R. Weber. 1978. "On the optimal assignment of customers to parallel servers," J. Appl. Prob. 15, pp. 406--413.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to performing loadbalancing is to choose the server with the least reported load from among a set of servers. This approach performs well in a homogeneous system where the task allocation is performed by a single centralized entity (dispatcher) which has complete up to date load information [Web78] Win77] In a system where multiple dispatchers are independently performing the allocation of tasks, this approach however has been shown to behave badly, especially if load information used is stale [ELZ86] MTS89] Mit97] SKS92] Mitzenmacher talks about the herd behavior that can ....

R. Weber. On the Optimal Assignment of Customers to Parallel Servers. Journal of Applied Probability, 15:406--413, 1978. 21

....scenario has also been considered, under the same restricted model described in the above paragraph, but where the ages (service time completed so far) of the jobs currently serving are known, so that it is possible to compute an arriving job s expected delay at each queue. In this scenario, Weber [27] considers the Shortest Expected Delay rule which sends each job to the host with the least expected work (note the similarity to the Least Work Remaining policy) Weber shows that this rule is optimal for job size distributions with increasing failure rate (including Exponential) Whitt [28] ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Joural of Applied Probability, 15:406 413, 1978.

....for heterogeneous tasks. In an experimental study, Spring and Wolski [75] compared a hybrid static and dynamic allocation policy against a purely dynamic policy for a single gene sequence comparison application. Purely analytical studies, including those by Harchol Balter [40] Whit [88] Weber [86], and Winston [89] have been performed using assumptions about workload characteristics which do not easily translate into generalizable allocation strategies in real world environments. With work flow analysis, we are able to identify when parameter uncertainty effects constraint terms which ....

Weber, R. W. On the optimal assignment of customers to parallel servers. Journal of Applied Probability 15 (1978), 406--413.

....of service distributed exponentially with mean 1. This model, a generalization of the natural M M 1 queueing model to many servers, has been widely studied in the case where incoming customers are placed at the server with the shortest queue. See, for example, the essential early work of Weber [Web78] Whitt [Whi86] and Winston [Win77] as well as the more recent work by Adan and others [AWZ90, Ada94] Of course, such a load balancing scheme requires some means of centralization. In a completely decentralized environment, attempting to determine the shortest queue might be expensive, in ....

R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probabiblities, 15:406-413, 1978.

....20 Winston [41] Shortest Queue Routing) considers a queueing system having K identical exponential servers. He shows that customers should be assigned to the shortest queue in order to maximize the number of departures by time t. The problem has been extensively studied in the literature (see [36], 11] 42] among others) Recently, by a sample path argument analogous to Definition 2.16, Menich [21] shows that the shortest queue policy minimizes Ef(Q t ) for all f 2 C 1 , where Q t is the numbers of customers in queues at time t. Thus, the shortest queue policy balances load in ....

R.R. Weber, "On the Optimal Assignment of Customers to Parallel Servers," J. Appl. Prob., vol. 15, pp. 406-413, 1978.

....of service distributed exponentially with mean 1. This model, a generalization of the natural M M 1 queueing model to many servers, has been widely studied in the case where incoming customers are placed at the server with the shortest queue. See, for example, the essential early work of Weber [Web78] Whitt [Whi86] and Winston [Win77] as well as the more recent work by Adan and others [AWZ90, Ada94] Of course, such a load balancing scheme requires some means of centralization. In a completely decentralized environment, attempting to determine the shortest queue might be expensive, in ....

R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probabiblities, 15:406--413, 1978.

....optimality of Shortest Line task assignment policy (send the task to the host with the shortest queue) has been proven by Winston [16] In this result, optimality is de ned as maximizing the discounted number of tasks which complete by some xed time t. This optimality result was extended by Weber [14] to include task size distributions with nondecreasing failure rate and arbitrary arrival process. Ephremides, Varaiya, and Walrand [4] showed that the Shortest Line task assignment policy also minimizes the expected total time for the completion of all jobs arriving by some xed time t, 2 under ....

