Structural properties of the optimal resource allocation policy for single-queue systems (original) (raw)
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Numerical Analysis of Optimal Control Policies for Queueing Systems with Heterogeneous Servers
INTRODUCTION The problem of optimal jobs assignment to heterogeneous servers arises in many applications. The problem of optimal jobs assignment for two heterogeneous servers with respect to minimization of long run average mean number jobs in the system was considered in [1], where it was shown that the policy, which minimizes the number of customers in the system, has a threshold property and consists in using the fastest server if necessary. For the multi-server system, these properties of an optimal policy were generalized in [2]. In the talk, an algorithm is proposed which gives the possibility to find optimal threshold levels for di#erent values of system parameters and investigate their behavior. Some numerical examples are also included. 2. THE PROBLEM Consider an M/M/K/N -K (K N<#) controllable queuing system with K heterogeneous exponential servers of intensities k (k = 1,K),N-K places in the bu#er, and a Poisson input of jobs with the intensity #. At the arrival ti
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ZOR - Methods and Models of Operations Research, 1993
A general single-server queueing network model is considered. It is well-known that an optimal policy is determined by the largest-index policy. There is an index for each given queue and one allocates the server to a queue with largest current index. Using discounted dynamic programming we give a new and short proof of this result and derive some characterizations and bounds of the indices. Moreover, it is shown that an approximate largest-index policy yields an approximately optimal policy. These results lead to efficient methods for computing the indices. In particular, we present a general largest-remaining-index method.
Optimal Control of Parallel Queues with Batch Service
Probability in the Engineering and Informational Sciences, 2002
We consider the problem of dynamic allocation of a single server with batch processing capability to a set of parallel queues+ Jobs from different classes cannot be processed together in the same batch+ The arrival processes are mutually independent Poisson flows with equal rates+ Batches have independent and identically distributed exponentially distributed service times, independent of the batch size and the arrival processes+ It is shown that for the case of infinite buffers, allocating the server to the longest queue, stochastically maximizes the aggregate throughput of the system+ For the case of equal-size finite buffers the same policy stochastically minimizes the loss of jobs due to buffer overflows+ Finally, for the case of unequalsize buffers, a threshold-type policy is identified through an extensive simulation study and shown to consistently outperform other conventional policies+ The good performance of the proposed threshold policy is confirmed in the heavy-traffic regime using a fluid model+
Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials
Communications in Computer and Information Science, 2016
Heterogeneous servers which can differ in service speed and reliability are becoming more popular in the modelling of modern communication systems. For a two-server queueing system with one nonreliable server and constant retrial discipline we formulate an optimal allocation problem for minimizing a long-run average cost per unit of time. Using a Markov decision process formulation we prove a number of monotone properties for the increments of the dynamic-programming value function. Such properties imply the optimality of a two-level threshold control policy. This policy prescribes the usage of a less productive server if the number of customers in the queue becomes higher than a predefined level which depends on the state of a non-reliable more powerful server. We provide also a heuristic solution for the optimal threshold levels in explicit form as a function of system parameters.
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Flow-control policies that balance server loads are well known for improving performance of queueing systems with multiple nodes. However, although load balancing benefits the system overall, it may negatively impact some of the queueing nodes. For example, it may reduce throughput rates or engender unfairness with respect to some performance measures. For queueing systems with multiple single-server nodes, we propose a set of constrained load-balancing policies that ensures the expected arrival rate to each queueing node is not reduced, and we show that such policies provide multiple benefits for each queueing node: stochastically fewer customers and lower variance of the number of customers at each queueing node. These results imply performance improvement as measured by multiple general objective functions, including but not limited to the expected number of customers at a queueing node, probability of having a high number of customers, variance of the number of customers, and ex...