
 Ti 
 
 
 2 
 1 
 1 
 
 T 2 
 
 
 4 
 2 
 2 
 
 \ 
 
 T 3 
 
 6 
 
 1 
 5 
 
 % 
 
 T 4 
 
 10 
 3 
 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 12 
 
 \ 
 
 T 6 
 
 15 
 1 
 14 
 
 C) INFORMATION VECTORS AFTER ASSIGNMENT. 
 FIG, 3.3- RESULTS OF PRIORITY ASSIGNMENTS H) 
 
012345678901 
 
 in 
 
 1 I 
 
 2 3 
 
 I 
 4 
 
 I 
 5 
 
 Ti 
 
 T 2 
 
 T 3 
 
 
 T 4 
 
 T 5 
 
 
 
 
 
 Ti 
 
 
 a) schedule of tasks before assignment, 
 
 234567890 
 
 I I I I 
 
 2 3 4 5 
 
 T 
 
 T 2 
 
 T 3 
 
 T 4 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment. 
 
 
 
 t 
 
 Ta 
 
 
 2 
 1 
 1 
 
 T 2 
 
 
 4 
 2 
 2 
 
 X 
 
 T 3 
 
 9 
 2 
 
 5 
 
 * 
 
 T 4 
 
 10 
 3 
 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 
 12 
 
 \ 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 c) information vectors after assignment, 
 
 FIG. 3. 4 -RESULTS OF PRIORITY ASSIGNMENTS (Ci) 
 
k2 
 
 012345678901234 
 
 I 
 5 
 
 T, T 2 
 
 
 T 3 
 
 
 T 4 
 
 T 5 
 
 
 
 
 
 
 
 
 
 Ti 
 
 
 a) schedule of tasks before assignment, 
 
 I I I I I I 
 
 23456789012345 
 
 Ti 
 
 T 2 
 
 T 3 
 
 T 4 
 
 T 5 
 
 T 6 
 
 b) schedule of tasks after assignment, 
 
 
 
 t 
 
 Ti 
 
 
 2 
 
 1 
 
 
 T 2 
 
 
 4 
 2 
 1 
 
 H 
 
 T 3 
 
 9 
 4 
 3 
 
 % 
 
 T 4 
 
 10 
 3 
 
 7 
 
 \ 
 
 T 5 
 
 14 
 2 
 12 
 
 % 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 c) information vectors after assignment. 
 
 FIG, 3, 5 -RESULTS OF PRIORITY ASSIGNMENTS (ill) 
 
iv) As a final example, suppose that the information vector for T. 
 
 is (T. t 9,5,^) . As before, we find that d < d. < d„, < d, < d r 
 1 2i—345 
 
 so we insert T. between T and T and renumber the tasks accordingly. 
 However, s + il> s> since h + 5 > 7, and a deadline could be 
 missed. Furthermore, F < s + t - s, since 1 < 2, and the 
 compacting scheme will not help us. Instead we leave the start 
 times at their latest critical values and hope that sufficient 
 float time is created later to enable the tasks to meet their 
 deadlines. The results of this assignment are shown in Figure 3.6. 
 Note that T\ is the task which is in danger of missing its deadline. 
 
 The last example brings up the problem of what to do with a task whose 
 deadline is missed. We simply treat it as though it had just entered the 
 system using the next specified deadline as the current deadline. If no 
 further deadlines are specified, the task is assigned priority R-l and will 
 be processed accordingly. 
 
 When a processor finishes executing a task the following scheduling 
 algorithm is used to determine which task is to be processed next. Generally, 
 the algorithm takes the highest priority task in the queue that is closest 
 to its latest starting time. 
 
 Scheduling Algorithm 
 
 Beginning with k=0, and using i- as an index, 
 
 1. We examine the float time, f , for the first task in priority class 
 k. Then for % = k+1: 
 
 2. If f of priority class k <_ t for the first task of priority 
 class £, we set k=& and continue with Step 1. Otherwise we 
 continue with Step 3. 
 
Uh 
 
 I I I 
 
 012345678901 
 
 I I I 
 2 3 4 5 
 
 I 1 1 I 1 1 1 1 1 I I 1 1 1 I I 
 
 Ti T 2 
 
 T 4 Yh 
 
 a) schedule of tasks before assignment, 
 
 234567890 
 
 1 1 1 111111 1 1 
 
 I I I I 
 
 2 3 4 5 
 
 n 
 
 T 2 
 
 T 3 
 
 b) schedule of tasks after assignment. 
 
 T 5 
 
 T 6 
 
 Ti 
 
 
 2 
 
 1 
 
 L 
 
 T 2 
 
 
 4 
 2 
 2 
 
 \ 
 
 T 3 
 
 9 
 5 
 
 \ 
 
 T* 
 
 1 4 
 
 10 
 3 
 
 7 
 
 iy 
 
 T 5 
 
 14 
 2 
 12 
 
 \ 
 
 T 6 
 
 15 
 
 1 
 
 14 
 
 C) INFORMATION VECTORS AFTER ASSIGNMENT, 
 FIG, 3,6 -RESULTS OF PRIORITY ASSIGNMENTS [iv) 
 
U5 
 
 3. Set I = £+1 and continue with Step 2 until all priority classes 
 have been considered. Then continue with Step h. 
 
 k. Assign the first task, T , in priority k to the available 
 processor. 
 
 The effect of this scheduling algorithm is quite simple. It instructs 
 the scheduler to schedule the important tasks first and then, if there is 
 sufficient time, schedule those lower priority tasks in such a way that as 
 many deadlines as possible are met. 
 
