Skip to main content

Optimality of the shortest line discipline

  • Wayne Winston (a1)

We consider a queuing system consisting of a finite number of identical exponential servers. Each server has its own queue, and upon arrival each customer must be assigned to some server's queue. Under the assumption that no jockeying between queues is permitted, it is shown that the intuitively satisfying rule of assigning each arrival to the shortest line maximizes, with respect to stochastic order, the discounted number of customers to complete their service in any time t.

Hide All
Bessler, S. and Veinott, A. Jr. (1966) Optimal policy for a dynamic multi-echelon inventory model. Naval Logist. Res. Quart. 13, 355389.
Howard, R. (1960) Dynamic Programming and Markov Processes. M.I.T. Press, Cambridge, Mass.
Lippman, S. A. (1975) Applying a new technique in the optimization of exponential queuing systems. Operat. Res. 23, 687710.
Miller, B. (1968) Finite state continuous time Markov decision processes with an infinite planning horizon. SIAM J. Control. 6, 266380.
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden–Day, San Francisco.
Stidham, S. Jr. (1970) On the optimality of single server queuing systems. Operat. Res. 18, 708732.
Whitt, W. (1975) Continuity of Markov processes and dynamic programs. Technical Report, Yale University, New Haven.
Yu, O. (1974) Stochastic bounds for heterogeneous-server queues with Erlang service times. J. Appl. Prob. 11, 785796.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed