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Two new heuristics for the \(GI/G/n/0\) queueing loss system with examples based on the two-phase coxian distribution. (English) Zbl 1171.90366

Summary: We introduce a new heuristic approach for the numerical analysis of queueing systems. In particular, we study the general, multi-server queueing loss system, the \(GI/G/n/0\) queue, with an emphasis on the calculation of steady-state loss probabilities. Two new heuristics are developed, called the GM Heuristic and the MG Heuristic, both of which make use of an exact analysis of the corresponding single-server \(GI/G/1/0\) queue. The GM Heuristic also uses an exact analysis of the \(GI/M/n/0\) queue, while the MG Heuristic uses an exact analysis of the \(M/G/n/0\) queue. Experimental results are based on the use of two-phase Coxian distributions for both the inter-arrival time and the service time; these include an error analysis for each heuristic and the derivation of experimental probability bounds for the loss probability. For the class of problems studied, it is concluded that there are likely to be many situations where the accuracy of the GM Heuristic is adequate for practical purposes. Methods are also developed for combining the GM and MG Heuristics. In some cases, this leads to approximations that are significantly more accurate than those obtained by the individual heuristics.

MSC:

90B22 Queues and service in operations research
90C59 Approximation methods and heuristics in mathematical programming
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