Simulation Estimation of Dynamic Properties in Queueing Systems

Kimmo E. E. Raatikainen: Simulation Estimation of Dynamic Properties in Queueing Systems. Report C-1993-35, Department of Computer Science, University of Helsinki, July 1993. 7 pages. <http://www.cs.helsinki.fi/TR/C-1993/35>

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Abstract

In simulation studies the focus has traditionally been on time-independent characteristics of queueing systems, particularly on the steady-state mean. The systems, even if they are in stochastic equilibrium, have also time-dependent or dynamic properties which are of great practical importance. Typically, the dynamic properties are related to the variation of traffic or load during some period of time.

In this paper we propose a way to examine dynamic properties of queueing systems through simulation. Our approach is based on the following idea: The original traffic rates are classified into low and heavy values. The resulting binary sequence of indicators characterize the traffic level of the system. The variation in the traffic level is summarized through estimating the two histograms of level durations. The rationale of translating the problem into simultaneous estimation of two histograms is that the estimates for the cell proportions are based on cumulative statistics. Therefore, we can use the Bonferroni inequality and the existing methods for assessing the precisions of estimated proportions.

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I.6.6

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Additional Key Words and Phrases: dynamic properties of queueing models, simulation estimation of proportions, simultaneous assessment of precisions