Get access

Optimal design of multi-server Markovian queues with polynomial waiting and service costs

Authors

  • Mahmut Parlar,

    1. DeGroote School of Business, McMaster University, Hamilton, Ontario L8S 4M4, Canada
    Search for more papers by this author
  • Moosa Sharafali

    Corresponding author
    1. Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Road, Singapore 178899
    • Correspondence to: Moosa Sharafali, Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Road, Singapore 178899.

      E-mail: sharafalim@smu.edu.sg

    Search for more papers by this author

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. Copyright © 2013 John Wiley & Sons, Ltd.

Get access to the full text of this article

Ancillary