A Markovian canonical form of second-order matrix-exponential processes

L. Bodrog, A. Heindl, G. Horváth and M. Telek

European Journal of Operational Research, 2008, vol. 190, issue 2, 459-477

Abstract: Besides the fact that - by definition - matrix-exponential processes (MEPs) are more general than Markovian arrival processes (MAPs), only very little is known about the precise relationship of these processes in matrix notation. For the first time, this paper proves the persistent conjecture that - in two dimensions - the respective sets, MAP(2) and MEP(2), are indeed identical with respect to the stationary behavior. Furthermore, this equivalence extends to acyclic MAPs, i.e., AMAP(2), so that AMAP(2)[reverse not equivalent]MAP(2)[reverse not equivalent]MEP(2). For higher orders, these equivalences do not hold. The second-order equivalence is established via a novel canonical form for the (correlated) processes. An explicit moment/correlation-matching procedure to construct the canonical form from the first three moments of the interarrival time distribution and the lag-1 correlation coefficient shows how these compact processes may conveniently serve as input models for arrival/service processes in applications.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:190:y:2008:i:2:p:459-477

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