....and performance results have not been developed, to the best of our knowledge. The scenario has been considered in which the ages (time in service) of the tasks currently serving are known, so that it is possible to compute an arriving task s expected delay at each queue. In this scenario, Weber [14] has shown that the Shortest Expected Delay rule is optimal for task size distributions with increasing failure rate, and Whitt [15] has shown that there exist task size distributions for which the Shortest Expected Delay rule is not optimal. 2.2 Measurements of task size distributions in ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406-413, 1978.

....scenario has also been considered, under the same restricted model described in the above paragraph, but where the ages (service time completed so far) of the jobs currently serving are known, so that it is possible to compute an arriving job s expected delay at each queue. In this scenario, Weber [27] considers the Shortest Expected Delay rule which sends each job to the host with the least expected work (note the similarity to the Least Work Remaining policy) Weber shows that this rule is optimal for job size distributions with increasing failure rate (including Exponential) Whitt [28] ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....is available. For example, suppose we have a system of n servers, and incoming tasks must choose a server and wait for service. If the incoming tasks know the current number of tasks already queued at each server, it is often best for the task to go to the server with the shortest queue [18]. In many actual systems, however, it is unrealistic to assume that tasks will have access to up to date load information; global load information may be updated only periodically, or the time delay for a task to move to a server may be long enough that the load information is out of date by the ....

....of processors may be possible. Going to the server with the smallest load appears natural in more centralized systems where global information is maintained. Indeed, going to the shortest queue has been shown to be optimal in a variety of situations in a series of papers, starting for example with [18, 20]. Hence it makes an excellent point of comparison in this setting. We develop analytical results for the limiting case as n # #, for which the system can be accurately modeled by an infinite system. The infinite system consists of a set of differential equations, which we shall describe below, ....

R. Weber, "On the Optimal Assignment of Customers to Parallel Servers", J. of Appl. Prob., Vol 15, 1978, pp. 406--413.

....reply more often than slower Matchers and, consequently, will receive more rules to evaluate. Also, if the speed of a Matcher decreases, it will start to reply less often and, consequently, will receive less and less rules to evaluate. The second policy we consider is the Join the Shortest Queue [14] (JSQ) policy. In this case, unlike work stealing, Executors do not store locally a new rule if no free Matchers are available, but rather they send it to a Matcher as soon as it is generated. If the chosen Matcher is busy, the rule waits into a FIFO queue and is evaluated later. Each time an ....

....broadcasts an evaluated rule to all the Executors, it piggy backs the information concerning its queue length on the messages containing the evaluated rule. Finally, the last policy we analyzed is called Join the Fastest Queue (JFQ) and is derived from the Join the Shorted Expected Delay Queue [14]. This policy is similar to the JSQ one, with the difference that now an Executor chooses the Matcher that minimizes the expected time required to evaluate a new rule. In order to allow Executors to perform their choices, each Matcher M i keeps track of the average time RET i it needs to evaluate ....

Weber, R. On the Optimal Assignment of Customers to Parallel Servers. Journal of Applied Probability 15 (1978), 406--413. This article was processed using the L A T E X macro package with LLNCS style

....The scenario has also been considered, under the same restricted model described in the above paragraph, but where the ages (time in service) of the tasks currently serving are known, so that it is possible to compute an arriving task s expected delay at each queue. In this scenario, Weber [17] considers the Shortest Expected Delay rule which sends each task to the host with the least expected work (note the similarity to the Least Work Remaining policy) Weber shows that this rule is optimal for task size distributions with increasing failure rate (including Exponential) Whitt [18] ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....are separate is to assign new jobs upon arrival to the more lightly loaded queues. When the service time distribution is exponential or has increasing failure rate, if jobs must be assigned to queues upon arrival without further intervention, then it is optimal to use the shortest queue; SQ) rule [12]. The advantage of the SQ rule is illustrated by the heavy traffic limit, which shows that SQ behaves as well as the combined system as ae 1 [14] Periodic redistribution has two potential advantages over dynamic assignment of arrivals. First, the periodic redistribution gives an alternative way ....

