Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T03:47:45.615Z Has data issue: false hasContentIssue false
  • English
  • Français

AN INDIVIDUAL AND SOCIALLY OPTIMAL POLICY MINIMIZING EXPECTED FLOW TIMES

Published online by Cambridge University Press:  02 March 2015

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA E-mail: smross@usc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider n servers having different exponential service distributions. All servers are initially busy and there are m customers waiting in queue in an ordered line. A server becoming idle is offered to the first in line, if rejected it is then offered to the second, and so on. The objective of each person in line is to minimize their expected time until service completion. We give a simple approach for finding the optimal policy and also show that this policy also minimizes the expected sum of the times the customers spend in the system.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 2 , April 2015 , pp. 147 - 151
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agrawala, A.K., Coffman, E.G., Garey, M.R. and Tripathi, S.K. (1984). A stochastic optimization algorithm minimizing expected flow times on uniform processors. IEEE Transactions on Computers C-33(4)CrossRefGoogle Scholar
Kumar, P.R. and Walrand, J. (1985). Individually optimal routing in parallel systems. Journal of Applied Probability 22(4): 989–995.CrossRefGoogle Scholar
Lu, H.P. and Viniotis, I. (2002). Threshold control policies for heterogeneous server systems. Mathematical Methods of Operations Research 55: 121–142.Google Scholar
Righter, R. and Xu, S. (1991). Scheduling jobs on nonidentical IFR processor to minimize general cost functions. Advances in Applied Probability 23: 909–924.CrossRefGoogle Scholar
Weber, R. (1993). On a conjecture about assigning jobs to processors of differing speeds. IEEE Transactions on Automatic Control 38(1): 166–170.CrossRefGoogle Scholar