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Heuristic Solution for the Optimal Thresholds in a Controllable Multi-server Heterogeneous Queueing System Without Preemption

Part of the Communications in Computer and Information Science book series (CCIS,volume 601)


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.


  • Controllable queueing system
  • Heterogeneous servers
  • Long-run average cost
  • Threshold policy
  • Optimal allocation

D. Efrosinin—This work was funded by the Russian Foundation for Basic Research (RFBR), Project No 15-08-08677-a.

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Correspondence to Dmitry Efrosinin .

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Efrosinin, D., Rykov, V. (2016). Heuristic Solution for the Optimal Thresholds in a Controllable Multi-server Heterogeneous Queueing System Without Preemption. In: Vishnevsky, V., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2015. Communications in Computer and Information Science, vol 601. Springer, Cham.

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