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Heuristic solution for the optimal thresholds in a controllable multi-server heterogeneous queueing system without preemption. (English) Zbl 1390.90209

Vishnevsky, Vladimir (ed.) et al., Distributed computer and communication networks. 18th international conference, DCCN 2015, Moscow, Russia, October 19–22, 2015. Revised selected papers. Cham: Springer (ISBN 978-3-319-30842-5/pbk; 978-3-319-30843-2/ebook). Communications in Computer and Information Science 601, 238-252 (2016).
Summary: As it known the optimal policy which minimizes the long-run average cost per unit of time in a multi-server queueing system with heterogeneous servers without preemption has a threshold structure. It means that the slower server must be activated whenever all faster servers are busy and the number of customers in the queue exceeds some specified for this server threshold level. The optimal thresholds can be evaluated using the Howard iteration algorithm or by minimizing the function of the average cost which can be obtained in closed form as a function of unknown threshold levels. The both cases have sufficient restrictions on dimensionality of the model. In present paper we provide a heuristic method to derive expressions for the optimal threshold levels in explicit form as functions of system parameters like service intensities, usage and holding costs for an arbitrary number of servers. The proposed method is based on the fitting of the boundary planes between the areas where the optimal threshold takes a certain value.
For the entire collection see [Zbl 1377.68015].

MSC:

90B22 Queues and service in operations research
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