Optimal Design of Multi-server Markovian Queues with Polynomial Waiting and Service Costs

Publication Type

Journal Article

Publication Date

7-2014

Abstract

This paper is concerned with the optimal design of queueing systems. The main decisions in the design of such systems are the number of servers, the appropriate control to have on the arrival rates, and the appropriate service rate these servers should possess. In the formulation of the objective function to this problem, most publications use only linear cost rates. The linear rates, especially for the waiting cost, do not accurately reflect reality. Although there are papers involving nonlinear cost functions, no paper has ever considered using polynomial cost functions of degree higher than two. This is because simple formulas for computing the higher moments are not available in the literature. This paper is an attempt to fill this gap in the literature. Thus, the main contributions of our work are as follows: (i) the derivation of a very simple formula for the higher moments of the waiting time for the M/M/s queueing system, which requires only the knowledge of the expected waiting time; (ii) proving their convexity with respect to the design variables; and (iii) modeling and solving more realistic design problems involving general polynomial cost functions.We also focus on simultaneous optimization of the staffing level, arrival rate and service rate.

Keywords

M/M/s queues, higher moments of waiting time, convexity, design and optimization

Discipline

Operations and Supply Chain Management | Operations Research, Systems Engineering and Industrial Engineering

Research Areas

Operations Management

Publication

Applied Stochastic Models in Business and Industry

Volume

30

Issue

4

First Page

429

Last Page

443

ISSN

1526-4025

Identifier

10.1002/asmb.1983

Publisher

Wiley

Additional URL

https://doi.org/10.1002/asmb.1983

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