 In the foregoing we have tacitly assumed that each task enters the 
 system sufficiently before its deadline to allow processing. The two 
 algorithms taken together facilitate meeting the deadlines, where possible, 
 of the higher priority tasks. Those tasks which do not meet their deadlines 
 will tend to be uniformly late. 
 
 3.3 Load Leveling in a Network of Centers 
 
 Thus far we have been concerned only with cost effectiveness in a 
 single center. Next, let us consider the more general problem of load 
 leveling within a network of centers. Each center may contain a single 
 computer or a subnet of computers. The topological and physical properties 
 of such networks have been illustrated [ 1,23,32,^2] and will not be 
 discussed here. 
 
 We wish to determine a strategy which optimizes the value of work 
 performed by the network computer. That is, to guarantee that every task 
 in each center will be processed, if possible, before its deadline and 
 only those tasks that offer the least reward to the network will miss their 
 deadlines. Implicit in this discussion is the simplifying assumption that 
 any task can be performed in any center. This assumption is not as 
 restrictive as it may sound since we can, for the purposes of load leveling, 
 
1+6 
 
 partition a nonhomogeneous network into sets of homogeneous subnetworks 
 which can be considered independently. Thus, in the discussion which follows 
 we will assume that the network computer is homogeneous. 
 
 We define the measure of cost effectiveness for a network of N centers 
 
 y , as follows: 
 
 N N 
 
 Y TO ■ I W n -Y- given that Y u. = 1 
 W i=l X X i=l x 
 
 where 
 
 the w are weighting factors that reflect the relative contribution 
 of the i center to the overall computational capability of the 
 network, 
 and y is the measure of cost effectiveness for the i th center. Note that 
 
 if a center is a subnet of computers, we could employ this definition to 
 determine the measure of cost effectiveness for the subnet. We also let 
 c. . denote the cost of communication between centers i and ,j : and t. . the 
 transmission time between centers i and j . 
 
 Ideally, we want the network computer to operate so that all tasks 
 within the network are processed before their deadlines. If a task is in 
 danger of missing its deadline, we want to consider it as a candidate for 
 transmission to another center for processing. The determination of which 
 tasks should be transferred follows the priority assignment (i.e., 
 priority tasks in danger of missing deadlines should be the first to be 
 considered, priority 1 tasks next, etc.). 
 
 We note that this scheme may not discover all tasks that are in 
 danger of missing their deadlines. In order to discover all tasks that 
 might be in danger of missing their deadlines, we would require a look 
 ahead scheme to determine the available float time and to fit lower priority 
 
^7 
 tasks into this float time. The value of such a scheme is quest ionahle, 
 however, since we assume some float time is created during processing and 
 additional float time may be created by sending high priority tasks to 
 other centers. Also, the overhead associated with executing the look ahead 
 scheme would further reduce the probable gain of such a scheme. 
 
 The determination of which center should be the recipient of a 
 transmitted task can be determined from the measure of cost effectiveness 
 of each center. Recall that the measure indicates the worth of the work 
 to be processed within a center. Thus, a center with a task in danger of 
 missing its deadline will generally have a larger measure than a center 
 with available float time. Thus, by examining the measures for each 
 center, we can determine the likely recipient of tasks to be transmitted. 
 
 These centers can in turn, examine their own queues and bid for additional 
 work on the basis of their available float time. This approach has a 
 decided economic advantage over broadcasting the availability of work 
 throughout the network and transmitting the tasks to the first center to 
 respond. The latter approach has previously been discussed and disguarded 
 by Farber [2l]. 
 
 Once a recipient center has been determined, we would transmit a 
 given task only if the loss in reward associated with not meeting its 
 deadline is greater than c. ., the cost of transmitting the task between 
 centers and transmitting back the results. 
 
 When a task is transmitted to a new center its deadline is diminished 
 
 by t. ., the time to transmit back the results, thus ensuring the task will 
 
 reach its destination before its true deadline. Similarly, the reward 
 
 associated with meeting the task's deadline is diminished by c.., since 
 
 - 1 - J 
 
U8 
 
 this represents a reduction in profit. Then the task's g/f ratio is used 
 to determine a new priority and the task is treated like one originating 
 in that center. 
 
 This heuristic algorithm provides the desired results that within 
 each center all deadlines are met, if possible, and if any task is in 
 danger of missing its deadline, it is considered for possible transmission 
 to another center which can meet the deadline. 
 
 3 . h Summary 
 
 We have introduced a priority assignment technique which, together 
 with the scheduling algorithm, provides a new approach to resource 
 allocation. The most important innovation in this approach is that it 
 allows a computing installation to maximize reward for the use of resources 
 while allowing the user to specify deadlines for his results. The demand 
 by users upon the resources of a computing installation is translated into 
 rewards for the center. 
 
 This approach offers advantages to the user and to the computing 
 installation. The user can exercise control over the processing of his 
 task by specifying its reward/cost ratio which, in turn, determines the 
 importance the installation attaches to his requests. The increased 
 flexibility to the user in specifying rewards for meeting deadlines yields 
 increased reward to the center. Thus the computing installation becomes 
 cost effective, since for a given interval of time, the installation can 
 process those tasks which return the maximum reward. A notable point 
 here, is that this system readily lends itself to measurement. 
 
^9 
 The measure of cost effectiveness is designed to reflect the status of 
 a center using the priority assignment technique. From its definition, 
 the value of the measure depends not only on the presence of tasks in the 
 system but upon the priority of these tasks. Thus the measure reflects 
 the worth of the tasks awaiting execution rather than just the number of 
 tasks. Therefore, the measure can "be used both, statically, to record 
 the operation of a center and, dynamically, to determine the probability 
 of available float time. This attribute enables us to predict the worth 
 of the work to be performed in any center in the network and facilitates 
 load-leveling between centers. 
 
