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Streams of events and performance of queuing systems: The basic anatomy of arrival/departure processes, when focus is set on autocorrelation

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Judging from the vast number of articles in the field of queuing simulation, that assumes i.i.d. in one or more of the stochastic processes used to model the situation at hand, often without much validation, it seems that sequence independence must be a very basic property of many real life situation or at least a very sound approximation. However, on the other hand, most actual decision making is based upon information taken from the past - where else! In fact the only real alternative that comes into my mind is to let a pair of dices fully and completely rule behaviour, but I wonder if such a decision setup is that widespread in consequent use anywhere. So, how come that sequence independence is so relatively popular in describing real system processes? I can only think of three possible explanations to this dilemma - (1) either sequence dependence is present, but is mostly not of a very significant nature or (2) aggregate system behaviour is in general very different from just the summing-up (even for finite sets of micro-behavioural patterns) and/or (3) it is simply a wrong assumption that in many cases is chosen by mere convention or plain convenience. It is evident that before choosing some arrival processes for some simulation study a thorough preliminary analysis has to be undertaken in order to uncover the basic time series nature of the interacting processes. Flexible methods for generating streams of autocorrelated variates of any desired distributional type, such as the ARTA method or some autocorrelation extended descriptive sampling method, can then easily be applied. The results from the Livny, Melamed and Tsiolis (1993) study as well as the results from this work both indicates that system performance measures as for instance average waiting time or average time in system are significantly influenced by the taken i.i.d. versus the autocorrelations assumptions. Plus/minus 35% in performance, but most likely a worsening, is easily observed, when comparing even moderate (probably more realistic) autocorrelation assumptions with the traditionally and commonly used i.i.d. assumptions.

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  • Nielsen, Erland Hejn, 2004. "Streams of events and performance of queuing systems: The basic anatomy of arrival/departure processes, when focus is set on autocorrelation," CORAL Working Papers L-2004-02, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbls:2004-002
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    1. Miron Livny & Benjamin Melamed & Athanassios K. Tsiolis, 1993. "The Impact of Autocorrelation on Queuing Systems," Management Science, INFORMS, vol. 39(3), pages 322-339, March.
    2. Marne C. Cario & Barry L. Nelson, 1998. "Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Processes," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 72-81, February.
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    1. Kjeldsen, Karina Hjortshøj, 2008. "Classification of routing and scheduling problems in liner shipping," CORAL Working Papers L-2008-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.

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