ON THE COMPARISON OF QUEUEING SYSTEMS WITH THEIR FLUID LIMITS

Eitan Altman · Tania Jiménez · Ger M. Koole

27 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

In this article, we study a method to compare queueing systems and their fluid limits. For a certain class of queueing systems, it is shown that the expected workload (and certain functions of the workload) is higher in the queueing system than in the fluid approximation. This class is characterized by convexity of the value function in the state component(s) where external arrivals occur. The main example that we consider is a tandem of multiserver queues with general service times and Markov-modulated arrivals. The analysis is based on dynamic programming and the use of phase-type distributions. Numerical examples to illustrate the results are also given.

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References

1985Applications of Queueing Theory 1977Queueing Systems, Vol. II: Computer Applications.1984Optimal control of a queueing system with two heterogeneous servers 1987Optimal control of service rates in networks of queues 1991Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations 1993Marked point processes as limits of Markovian arrival streams 1998Structural results for the control of queueing systems using event-based dynamic programming 1993Regularity of Stochastic Processes: A Theory Based on Directional Convexity

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