Weber, R. W. (1978) On the optimal assignment of customers to parallel servers. J. Appl. Prob. 15, 406-- 413.

.... the case where task sizes are unknown, the following results exist: Under an exponential task size distribution, the optimality of Shortest Line task assignment policy (send the task to the host with the shortest queue) has been proven by Winston [15] This optimality result was extended by Weber [13] to include task size distributions with nondecreasing failure rate. The actual performance of the Shortest Line policy is not known exactly, but is approximated by Nelson and Phillips [8] These approximations have been exteded to include more general task size distributions than the exponential ....

....and performance results have not been developed, to the best of our knowledge. The scenario has been considered in which the ages (time in service) of the tasks currently serving are known, so that it is possible to compute an arriving task s expected delay at each queue. In this scenario, Weber [13] has shown that the Shortest Expected Delay rule is optimal for task size distributions with increasing failure rate, and Whitt [14] has shown that there exist task size distributions for which the Shortest Expected Delay rule is not optimal. 2.2 Measurements of task size distributions in computer ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....questions remain open. In the case where task sizes are unknown, the following results exist: Under an exponential task size distribution, the optimality of Shortest Line task assignment policy (send the task to the host with the shortest queue) was proven by Winston [14] and extended by Weber [12] to include task size distributions with nondecreasing failure rate. The actual performance of the Shortest Line policy is not known exactly, but is approximated by Nelson and Phillips [9] In fact as the variability of the task size distribution grows, the Shortest Line policy is no longer ....

....[13] In the case where the individual task sizes are known, as in our model, equivalent optimality and performance results have not been developed for the task assignment problem, to the best of our knowledge. For the scenario in which the ages of the tasks currently serving are known, Weber [12] has shown that the Shortest Expected Delay rule is optimal for task size distributions with increasing failure rate, and Whitt [13] has shown that there exist task size distributions for which the Shortest Expected Delay rule is not optimal. Distribution of process lifetimes (log plot) ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....above policy will perform very well when there is no overhead involved in reassigning processors. Keeping server utilization maximized has shown to be a key to performance in routing customers to parallel queues: shortest queue routing is the optimal routing policy for homogeneous parallel queues [24, 27]. Shortest queue routing attempts to balance the queue lengths in the system which in turn maximizes server utilization. Thus the idea behind the policy is similar to the idea behind our dynamic algorithm. However, if it is costly to reassign processors the algorithm will suffer from high ....

R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....for symmetric convex objective functions we develop ourselves. Overall, our main contribution is in demonstrating how majorization can be applied to parallel processing s mapping problem. We also comment on the limitations of this application. Previous work on load balancing or task assignment [3, 4, 7, 8, 9, 12, 21] in parallel systems may be loosely divided into three categories. The first category, with deterministic structure, involves task structures and execution times which are known prior to assignment. In this case [15] includes a study of problem complexity under various constraints and heuristic ....

....known prior to assignment. In this case [15] includes a study of problem complexity under various constraints and heuristic algorithms for task scheduling. A second class of load balancing formulations, in which task execution times are random, is characterized by queueing theoretic considerations [4, 19, 21]. Much of this work pertains to steady state expectations of task delays with state dependent [4, 21] and state independent [19] assignment policies. Our work is closest to the third category [7, 8, 9, 13] which also takes task execution times to be random but focuses on minimizing expected ....

[Article contains additional citation context not shown here]

R.R.Weber, "On the Optimal Assignment of Customers to Parallel Servers", J. Applied Probability, Vol. 15, pp. 406-413.

