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A continuous polling system with general service times. (English) Zbl 0772.60075
When not busy, a single server moves at constant speed in the same direction on a circle. Customers arrive according to a constant-rate Poisson process and drop independently and uniformly on to the circle. The server stops to serve a customer whenever he encounters one. Service times are i.i.d. random variables with general distribution. When a service has been completed the server continues his journey and the customer departs. For every \(t\), the locations of customers that are waiting for service and the positions of clients that have been served during the last tour of the server are represented as random counting measures. These measures are shown to converge in distribution as \(t\to\infty\). A recursive expression for the Laplace functionals of the limiting random measures is found from which the corresponding \(k\)-th moment measures can be derived.

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G57 Random measures
60H05 Stochastic integrals
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