 We have spent a good deal of time discussing what this system does 
 and the problems it attempts to solve. In the interest of fair play, we 
 feel that we should also discuss the things it does not do and the problems 
 it does not solve. 
 
 In Chapter 2, one of the proposed benefits of a network computer was 
 that it was possible to provide, well in advance, a guarantee that, at a 
 predetermined price, a deadline would be met. This guarantee is especially 
 important for scheduled production runs, such as payroll runs, which must 
 be processed within specified time periods. The system as presented does 
 not allow for such a long range guarantee. To implement such an option, 
 however, is not difficult. Notice first of all that we say nothing that 
 requires rewards to be strictly monetary in nature. This allows us to say 
 that in order to meet such absolute guarantees we simply modify the reward 
 to include the loss of goodwill which would be incurred should such a dead- 
 line be missed. Perhaps the easiest way to implement this would be to 
 reserve priority class zero for tasks whose deadlines were previously 
 guaranteed. Under this system we could assure the user, with confidence, 
 that the deadlines could be met at a predetermined price. The difficulty 
 
50 
 which arises under such a modification is that we have no way of ensuring 
 that the user does not submit tasks to priority class zero which have not 
 been guaranteed in order to get the best possible service at a (possibly) 
 lower price. This problem is one of security and remains unsolved in this 
 paper . 
 
 A second problem with the system is that the algorithms presented in 
 no way attempt to optimize the mix of tasks which would be processed 
 concurrently in a multiprogramming environment. This is a valid difficulty 
 which we can answer only by saying (perhaps hopefully) that the system 
 
 will tend to keep itself balanced. A common strategy in obtaining a good 
 mix is to choose tasks in such a way that most of the tasks being processed 
 at one time are input /output bound (this is especially common in large 
 systems which can support a large number — five or more — tasks concurrently) . 
 Generally smaller tasks are the ones selected to fill this bill. Under our 
 system, it seems reasonable that the higher priority classes will tend to 
 contain the smaller and less expensive tasks since priority is assigned on 
 the basis of a cost multiplier which is user supplied. It seems fair to 
 conclude that a user would be much more reluctant to double (give a reward/ 
 cost ratio of 2) the cost of a $100 task than to double the cost of a $5 
 task. This reluctance, we feel, will tend to keep a good mix present in 
 a multiprogramming environment. 
 
 The final loose end which we would like to tie down here is the problei 
 of what to do with a task if (horror of horrors) all of its deadlines are 
 missed. There are basically two options, both feasible for certain 
 situations, which will be discussed. We feel that the ultimate decision 
 as to which is best belongs to the folks who manage the centers so we will 
 attempt to present the alternatives objectively without any intent to 
 influence their decision. 
 
51 
 The first alternative made obvious "by the presentation is that when 
 a task misses all of its deadlines the results it would produce are of no 
 further use. Continued attempts to process a task in this instance would 
 be analogous to slamming on the brakes after your car hits a brick wall; 
 simply a waste of resources. Thus we might say that if the deadlines are 
 firm, a task which misses all of its deadlines should be considered lost 
 to the system. 
 
 On the other hand, it is conceivable that the results produced by a 
 task are of value even after the last deadline is missed. In this case 
 it is reasonable to require that a system offer a "low cost" service under 
 which tasks are processed at a reduced rate but at the system's leisure. 
 A danger in this system is that it is conceivable that, if run without 
 outside supervision, the system could become saturated with low cost tasks 
 to the detriment of more immediately valuable work. This actually happened 
 at the University of Illinois during early attempts to institute a low cost 
 option. From the results of this experience, it is safe to say that it 
 will never happen more than once to the same installation manager. The 
 confusion and headaches which resulted from the saturation were more than 
 enough to institute protective measures. 
 
 Despite a few admitted shortcomings, we feel that our system represents 
 a definite positive step in the analysis of network computers. 
 
 Our approach treats a network computer as the economic entity that it 
 should be: a market place in which vendors compete for customers and in 
 which users contend for scarce resources. The development of this approach 
 is a first step in the long road to achieving economic viability in network 
 computers. 
 
52 
 
 k. QUEUEING THEORY ANALYSIS OF THE SINGLE SERVER 
 
 PRIORITY CASE WITH BRIBING AND RENEGING 
 
 The priority assignment and scheduling algorithms presented in 
 Chapter 3 give rise to an interesting queueing theory problem. We 
 are presented with a situation in which customers offer overt bribes 
 (a term introduced in queueing theory by Kleinrock [33]) to improve 
 their queue position. Furthermore these customers can, and will, 
 renege (give up their queue position and leave the system) if their 
 bribe is not accepted and their demand for services not met. It is to the 
 analysis of this problem that we direct our efforts in this chapter. 
 
 In the analysis we will assume the following: 
 
 1. Input population: We assume an infinite input population 
 with average arrival rate for priority class r of A . 
 The arrival rate for the system is 
 
 RKT 
 
 x = y x 
 
 Lt y* 
 
 r=o 
 where R is the number of priority classes. 
 
 2. Queue discipline: R priority classes. Finite queue with 
 maximum length M > 1. Bribes are random with arbitrary 
 cumulative distribution function B. Priority class for 
 an entering task is assigned on the basis of its bribe. 
 
 3. Service mechanism: Single server with constant service rate y . 
 h. Service pattern: Within a priority class on the basis of 
 
 closeness to deadline. Tasks renege and are lost to the system 
 if their deadline is missed. Tasks from priority class r are 
 scheduled for processing on the basis of available float time 
 from classes r-1 and higher as described in Chapter 3. 
 
