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Markov MECO: A simple Markovian model for approximating nonrenewal arrival processes. (English) Zbl 0930.60082

Summary: This paper introduces a special case of the Markovian arrival process that can easily be used to approximate both the interarrival-time distribution and the autocorrelation function of an arrival process. This model is labeled a Markov MECO (Mixture of Erlangs of Common Order). The proposed interarrival-time approximation matches the first three moments of the interarrival time. The Markov MECO autocorrelation function is geometric and determined by a single parameter, once the interarrival-time distribution is fixed. Closed-form expressions are given for matching either the lag-one autocorrelation or the asymptotic index of dispersion for intervals. By applying the resulting arrival-process approximations to a single-server queue with exponential service times, the approximations are empirically evaluated on the basis of the associated error in the steady-state mean number in the system. In these experiments, the original arrival processes are superpositions of independent renewal processes. The numerical results show that the nonrenewal approximations outperform the corresponding renewal approximation that simply ignores autocorrelation, and in some cases, the improvement is an order of magnitude.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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