POLLING, GREEDY AND HORIZON SERVERS ON A CIRCLE

Service in a loop-based polling system consists of a single server mov ing around a closed tour, stopping to perform services wherever reques ts are encountered. There are N stations (unit buffer queues) spaced o ne unit of distance apart, and the server moves at a unit speed. All q ueues are identical, and the service time is deterministic. We compare the two well known cyclic polling and greedy servers with a new contr ol policy called the horizon server. The cyclic polling server moves i n one direction, even ii no requests are waiting, and stops whenever i t encounters a request. The greedy server selects the nearest request for its next service. At any station the greedy server can reverse its direction ii a new request arrives nearby, and if no requests are wai ting the greedy server does not move. The horizon server, with paramet er d, ignores all requests for service from a distance farther than d. Within its horizon (less than or equal to d) it acts like the greedy server. Analytical solutions for N = 2 and 3 and numerical results for N less than or equal to 6 show that the horizon server, with the opti mum value of d, outperforms the polling and the greedy servers.