Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
On Job Assignment for a Parallel System of Processor Sharing Queues
IEEE Transactions on Computers
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Time-shared Systems: a theoretical treatment
Journal of the ACM (JACM)
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
On choosing a task assignment policy for a distributed server system
Journal of Parallel and Distributed Computing - Special issue on software support for distributed computing
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Optimal state-free, size-aware dispatching for heterogeneous M/G/-type systems
Performance Evaluation - Performance 2005
Analysis of join-the-shortest-queue routing for web server farms
Performance Evaluation
Dynamic Programming
Dispatching problem with fixed size jobs and processor sharing discipline
Proceedings of the 23rd International Teletraffic Congress
The price of anarchy in an exponential multi-server
Operations Research Letters
Markov decision algorithms for dynamic routing [telephone networks]
IEEE Communications Magazine
Minimizing slowdown in heterogeneous size-aware dispatching systems
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Lookahead actions in dispatching to parallel queues
Performance Evaluation
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We consider a distributed server system in which heterogeneous servers operate under the processor sharing (PS) discipline. Exponentially distributed jobs arrive to a dispatcher, which assigns each task to one of the servers. In the so-called size-aware system, the dispatcher is assumed to know the remaining service requirements of some or all of the existing jobs in each server. The aim is to minimize the mean sojourn time, i.e., the mean response time. To this end, we first analyze an M/M/1-PS queue in the framework of Markov decision processes, and derive the so-called size-aware relative value of state, which sums up the deviation from the average rate at which sojourn times are accumulated in the infinite time horizon. This task turns out to be non-trivial. The exact analysis yields an infinite system of first order differential equations, for which an explicit solution is derived. The relative values are then utilized to develop efficient dispatching policies by means of the first policy iteration (FPI). Numerically, we show that for the exponentially distributed job sizes the myopic approach, ignoring the future arrivals, yields an efficient and robust policy when compared to other heuristics. However, in the case of highly asymmetric service rates, an FPI based policy outperforms it. Additionally, the size-aware relative value of an M/G/1-PS queue is shown to be sensitive with respect to the form of job size distribution, and indeed, the numerical experiments with constant job sizes confirm that the optimal decision depends on the job size distribution.