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

Margaret L. Brandeau
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Margaret L. Brandeau: Stanford University, Stanford, California

Operations Research, 1992, vol. 40, issue 2, 331-341

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.

Keywords: facilities/equipment planning; location: continuous; stochastic (search for similar items in EconPapers)
Date: 1992
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