53 
 
 5. Reneging mechanism: Reneges for priority class r are 
 
 distributed in a Poisson manner about mean rate a . The 
 
 r 
 
 renege rate for the system is distributed about mean 
 
 R-l 
 
 1 a • 
 
 a = 
 
 r=0 r 
 
 We find the steady state probabilities for the system in the 
 
 following manner. First look at the no priority case (R = l). Let 
 
 P (t) be the probability that at time t an arrival finds (n-l) waiting 
 n 
 
 th 
 tasks already in the system; that is, he is n away from service. 
 
 Then P n (t) is the probability that an arriving task goes directly into 
 
 service. Using classical techniques (well discussed in the literature 
 
 [11, 18, 32, 39]) we proceed by generating difference equations. We find 
 
 P Q (t+At) = P Q (t)(l-XAt)(l) + P 1 (t)(l-AAt)(yAt) + o(At) 2 . 
 Continuing in the usual way we find that 
 
 P Q '(t) = -XP Q (t) + pP 1 (t) 
 which leads to the steady state equation 
 
 P 1 = (X/y)P Q . 
 
 To find the steady state equations for M >_ n > 1 we adopt the 
 approach taken by Ancker and Gafarian [5]. Since any of the (n-l) 
 customers in the queue can renege during a time interval of length At, 
 the probability that one of these will renege is (n-l)aAt. Furthermore, 
 because of the ordering of tasks within a priority class, we know that 
 should a task renege, it is the task which is first in the queue. 
 Utilizing this result we find that 
 
P (t+At) = P (t)(l-XAt)(l-yAt)(l-(n-l)aAt) 
 n n 
 
 + P (t)(XAt)(l-yAt)(l-(n-2)aAt) 
 + P (t)(l-XAt)(yAt)(l-naAt) 
 + P (t)(l-XAt)(l-yAt)(naAt) + o(At) 2 , 
 Continuing again we find that 
 
 P - ( X+y+(nr-l)a )p _ _X 
 
 n+1 y+na n y+na n-1* 
 
 By induction we can show that 
 
 and 
 
 P n = n^T J P n=l,2,...,M+l 
 
 II (y+ia) 
 i=0 
 
 M n-1 
 
 P" 1 = I (X n )/ n (y+ia). 
 
 n=0 i=0 
 
 Note that P M ,-, is the steady state probahility that an arriving 
 
 task finds the queue full. 
 
 The no priority case which we have just solved has been 
 
 discussed previously in the literature. Though different in form, our 
 
 results agree with those of Ancker and Gafarian [5,6] . The problem 
 
 which has not been solved is that of a single server multiple 
 
 priority class system. This is the system described in Chapter 3. 
 
 The interesting thing about the problem is that difficulties 
 
 raised by bribing disappear. Since priority class is assigned on 
 
 the basis of the bribe, the distribution of bribes is absorbed in 
 
 the arrival rates. Thus the problem which we have to solve is the 
 
 single server multiple priority class problem with reneging. An 
 
 illustration of the model is given in Figure k.l. 
 
55 
 
 Arrival 
 Population 
 
 Priority 
 Queue 
 
 Service 
 Mechanism 
 
 Figure U.l A Model of our Queueing System with Reneging 
 
56 
 
 To simplify notation, let us define 
 
 r 
 
 a = 7 \. , a = a_. , 
 r . 6 _ 1' R-l 
 
 i=0 
 
 B r ' ,1 a i 6 ■ Vr 
 
 1=0 
 
 Let P (t) denote the probability that at time t an arrival of 
 
 m,r 
 
 priority r finds (m-l) waiting tasks of priority r or higher; 
 
 th 
 that is, he is m away from service. 
 
 As before, let us begin by generating difference equations. 
 
 Starting with P (t+At), the probability that at time t+At a 
 ±,r 
 
 priority r arrival finds himself first in the queue, we note that 
 this probability is given by the sum of the following mutually 
 exclusive and collectively exhaustive events: 
 
 a) an arrival of priority r at time t would have been first 
 in the queue and during the interval of length At there 
 were no arrivals of priority r or higher (with probability 
 (l-a At)), no services (with probability (l-yAt), and no 
 reneges from priority r or higher (with probability (l)). 
 This term is given by 
 
 P n (t)(l-a At)(l-uAt)(l) + o(At) 2 . 
 l,r r 
 
 b) an arrival of priority r at time t would have been 
 second in the queue and during the interval there was 
 no arrival of priority r or higher and either a service 
 or a renege. This term is given by 
 
 P_ (t)(l-o At)(yAt)(l-B At) 
 2,r r r 
 
 + P (t)(l-a At)(l-yAt)(3 At) + o(At) 2 . 
 
 2,r r r 
 
57 
 
 c) an arrival of priority r at time t would have found the 
 server idle (and hence gone directly into service) and 
 during the interval there "was an arrival of any priority. 
 This term is given by 
 
 P (t)(aAt)(l)(l) + o(At) 2 . 
 
 d) an arrival of priority r at time t would have been first 
 in the queue and during the interval there was a service, 
 if this occurred and there was more than one customer in 
 the queue, another would have entered service and an 
 arrival at time t+At would still be first in the queue. 
 This term is given by 
 
 P n (t)(l-a At)(yAt)(l) - P_(t)(l-a At)(yAt)(l) + o(At) 2 , 
 l,r r 1 r 
 
 Thus we have 
 
 P n (t+At) = P. (t)(l-a At)(l-yAt)(l) 
 l,r l,r r 
 
 + P. (t)(l-c At)(yAt)(l-3 At) 
 2,r r r 
 
 + P (t)(l-a At)(l-yAt)(B At) 
 2,r r r 
 
 + P (t)(l-a At)(yAt)(l) 
 
 r 
 
 + P (t)(l-a At)(yAt)(l) 
 
 l,r r 
 
 - P.(t)(l-a At)(yAt)(l) + o(At) 2 . 
 
