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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Rojas-Nandayapa, L., Foss, S. & Kroese, D.P. Stability and performance of greedy server systems. Queueing Syst 68, 221–227 (2011). https://doi.org/10.1007/s11134-011-9235-0
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DOI: https://doi.org/10.1007/s11134-011-9235-0