Leonard Kleinrock HDA 903 - 87 - C - 0663

the aggregate computing power of the workstations. In the same manner that it has been possible for many Distributed systems frequently have large people to share a single machine, by using the idle time numbers of idle computers and workstations. of one person to run the program of another, so it is If these could be harnessed, then considernow possible to share a network of workstations for able computing power would be available at large, distributed computations. low cost. We analyze such systems using a Whether this is technically feasible or not depends very simple model of a distributed program on a variety of factors, such as the characteristics of (a fixed amount of work) to see how the use the communications medium, the characteristics of the of transient processors affects the program's computers, and the statistical characteristics of the service time. user population. Mutka and Livny [13], and Nichols [14] have shown that under at least some circum1 Networks of Transient stances, this is very practical and useful. From an analytical point of view, we would like to Processors. have a queueing model of a network of transient processors executing distributed programs. In this paper Networks of computers are fairly common in busietk frs t st td this In th e ness and research environments throughout the world, we take a first step toward this end by analyzing the Originally motivated by a desire to ease data and de service time for a very simple model of a distributed vice sharing, many networks have grown in speed and program (a fixed amount of work) to see how the use sophistication to the point that distributed processing be a deterministic service process. can be performed on them. These networks vary in size from a handful of personal computers on a low-speed network, to thousands of workstations and a variety of 2 The Model. larger machines on a high-speed, fiber-optic network. Assume that we have a network of M identical procesA typical example is that of workstations on a highsors, and we wish to run a program that will require speed, local area network in a research laboratory. Not a total of W seconds of work. In general, a program only are there many machines, well connected by the consists of multiple stages of work, each of which must network, but the users are likely to demand more and be completed before the start of the next. For this more computing power. paper we smume that the program has only one stage On these networks, we often have the situation that of work, and furthermore, we assume that the work in many of the personal computers and workstations are any stage is infinitely divisible, and therefore is always sitting idle, waiting for their users, and thus being spread evenly among the available processors. wasted. If we could recover this wasted time for useful Each processor has a capacity of one second of work processing, then we would have considerable computper second. A processor alternates between a noning power available to us at low cost (6]. We refer to available period, when someone is using it, and an these processors, which are sometimes busy and someavailable period, when it is sitting idle. We assume times not, as traaiemt processors. that the length of non-available periods is randomly This situation has analogies to time-sharing. In the distributed with mean tn and variance v.2, and that past, institutions had one large resource, a mainframe the length of available periods is also randomly discomputer, that was shared by many users. As nettributed from a (possibly different) distribution with works of workstations develop, the largest computing mean t. and variance v.. We wish to run our program resource is no longer a single machine, but is instead on the network of processors, using processors while *This work was supported by the Defense Advanced they are in their available periods. The finishing time Research Projects Agency %&der contract MDA 03-S2of the program is given by a random variable f, with C0064, Advanced Telepmemoing Systems, and contract probability distribution f(t) , average 7, and Laplace MDA 903-87-CO663, Parallel Systems Laboratory. transform FO(s). The purpose of this paper is to find CH27...,Y .. 1AG 0 19S9 M 482