 1 r 
 
 In a similar manner, we find that for 1 < m < M 
 
 P (t+At) = P (t)(l-a At)(l-yAt)(l-(m-l)B At) 
 m,r m,r r r 
 
 + P ._ (t)(l-a At)(yAt)(l-m3 At) 
 m+l,r r r 
 
 + P . (t)(l-a At)(l-yAt)( m 3 At) 
 m+l,r r r 
 
 + P . (t)(a At)(l-yAt)(l-( m -2)3 At) + o(At) 2 , 
 m-l,r r r 
 
58 
 These lead to the steady state results 
 
 P 2,r " <° r ^ +B r » P l, r 
 
 P m + l,r " ((V 1J+ ' m ~ 1)B r )/(,J+mB r )) V " <V (lJ+mB r » ' P m-l, r 
 
 for m = 1, 2, .,., M. By induction on m we can show that 
 
 m 
 
 P m+1 r = ((a r ^ )m /( n d + iB r /y))) P. m = 1, 2, ..., M, 
 ' i=l ' ' 
 
 In addition 
 
 P n (t+At) = P_ Jt) (l-o At)(l)(l) 
 0,r 0,r r 
 
 + P. (t)(l-a At)(yAt)(l) + o(At) 2 
 l,r r 
 
 so that 
 
 V (t) - -°r P 0,r (t) + uP l,r (t) 
 
 or at steady state 
 
 P n = (a /y) P. 
 l,r r 0,r 
 
 which leads to the result that 
 
 P m+1 r = ((a r ^ )m / ( n(l+i3 r /v))) P Q m = 0, 1, 2, ..., M. 
 
 ' i=l ' 
 
 
 (We define n (l+ip /y ) = 0.) 
 i=l 
 
 With the steady state probabilities found, it remains to find some 
 
 representative system descriptors. The one descriptor we are most 
 
 interested in is the expected waiting time for a priority r task which 
 
 gives renege time of t. In addition, we find the average number of 
 
 tasks of priority r or higher and the average number of tasks of 
 
59 
 
 priority r or higher which give renege time less than or equal to t. 
 
 Let W denote the waiting time of a priority r task which 
 r ,t 
 
 gives us renege time t. First look at the waiting time for a priority 
 
 R-l task. Let n be the number of tasks in the queue with renege time 
 
 less than or equal to t and N be the total number of tasks in the queue. 
 
 Our tagged task must first of all wait for service to those n tasks 
 
 ahead of him. In addition he must wait for service to those tasks which 
 
 arrive during his waiting time and take position in the queue ahead of 
 
 him. Since the expected number of arrivals is AW and the probability 
 
 K— 1, t 
 
 of an arriving task giving renege time less than or equal to t is 
 
 — ctt 
 (l-e ) we expect that the number of tasks which will arrive and 
 
 —at 
 take position in front of our tagged task is (l-e )XW . Since 
 
 K-lj "t 
 
 each unit serviced contributes l/y time units to our task's waiting 
 time, the total contribution of these new arrivals plus that of those 
 in the queue already is 
 
 l/w(n t + (i-e- at )xw R _ ljt ). (1) 
 
 However, during our task's waiting time some of the N tasks already 
 
 in the queue will renege. By virtue of the ordering of tasks within 
 
 the queue we know that should a task renege it must be a task positioned 
 
 ahead of our tagged task in the queue. We expect that, of the N tasks 
 
 in the queue, NaW will renege during our tagged task's waiting 
 K— t ,"t 
 
 time. Thus expression (l) is too large by a factor of l/yNaW^ . . 
 
 n— J., "C 
 
 Therefore we immediately find that 
 
 W R-l,t " lM \ + '^^'"R-Lt' " ^"R-Lt 
 which reduces to 
 
6o 
 
 W R-1 t = \foWl 1 + l/yNa " (l-e" at )A/vi). 
 
 Let us now examine the case for r = R-2. Let n denote the 
 
 r,t 
 
 number of tasks of priority r or higher which give renege time less 
 
 than or equal to t and let N denote the number of tasks of priority 
 
 r or higher in the queue. Also let 3 and a denote the average renege 
 
 rate and average arrival rate of tasks of priority r or higher. As 
 
 before, our task must wait for service to those n tasks already 
 
 r , t 
 
 ahead of him in the queue and to those (l-e r )o W tasks which 
 
 r r ,t 
 
 will arrive and take position in the queue ahead of him. Again, there 
 are N 3 W tasks which will renege (all of which originate in a 
 queue position ahead of our task) so that 
 
 W , > l/y(n , + (l-e" Pr °)a W . ) - 1/uN 3 W 
 r,t — r,t r r,t p r r : 
 
 which again reduces to 
 
 w r t - ( n r t /V)/(1 + lM r 3 r - (l-e" 3 r t ) a ^/y). ( 2 ) 
 
