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Characterization of the Stochastic Median Queue Trajectory in a Plane with Generalized Distances

Author

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  • Margaret L. Brandeau

    (Stanford University, Stanford, California)

Abstract

We characterize the trajectory of the Stochastic Queue Median (SQM) location problem in a planar region with discrete demands and a general L p travel metric (1 p s *∣ε and s 2*∣ε, respectively); all optimal locations can be characterized by a simple ratio condition relating the derivatives of the first and second moments of service time; and the trajectory as a function of the customer call rate moves monotonically along a path from s *∣ε toward s 2*∣ε, then turns and retraces the same path back to s *∣ε. Finally, we establish convergence of the ε-optimal solution to an optimal SQM solution as ε approaches zero, as well as a general condition under which we can solve the SQM problem directly, with no perturbation.

Suggested Citation

  • Margaret L. Brandeau, 1992. "Characterization of the Stochastic Median Queue Trajectory in a Plane with Generalized Distances," Operations Research, INFORMS, vol. 40(2), pages 331-341, April.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:2:p:331-341
    DOI: 10.1287/opre.40.2.331
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    Cited by:

    1. Gregory Dobson & Euthemia Stavrulaki, 2007. "Simultaneous price, location, and capacity decisions on a line of time‐sensitive customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 1-10, February.

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