A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem

Authors:
Paul Dupuis;Kavita Ramanan
Affiliations:
Division of Applied Mathematics, 182 George St, Brown University, Providence, RI 02912, USA E-mail: dupuis@cfm.brown.edu;Bell Laboratories, Room 2C-319, 600 Mountain Avenue, Murray Hill, NJ 07974, USA E-mail: kavita@research.bell-labs.com
Venue:
Queueing Systems: Theory and Applications
Year:
2000

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Abstract

We consider a four-class two-station network with feedback, with fluid inputs and a head-of-the-line generalized processor sharing discipline at each station. We derive the Skorokhod Problem associated with the network and obtain algebraic sufficient conditions for Lipschitz continuity of the associated Skorokhod Map. This provides the first example of a multiclass network with feedback for which the associated Skorokhod Problem has been proved to be regular. As an elementary application, we show that under the conditions which guarantee Lipschitz continuity the network is stable if and only if the usual load conditions apply.