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February 1996 Stability of polling systems with exhaustive service policies and state-dependent routing
Serguei Foss, Günter Last
Ann. Appl. Probab. 6(1): 116-137 (February 1996). DOI: 10.1214/aoap/1034968068


We consider a polling system with a finite number of stations fed by compound Poisson arrival streams of customers asking for service. A server travels through the system and upon arrival at a station the server serves all waiting customers until the queue is empty, where the service time distribution depends on the station. The choice of the station to be visited next as well as the corresponding walking time may depend on the whole current state. Examples are systems with a greedy-type routing mechanism. Under appropriate independence assumptions it is proved that the system is stable if and only if the workload is less than 1.


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Serguei Foss. Günter Last. "Stability of polling systems with exhaustive service policies and state-dependent routing." Ann. Appl. Probab. 6 (1) 116 - 137, February 1996.


Published: February 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0863.60091
MathSciNet: MR1389834
Digital Object Identifier: 10.1214/aoap/1034968068

Primary: 60K25
Secondary: 60J27

Keywords: Ergodicity of Markov chains , Greedy server , Polling system , stability

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 1 • February 1996
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