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Polling and greedy servers on a line. (English) Zbl 0653.90021
A single server moves with speed $\nu$ on a line interval (or a circle) of length (circumference) L. Customers, requiring service of constant duration b, arrive on the interval (or circle) at random at mean rate $\lambda$ customers per unit length per unit time. A customer’s mean wait for service depends partly on the rules governing the server’s motion. We compare two different servers; the polling server and the greedy server. Without knowing the locations of waiting customers, a polling server scans endlessly back and forth across the interval (or clockwise around the circle), stopping only where it encounters a waiting customer. Knowing where customers are waiting, a greedy server always travels toward the current nearest one. Except for certain extreme values of $\nu$, L, b, and $\lambda$, the polling and greedy servers are roughly equally effective. Indeed, the simpler polling server is often the better. Theoretical results show, in most cases, that the polling server has a high probability of moving toward the nearest customer, i.e. moving as a greedy server would. The greedy server is difficult to analyze, but was simulated on a computer.
##### MSC:
 90B22 Queues and service (optimization)
##### References:
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