4 research outputs found
Stability of the Greedy Algorithm on the Circle
We consider a single-server system with service stations in each point of the
circle. Customers arrive after exponential times at uniformly-distributed
locations. The server moves at finite speed and adopts a greedy routing
mechanism. It was conjectured by Coffman and Gilbert in~1987 that the service
rate exceeding the arrival rate is a sufficient condition for the system to be
positive recurrent, for any value of the speed. In this paper we show that the
conjecture holds true
Stability and performance of greedy server systems: A review and open problems
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