Optimal Routing in Two Parallel Queues with Exponential Service Times
Discrete Event Dynamic Systems
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In this paper, we address the problem of routing a stream of customers in two parallel networks of queues in tandem with deterministic service times in order to minimize the average response time. We show that the optimal routing is a Sturmian word which density depends on maximum service time on each route. In order to do this, we particularly study the output process of deterministic queues when the input process is Sturmian.