Stability and performance of greedy server systems

Authors:
Leonardo Rojas-Nandayapa;Sergey Foss;Dirk P. Kroese
Affiliations:
Department of Mathematics, The University of Queensland, Brisbane, Australia;School of Mathematics and Computer Sciences, Heriot-Watt University, Edinburgh, UK;Department of Mathematics, The University of Queensland, Brisbane, Australia
Venue:
Queueing Systems: Theory and Applications
Year:
2011

Citing 8
Cited 4

Analysis of polling systems

Analysis of polling systems
Polling and greedy servers on a line

Queueing Systems: Theory and Applications
Stochastic and dynamic vehicle routing in the Euclidean plane with multiple capacitated vehicles

Operations Research
Light-traffic analysis for queues with spatially distributed arrivals

Mathematics of Operations Research
Queueing analysis of polling models: progress in 1990-1994

Frontiers in queueing
The Snowblower Problem

Queueing Systems: Theory and Applications
From Polling to Snowplowing

Queueing Systems: Theory and Applications
Polling on a space with general arrival and service time distribution

Operations Research Letters

On the greedy walk problem

Queueing Systems: Theory and Applications
Controlled mobility in stochastic and dynamic wireless networks

Queueing Systems: Theory and Applications
Greedy servers on a torus

Proceedings of the Winter Simulation Conference
On ergodicity conditions in a polling model with Markov modulated input and state-dependent routing

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

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.