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The shortest queue problem

  • Shlomo Halfin (a1)
Abstract

A Poisson stream of customers arrives at a service center which consists of two single-server queues in parallel. The service times of the customers are exponentially distributed, and both servers serve at the same rate. Arriving customers join the shortest of the two queues, with ties broken in any plausible manner. No jockeying between the queues is allowed. Employing linear programming techniques, we calculate bounds for the probability distribution of the number of customers in the system, and its expected value in equilibrium. The bounds are asymptotically tight in heavy traffic.

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Postal address: Bell Communications Research, Room 2L-379, Morris Research and Engineering Center, Morristown, NJ 07960, USA.
References
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Conolly, B. W. (1984) The autostrada queueing problem. J. Appl. Prob. 21, 394403.
Flatto, L. and Mckean, H. P. (1977) Two queues in parallel. Comm. Pure. Appl. Math. 30, 255263.
Haight, F. A. (1958) Two queues in parallel. Biometrika 45, 401410.
Kingman, J. F. C. (1961) Two similar queues in parallel. Ann. Math. Statist. 32, 13141323.
Smith, D. R. and Whitt, W. (1981) Resource sharing for efficiency in traffic systems. Bell System Tech. J. 60, 3955.
Wolff, R. W. (1977) An upper bound for multi-channel queues. J. Appl. Prob. 14, 884888.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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