Locating a Mobile Server Queueing Facility on a Tree Network

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Abstract
This paper extends recent work on finding the stochastic queue median (SQM) on a network. The SQM is the optimal location of a single mobile server, when idle, who travels to customers in response to requests for service. Customer demands are limited to the nodes of the network and their requests for service arrive according to a time homogeneous Poisson process, independently from each node. When a service request finds the server busy with a previous customer, it is entered into an M/G/1 queue that is depleted in a first-in, first-out (FIFO) manner. The SQM is the point on the network at which the sum of mean queueing delay and mean travel time is minimized. In this paper the transportation network is restricted to be a tree. By discovering and exploiting convex properties of the objective function and related functions, an efficient finite-step algorithm is found for locating the SQM on a tree.

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