Using discrete event simulation to fit probability distributions for autocorrelated service times

Abstract

In the literature, it has been shown that autocorrelation in service times has a dramatic impact on performance measures in delay systems. Although some studies deal with systems having autocorrelated service times, a general renewal approximation methodology that can incorporate this information in analytical models has not been previously proposed. In this paper, we develop a discrete event simulation based analytical method to fit approximating distributions to capture the characteristics of autocorrelated service times. Our observations indicate that a single approximating service time distribution fails to accurately predict the behaviour of the delay system. Therefore, we include the server utilization information in the developed method, which, in turn, provides a family of approximating service times. Testing our approximation both in predicting the mean delay and the system size distribution of the original systems with autocorrelated service times show that it can be highly accurate.

Keywords:

• Autocorrelation
• index of dispersion
• mean waiting time
• queueing
• make-to-stock queues

Acknowledgements

The authors thank the anonymous referee and the editor for their invaluable suggestions to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada [Grant number 458081].