Stability and performance of greedy server systems

Stability and performance of greedy server systems

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Article ID: iaor20119067
Volume: 68
Issue: 3
Start Page Number: 221
End Page Number: 227
Publication Date: Aug 2011
Journal: Queueing Systems
Authors: , ,
Keywords: greedy algorithms, polling systems
Abstract:

Consider a queueing system in which arriving customers are placed on a circle and wait for service. A traveling server moves at constant speed on the circle, stopping at the location of the customers until service completion. The server is greedy: always moving in the direction of the nearest customer. Coffman and Gilbert conjectured that this system is stable if the traffic intensity is smaller than 1; however, a proof or counterexample remains unknown. In this review, we present a picture of the current state of this conjecture and suggest new related open problems.

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