We consider a service system with two Poisson arrival queues. There is a single server that chooses which queue to serve at each moment. Once a queue is served, all the customers are served within a fixed time. This model is useful in studying airport
shuttling or certain online computing systems. In this thesis, we first establish a Markov.
Decision Process (MDP) model for this problem and study its structures. We then
propose a simple yet optimal state-independent policy for this problem which is not
only easy to implement, but also performs very well. If the service time of both queues
equals to one unit of time, we prove that the optimal state-independent policy has
the following structure: serve the queue with the smaller arrival rate once followed
by serving the other queue k times, and we obtain an explicit formula to capture k.
We conduct numerical tests for our policy and it performs very well. We also extend
our discussions to a more general case in which the service time of the queues can be
any integer. We also obtain the optimal the optimal state-independent policies in that
University of Minnesota M.S. thesis. May 2013. Major: Industrial and Systems Engineering. Advisor: Zizhuo Wang. 1 computer file (PDF); v, 37 pages.
Optimal serving schedules for multiple queues with size-independent service times.
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