A continuous polling system with general service times


Kroese, Dirk P. and Schmidt, Volker (1992) A continuous polling system with general service times. Annals of applied probability, 2 (4). pp. 906-927. ISSN 1050-5164

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Abstract:Consider a ring on which a server travels at constant speed. Customers arrive on the ring according to a Poisson process, at locations independently and uniformly distributed over the circle. Whenever the server encounters a customer, he stops and serves the client according to a general service time distribution. After the service is completed, the server removes the customer from the ring and resumes his round. The model is analyzed by means of point processes and regenerative processes in combination with some stochastic integration theory. This approach clarifies the analysis of the continuous polling model and provides the means for further generalizations. For every time $t$, 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 by random counting measures. These measures converge in distribution as $t \rightarrow \infty$. 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.
Item Type:Article
Additional information:Open Access
Copyright:© 1992 Institute of Mathematical Statistics
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/70358
Official URL:https://doi.org/10.1214/aoap/1177005580
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