 Now, "however, (2) is really the amount of time which our task 
 
 would wait if no tasks from a lower priority class were serviced before 
 
 him. Under our system, however, if there are l/y or more time units 
 
 of float time in priority r and higher, a task of priority r+1 will 
 
 be serviced. In other words, after tasks from all lower priority 
 
 classes are scheduled and those of priority r are scheduled there are 
 
 still l/y time units of float time available, then a task of priority 
 
 r+1 will be processed. Let P[fl >l/y] denote the probability that the 
 
 cumulative float time for priority classes r and higher is greater than 
 
 l/y. Then P[fl > l/y] is also the probability that a priority r+1 
 r — 
 
61 
 
 task is processed if one exists. Since the number of tasks which 
 
 can be processed during a time interval of length t units is yt, we 
 
 find that the contribution of priority r+1 (=R-1 in this case) to a 
 
 priority r task's waiting time is ytP[fl >_ l/y]l/y = tP[fl >_ l/y] 
 
 since we are effectively conducting yt independent trials with 
 
 probability of success P[fl >_l/y] each time and contribution l/y 
 
 from each success. Thus we find that (2) is too small by a factor 
 
 of tP[fl > l/y] and hence 
 r — 
 
 W = 1/Mn r,t + tP[fl > l/y] 
 
 1 + 1/uN 6 - (l-e" 3rt )a /y 
 r r r 
 
 for r = R-2. Continuing this reasoning we find, that 
 
 i / R_1 
 
 W r t = ±/yn r,t + I tPffl_.ll/y] (3) 
 
 1 + l/yN r 3 r - (l-e- 3rt )a r /y i=r 
 
 for r = 0, 1, ..., R-l where we define P[fl >_ l/y] = for r = R-l, 
 to make things more compact. 
 
 The average number of tasks of priority r or higher in the 
 queue, N , is given by the well known formula 
 
 M 
 
 N = V mp _,_.. 
 r L ^ m+l,r 
 m=0 
 
 where M is the maximum queue size. Substituting earlier results we 
 
 find that 
 
 M (a /y) m 
 
 N = I m P. . (U) 
 
 r L . m l,r 
 
 m=0 n (1+iB /y) 
 l-i 
 
 Unfortunately, a closed form of this result is not available. 
 
62 
 
 The more important descriptor is n , the average number of 
 
 r , t 
 
 tasks of priority r or higher which give renege time less than or 
 equal to t. We find that 
 
 n = (l-e-^t) p I «_* ( 5) 
 
 r ,t l,r L . m 
 
 m=0 n (i ♦ is M 
 i-i 
 
 which, even more unfortunately, is not in a closed form. 
 
 Substituting equations (k) , and (5) into equation (3) completes 
 
 the development of W . These last tvo descriptors, while useful in 
 
 r ,t 
 
 their own right, do not make W any simpler. We will content 
 
 r ,t 
 
 ourselves, therefore, with the expressions in their more compact forms. 
 
 We have completed our analysis of priority assignment. Oppor- 
 tunities remain for future research, especially in the queueing theory 
 area. The K processor case is an obvious choice for immediate work. In 
 addition, we expect that our algorithms will be modified as the realities 
 of resource sharing become better known. 
 
63 
 
 5. CONCLUSION 
 
 In this paper we have taken a slightly different approach to the 
 study of network computers. Instead of looking at the technology of network 
 computers, we have concerned ourselves with possible methods of making (dare 
 we say that crass word) money. We feel that this approach will find greater 
 popularity as time goes by. Network computers must be treated in the same 
 fashion as any other commodity. This is not a surprising point of view. In 
 the early days of the digital computer, there was widespread opinion that 
 these machines were too expensive and too limited to be of much value to 
 anyone but scientists and census takers. The situation has changed. Computer 
 manufacturers are subject to the same economic principles and constraints as 
 most industries. Given time, network computers will also enter the business 
 world where good management and cost effectiveness reign as king and queen. 
 
 We have seen, in Chapter 1, that all network computers have many things 
 in common. The key to cost efficiency is clearly effective resource sharing 
 since, without resource sharing, network computers have nothing of value to 
 offer. However, in Chapter 2, we saw that there is no formula for success in 
 the construction of network computers. The available options are numerous 
 and it is quite possible that networking will be the focus of innovative 
 businessmen for some time to come. 
 
 There remain many problems which have not been solved. Many of these 
 are business problems. Perhaps the most difficult of these will be 
 developing a realistic guarantee which will be firm enough to attract contract 
 customers. These customers certainly make up a customer base which must be 
 courted. They are, however, the most difficult customers to attract. They 
 can be expected to demand much and forgive few mistakes. But to the network 
 
6k 
 
 which can attract and keep these customers will belong a lucrative and 
 
 stable base of operations. 
 
 Other difficulties also remain. Questions of protocol are difficult 
 and presently poorly answered. Technology still has some work to do in 
 terms of getting prices down and speed and reliability up. Studies which 
 involve using microprogrammable minicomputers for communication purposes 
 appear to be promising. They indicate a forthcoming advance in this area. 
 
 The principle roadblock removed by this paper was across the road 
 which leads to successful sharing of common resources. Network computers 
 open up new possibilities for task scheduling. We feel that the algorithms 
 and ideas presented in Chapter 3 represent a first step towards successful 
 customer oriented computing. 
 
 In the interest of completeness, we took a stab, in Chapter k 9 
 at solving the previously unconsidered queueing theory problem of priority 
 classes with bribing and reneging. This effort represents an attempt to 
 advance queueing theory in terms of more complex, yet more practical, priorit 
 assignment techniques. The results are not complete, but we are encouraged 
 by the results obtained thus far. 
 
