Fitting correlated arrival and service times and related queueing performance

Peter Buchholz () and Jan Kriege ()
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Peter Buchholz: TU Dortmund
Jan Kriege: TU Dortmund

Queueing Systems: Theory and Applications, 2017, vol. 85, issue 3, No 6, 337-359

Abstract: Abstract In this paper, we consider a queue where the inter-arrival times are correlated and, additionally, service times are also correlated with inter-arrival times. We show that the resulting model can be interpreted as an MMAP[K]/PH[K]/1 queue for which matrix geometric solution algorithms are available. The major result of this paper is the presentation of approaches to fit the parameters of the model, namely the MMAP, the PH distribution and the parameters introducing correlation between inter-arrival and service times, according to some trace of inter-arrival and corresponding service times. Two different algorithms are presented. The first algorithm is based on available methods to compute a MAP from the inter-arrival times and a PH distribution from the service times. Afterward, the correlation between inter-arrival and service times is integrated by solving a quadratic programming problem over some joint moments. The second algorithm is of the expectation maximization type and computes all parameters of the MAP and the PH distribution in an iterative way. It is shown that both algorithms yield sufficiently accurate results with an acceptable effort.

Keywords: Markovian arrival process; Marked Markovian arrival processes; Phase type distributions; Multi-class queues; Expectation maximization algorithm; 65C40; 60K20; 68M20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s11134-017-9514-5

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