Simultaneous buffer and service rate allocation in open finite queueing networks

James MacGregor Smith

IISE Transactions, 2018, vol. 50, issue 3, 203-216

Abstract: Simultaneous buffer and service rate allocation in open finite queueing networks is a nonlinear mixed-integer programming problem that is NP${\cal NP}$-Hard. A queueing network decomposition methodology is coupled with a nonlinear sequential quadratic programming algorithm to compute the simultaneous optimal buffer allocations and service rates via a branch-and-bound scheme for various network topologies. It is shown that the optimization problem is a nonlinear convex programming problem, which assists in the search for local optimal solutions. The material handling or transportation system for transferring the finite customer population between the nodes in the network is also included. Extensive numerical results demonstrate the efficacy of the methodology for series, split, and merge topology networks. Examination of the persistence or absence of the allocation patterns of the service rates and buffers is one of the focal points of this work.

Date: 2018
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DOI: 10.1080/24725854.2017.1300359

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