Queueing systems on a circle View Full Text


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Article Info

DATE

1993-10

AUTHORS

Dirk P. Kroese, Volker Schmidt

ABSTRACT

Consider a ring on which customers arrive according to a Poisson process. Arriving customers drop somewhere on the circle and wait there for a server who travels on the ring. Whenever this server encounters a customer, he stops and serves the customer according to an arbitrary service time distribution. After the service is completed, the server removes the client from the circle and resumes his journey. We are interested in the number and the locations of customers that are waiting for service. These locations are modeled as random counting measures on the circle. Two different types of servers are considered: The polling server and the Brownian (or drunken) server. It is shown that under both server motions the system is stable if the traffic intensity is less than 1. Furthermore, several earlier results on the configuration of waiting customers are extended, by combining results from random measure theory, stochastic integration and renewal theory. More... »

PAGES

303-331

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01415999

DOI

http://dx.doi.org/10.1007/bf01415999

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033733488


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