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Improved design of queueing simulation experiments with highly heteroscedastic responses

Improved design of queueing simulation experiments with highly heteroscedastic responses
Improved design of queueing simulation experiments with highly heteroscedastic responses
Simulation experiments for analysing the steady-state behaviour of queueing systems over a range of traffic intensities are considered, and a procedure is presented for improving their design. In such simulations the mean and variance of the response output can increase dramatically with traffic intensity; the design has to be able to cope with this complication. A regression metamodel of the likely mean response is used consisting of two factors, namely, a low-degree polynomial and a factor accounting for the exploding mean as the traffic intensity approaches its saturation. The best choice of traffic intensities at which to make simulation runs depends on the variability of the simulation output, and this variability is estimated using analytical heavy traffic results. The optimal numbers of customers simulated at each traffic intensity are built up using a multistage procedure. The asymptotic properties of the procedure are investigated theoretically. The procedure is shown to be robust and to be more efficient than more naive procedures. A result of note is that even when the range of interest includes high traffic intensities, the highest traffic load simulated should remain well away from its upper limit; but the number of customers simulated should be concentrated at the higher traffic intensities used. Empirical results are included for simulations of a single server queue with different priority rules and for a complicated queueing network. These results support the theoretical results, demonstrating that the proposed procedure can increase the accuracy of the estimated metamodel significantly compared with more naive methods.
queues, efficiency, optimal design of experiments with queues, simulation, simulation of nearly saturated queues
0030-364X
762-777
Cheng, Russell C.H.
a4296b4e-7693-4e5f-b3d5-27b617bb9d67
Kleijnen, Jack P.C.
ccf6daf6-ea64-4800-ab07-9565bf6839b3
Cheng, Russell C.H.
a4296b4e-7693-4e5f-b3d5-27b617bb9d67
Kleijnen, Jack P.C.
ccf6daf6-ea64-4800-ab07-9565bf6839b3

Cheng, Russell C.H. and Kleijnen, Jack P.C. (1999) Improved design of queueing simulation experiments with highly heteroscedastic responses. Operations Research, 47 (5), 762-777.

Record type: Article

Abstract

Simulation experiments for analysing the steady-state behaviour of queueing systems over a range of traffic intensities are considered, and a procedure is presented for improving their design. In such simulations the mean and variance of the response output can increase dramatically with traffic intensity; the design has to be able to cope with this complication. A regression metamodel of the likely mean response is used consisting of two factors, namely, a low-degree polynomial and a factor accounting for the exploding mean as the traffic intensity approaches its saturation. The best choice of traffic intensities at which to make simulation runs depends on the variability of the simulation output, and this variability is estimated using analytical heavy traffic results. The optimal numbers of customers simulated at each traffic intensity are built up using a multistage procedure. The asymptotic properties of the procedure are investigated theoretically. The procedure is shown to be robust and to be more efficient than more naive procedures. A result of note is that even when the range of interest includes high traffic intensities, the highest traffic load simulated should remain well away from its upper limit; but the number of customers simulated should be concentrated at the higher traffic intensities used. Empirical results are included for simulations of a single server queue with different priority rules and for a complicated queueing network. These results support the theoretical results, demonstrating that the proposed procedure can increase the accuracy of the estimated metamodel significantly compared with more naive methods.

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More information

Published date: 1999
Keywords: queues, efficiency, optimal design of experiments with queues, simulation, simulation of nearly saturated queues
Organisations: Operational Research

Identifiers

Local EPrints ID: 29713
URI: http://eprints.soton.ac.uk/id/eprint/29713
ISSN: 0030-364X
PURE UUID: 610f31fc-9f76-4c83-8255-a5b5ffd9b453

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Date deposited: 03 May 2007
Last modified: 15 Jul 2019 19:08

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Contributors

Author: Jack P.C. Kleijnen

University divisions

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