.... the case where task sizes are unknown, the following results exist: Under an exponential task size distribution, the optimality of Shortest Line task assignment policy (send the task to the host with the shortest queue) has been proven by Winston [15] This optimality result was extended by Weber [13] to include task size distributions with nondecreasing failure rate. The actual performance of the Shortest Line policy is not known exactly, but is approximated by Nelson and Phillips [8] These approximations have been extended to include more general task size distributions than the exponential ....

....and performance results have not been developed, to the best of our knowledge. The scenario has been considered in which the ages (time in service) of the tasks currently serving are known, so that it is possible to compute an arriving task s expected delay at each queue. In this scenario, Weber [13] has shown that the Shortest Expected Delay rule is optimal for task size distributions with increasing failure rate, and Whitt [14] has shown that there exist task size distributions for which the Shortest Expected Delay rule is not optimal. 2.2 Measurements of task size distributions in computer ....

R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....is available. For example, suppose we have a system of n servers, and incoming tasks must choose a server and wait for service. If the incoming tasks know the current number of tasks already queued at each server, it is often best for the task to go to the server with the shortest queue [22]. In many actual systems, however, it is unrealistic to assume that tasks will have access to up to date load information; global load information may be updated only periodically, or the time delay for a task to move to a server may be long enough that the load information is out of date by the ....

....of processors may be possible. Going to the server with the smallest load appears natural in more centralized systems where global information is maintained. Indeed, going to the shortest queue has been shown to be optimal in a variety of situations in a series of papers, starting for example with [22, 24]. Hence it makes an excellent point of comparison in this setting. Other simple schemes that we do not examine here but can easily be studied with this model include threshold based schemes [5, 17] where a second choice is made only if the first appears unsatisfactory. We develop analytical ....

R. Weber, "On the Optimal Assignment of Customers to Parallel Servers", J. of Appl. Prob., Vol 15, 1978, pp. 406--413.

....that integrate probabilistic failure and recovery models with transaction routing. We will focus on the case of one router as shown in Figure 2. The techniques we discuss easily generalize to multiple routers. Previous routing algorithms have not dealt with these kinds of failures in the systems [2, 3, 8, 7, 9, 10]. Our algorithms are described in Section 2. Section 3 presents detailed simulation results of the performance of the algorithms. Section 4 describes a simplified analytical model of the system and a new algorithm based on this model. Finally, section 5 draws conclusions from the simulation and ....

R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

....system, 1 We note that our results also hold with minor variations if the d queues are chosen without replacement. 52 each server acts like an M M 1 server with Poisson arrival rate , which is known to be stable (see, for example, 46] The comparison argument is entirely similar to those in [74] and [75] which show that choosing the shortest queue is optimal subject to certain assumptions on the service process; alternatively, an argument based on majorization is given in [10] We also remark that a similar argument shows that the size of the longest queue in a supermarket system is ....

R. R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

.... comparison argument against the system in which each customer queues at a random server (that is, where d = 1) in this system,each server acts like an M M 1 server with arrival rate , which is known to be stable (see, for example, 19] The comparison argument is entirely similar to those in [29, 30], which show that choosing the shortest queue is optimal subject to certain assumptions on the service process; alternatively, an argument based on majorization, such as that in [6] is possible. A similar argument also shows that the size of the longest queue in a supermarket system of size n is ....

R. R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

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R. Weber. 1978. "On the optimal assignment of customers to parallel servers," J. Appl. Prob. 15, pp. 406--413.

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Richard R. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406--413, 1978.

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R. R. Weber. On the optimal assignment of customers to parallel servers. Journal of AppliedProbability, 15:406--413, 1978.

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R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406-413, 1978.

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R.R. Weber, "On the Optimal Assignment of Customers to Parallel Servers," J. Appl. Prob., 15, (406-413) 1978.

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R. Weber. 1978. "On the optimal assignment of customers to parallel servers," J. Appl. Prob. 15, pp. 406--413.

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