65 
 
 LIST OF REFERENCES 
 
 [l] Abramson, Norman, "THE AL0HA SYSTEM," AL0HA SYSTEM Technical Report 
 
 BT2-1, January/1972, 30 pages. 
 [2] Abramson, Norman, "THE AL0HA SYSTEM — Another Alternative for Computer 
 
 Communications," AL0HA SYSTEM Technical Report B70-1, ABRIO, 1970, 
 
 29 pages. 
 [3] Adiri, Igal, "A Dynamic Time-Sharing Priority Queue," Journal of the 
 
 ACM , Vol. 18, No. k, October, 1971, pp. 603-610. 
 [k] Adiri, Igal, "A Note on Some Mathematical Models of Time-Sharing 
 
 Systems," Journal of the ACM , Vol. 18, No. U, October, 1971, pp. 6ll-6l5. 
 [5] Ancker, C. J. Jr., and Grafarian, A. V., "Queuing with Impatient 
 
 Customers Who Leave at Random," Journal of Industrial Engineering , 
 
 Vol. 13, No. 2, March-April, 1962, pp. 8U-90. 
 [6] Ancker, C. J., Jr., and Grafarian, A. V., "Queuing with Reneging and 
 
 Multiple Heterogeneous Servers," Naval Research Logistics Quarterly , 
 
 Vol. 10, No. 2, June, 1963, pp. 125-1^9. 
 [7] Benes, V. E., "On Some Proposed Models for Traffic in Connecting 
 
 Networks," The Bell System Technical Journal , Vol. U6, January, 1967, 
 
 pp. 105-116. 
 [8] Bortels, W. H., "Simulation of Interference of Packets in time AL0HA 
 
 Time-Sharing System," AL0HA SYSTEM Technical Report B70-2, March, 
 
 1970, 26 pages. 
 [9] Bowdon, E. K., Sr., "Design Automation in Network Computers," The 
 
 Ninth Design Automation Workshop Proceedings , 1972, pp. 350-356. 
 [10] Bowdon, E. K., Sr., "Dispatching in Network Computers," Proc . of the 
 
 Symposium on Computers -Communications Networks and Teletraffic , 
 
 April, 1972. 
 
66 
 
 [ll] Bowdon, E. K., Sr., "Modeling and Analysis of a Network of Computers," 
 
 Ph.D. dissertation, University of Iowa, Iowa City, Iowa, 1969. 
 [12] Bowdon, E. K., Sr . , "Network Computer Analysis," Proc . of the Fifth 
 
 International Conference on System Sciences , January, 1972, pp. 201-203. 
 [13] Bowdon, E. K., Sr., and Barr, W. J., "Cost Effective Priority 
 
 Assignment in Network Computers," University of Illinois Department 
 
 of Computer Science Report No. UIVCDCS-R72-509, March 1972, 23 pages. 
 [ik] Bowdon, E. K. , Sr., and Barr, W. J., "Throughput Optimization in 
 
 Network Computers," Proc. of the Fifth Hawaii International Conference 
 
 on System Sciences , January, 1972, pp. 528-530. 
 [15] Carr, C. S., Crocker, S. D., and Cerf, V. G., "Host-Host Communication 
 
 Protocol in the ARPA Network," Proc. of the Spring Joint Comp. Conf ., 
 
 Vol. 36, 1970, pp. 589-597. 
 [l6] Cobham, A., "Priority Assignments in Waiting Line Problems," Operations 
 
 Research , Vol. 2, 195^» PP. 70-76, "A Correction," Operations Research , 
 
 Vol. 3, 1955, p. 5^7. 
 [17] Cole, G. P., "Computer Network Measurements: Techniques and Experiments! 
 
 University of California, Los Angeles School of Engineering and Applied 
 
 Science. Report No. UCLA-ENG-7165, October, 1971, 350 pages. 
 [18] Conway, R. W. , Maxwell, W. L., and Miller, L. W. , Theory of Scheduling , 
 
 Addison-Wesley Publishing Company, Reading, Mass., 1967. 
 [19] Farber, D. J., "Networks: An Introduction," Datamation , Vol. 18, 
 
 No. h, April, 1972, pp. 36-39. 
 [20] Farber, D. J., "Progress Report on the Distributed Computing System," 
 
 University of California at Irvine, Technical Report, January, 1972. 
 [21] Farber, D. J., and Larson, K. C, Supplement to Proposal for Research 
 
 Submitted to the National Science Foundation on Distributed Computing 
 
 System , University of California, Irvine, Technical Report, October, 1970 
 
 ' 
 

 67 
 [22] Farber, D. J., and Larson, K. C, "The System Architecture of the 
 
 Distributed Computer System — An Informal Description," University of 
 
 California, Irvine, Technical Report No. 11, Septermber, 1971, 36 
 
 pages. 
 [23] Frank, H., and Frisch, I. T., Communication, Transmission and 
 
 Transportation Networks , Addison-Wesley Publishing Company, Reading, 
 
 Massachusetts, 1971. 
 [2k] Frank, H. et. al., "Topological Considerations in the Design of the 
 
 ARPA Net," Froc. of the Spring Joint Comp. Conf ., Vol. 36, 1970, 
 
 pp. 581-587. 
 [25] Gilbert, E. N., "Minimum Cost Communication Networks," The Bell System 
 
 Technical Journal , Vol. U6, November, 1967, pp. 2209-2227. 
 [26] Greenberger, M., "The Priority Problem and Computer Time Sharing," 
 
 Management Science , Vol. 12, No. 11, July, 1966, pp. 888-906. 
 [27] Gupta, S. F., and Goyal, J. K., "Queues with Poisson Input and 
 
 Hyper-Exponential Output with Finite Waiting Space," Operations 
 
 Research , Vol. 12, No. 1, 196U, pp. 75-81. 
 [28] Heart, F. E., et. al., "The Interface Message Processor for the ARPA 
 
 Computer Network," Proc. of the Spring Joint Comp. Conf ., Vol. 36, 
 
 1970, pp. 551-567. 
 [29] Hootman, J. T., "The Computer Network as a Marketplace," Datamation , 
 
 Vol. 18, No. k, April, 1972, pp. h3-h6. 
 [30] Jackson, R. R. P., and Henderson, J. C, "The Time-Dependent Solution 
 
 to the Many-Server Poisson Queue," Operations Research , Vol. lU, 1966, 
 
 pp. 720-722. 
 [3l] Kleinrock, L., "Analytic and Simulation Methods in Computer Network 
 
 Design," Proc. of the Spring Joint Comp. Conf ., Vol. 36, 1970, 
 
 pp. 569-579. 
 
