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The shortest queue problem

  • Shlomo Halfin (a1)

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.

Corresponding author
Postal address: Bell Communications Research, Room 2L-379, Morris Research and Engineering Center, Morristown, NJ 07960, USA.
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Smith, D. R. and Whitt, W. (1981) Resource sharing for efficiency in traffic systems. Bell System Tech. J. 60, 3955.
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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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