Finding an optimal core on a tree network with M/G/c/c state-dependent queues

Mehrdad Moshtagh (), Jafar Fathali (), James MacGregor Smith () and Nezam Mahdavi-Amiri ()
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Mehrdad Moshtagh: Shahrood University of Technology
Jafar Fathali: Shahrood University of Technology
James MacGregor Smith: University of Massachusetts
Nezam Mahdavi-Amiri: Sharif University of Technology

Mathematical Methods of Operations Research, 2019, vol. 89, issue 1, No 4, 115-142

Abstract: Abstract We consider the stochastic queue core problem on a tree network. Our aim is to find an optimal path on a tree network subject to the average travel time of particles moving along the tree for service given by a server traversing along the optimal path. We assume that particles originating at a node on a tree network request their demands for service randomly and the server is modeled first by an M/M/1 and then by an M/G/1 queue using the FIFO discipline. We consider that all paths along which the particles travel are modeled with an M/G/c/c state-dependent queue with the particles being independent of each other having demands according to the Poisson distribution. Two algorithms are developed for computing the optimal path on a tree network along with the M/M/1 and the M/G/1 queues. The computational complexity of the algorithms and illustrative numerical results obtained by implementations of the algorithms in MATLAB software environment are given.

Keywords: Facility location; Core of a tree network; Stochastic queue core; M/G/c/c state-dependent queue; Queueing theory (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00186-018-0651-3

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