68 
 [32] Kleinrock, L., Communication Nets: Stochastic Message Flow and Delay , 
 
 McGraw-Hill, New York, I96U. 
 [33] Kleinrock, L., "Optimum Bribing for Queue Position," Operations Research , 
 
 Vol. 15, 1967, pp. 30U-318. 
 [3*0 Kruskal, J. B., "Work-Scheduling Algorithms: A Nonprobabilistic 
 
 Queuing Study (With Possible Application to No. 1 ESS)," The Bell 
 
 System Technical Journal, Vol. U8, November, 1969, pp. 2963-297 1 *. 
 [35] Mosmann, C, and Stefferud, E., "Computer Management," College and 
 
 University Business , January, 1971, pp. 50-52. 
 [36] Mossman, C, and Stefferud, E., "Campus Computing Management," 
 
 Datamation , Vol. 17, No. 5, March, 1971. 
 [37] Parker, L. T., Jr., Gallie, T. M., Brooks, F. P., Jr., and Ferrell, 
 
 J. K., "Introducing Computing to Smaller Colleges and Universities — 
 
 a Progress Report," Comm. ACM , Vol. 12, No. 6, June, 1969, pp. 319-323. 
 [38] Roberts, L. G. and Wessler, B. D., "Computer Network Development to 
 
 Achieve Resource Sharing," Proc. of Spring Joint Comp. Conf. , Vol. 36, 
 
 1970, pp. 5^3-5^9. 
 [39] Saaty, T. 1., Elements of Queueing Theory , McGraw-Hill, New York, 
 
 1961. 
 [U0] Stefferud, E., "Management's Role in Networking," Datamation , Vol. 18, 
 
 No. k, April, 1972, pp. U0-U2. 
 [Ul] Stefferud, E., "The Environment of Computer Operating System Scheduling: 
 
 Toward an Understanding," AEDS Journal , March, 1968, pp. 135-1^1. 
 [U2] Syski, R., Introduction to Congestion Theory in Telephone Systems , 
 
 Oliver and Boyd, Edinburgh, i960. 
 [1+3] Williams, L. H., "A Functioning Computer Network for Higher Education 
 
 in North Carolina," Submitted for Fall Joint Computer Conference, 1972. 
 [kh] Private conversation with Michael Sher, Center for Advanced Computation, 
 
 University of Illinois, Urbana, Illinois. 
 
BIBLIOGRAPHIC DATA 
 SHEET 
 
 1. Report No. 
 
 UIUCDCS-R-72-538 
 
 3. Recipient's Accession No. 
 
 4. Title and Subtitle 
 
 Cost Effective Analysis of Network Computers 
 
 5. Report Date 
 
 August 1972 
 
 6. 
 
 7. Author(s'> 
 
 William J. Barr 
 
 8. Performing Organization Rept. 
 No. 
 
 9. Performing Organization Name and Address 
 
 Department of Computer Science 
 
 University of Illinois at Urbana-Champaign 
 
 Urbana, Illinois 61801 
 
 10. Project/Task/Work Unit No. 
 
 11. Contract /Grant No. 
 
 NSF GJ 28289 
 
 12. Sponsoring Organization Name and Address 
 
 National Science Foundation 
 Washington, D.C. 
 
 13. Type of Report & Period 
 Covered 
 
 Thesis Research 
 
 14. 
 
 15. Supplementary Notes 
 
 16. Abstracts 
 
 With the advent of network computers, a new area of computer systems analysis 
 has evolved. Unfortunately, most of the work to date merely extends the 
 previously existing theory of communications. Our analysis is predicated on the 
 assumption that a geographically distributed network computer is quite different 
 from telephone networks and individual computing centers. The potential advantages, 
 from a businessman's point of view, of network computers are discussed and some 
 of the more important problems which arise are presented. We take a look at 
 several existing networks and examine their goals and solutions to these kinds 
 of problems. We develop a priority assignment techniaue for the individual centers 
 that comprise the network and determine load leveling rules for the entire network. 
 In addition, we analyze this sytem using classical queueing theory techniques. 
 
 17. Key Words and Document Analysis. 17a. Descriptors 
 
 Network Computer, Queueing Theory, System Modeling, Throughput Analysis, 
 Dispatching, Load Leveling 
 
 1 7b. Identifiers /Open-Ended Terms 
 
 7c. COSATI Fie Id /Group 
 
 8. Availability Statement 
 
 Unlimited Distribution 
 
 ORM NTIS-35 ( 10-70) 
 
 19. Security Class (This 
 Report) 
 
 UNCLASSIFIED 
 
 20. Security Class (This 
 
 Page 
 UNCLASSIFIED 
 
 21. No. of Pages 
 
 73 
 
 22. Price 
 
 None 
 
 USCOMM-DC 40329-P71 
 
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