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Stability of spatial queueing systems

Part of: Operations research and management science Stochastic processes Special processes

Published online by Cambridge University Press:  01 July 2016

C. Bordenave
C. Bordenave*
Affiliation:
Ecole Normale Supérieure and INRIA
*
∗ Postal address: DI/TREC, Ecole Normale Supérieure, 45 rue d'Ulm, F-75230 Paris Cedex 05, France. Email address: [email protected]
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Abstract

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In this paper, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at points in space and the server stations have space-dependent processing rates. The workload is seen as a Radon measure and the server stations can adapt their power allocation to the current workload. We derive the stability region of the queueing system in the usual stationary ergodic framework. The analysis of this stability region gives some counter-intuitive results. Some specific subclasses of policy are also studied. Wireless communications networks is a natural field of application for the model.

Keywords

Stability regionspace-time point processwireless networkdynamic schedulingoptimal resource allocation

MSC classification

Primary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B15: Network models, stochastic
Secondary: 60G55: Point processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 2 , June 2006 , pp. 487 - 504
Copyright
Copyright © Applied Probability Trust 2006 

Footnotes

Presented at the ICMS Workshop on Spatial Stochastic Modelling with Applications to Communications Networks (Edinburgh, June 2004).

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