Polling, Greedy and Horizon Servers on a Circle

Service in a loop-based polling system consists of a single server moving around a closed tour, stopping to perform services wherever requests are encountered. There are N stations (unit buffer queues) spaced one unit of distance apart, and the server moves at a unit speed. All queues are identical, and the service time is deterministic. We compare the two well known cyclic polling and greedy servers with a new control policy called the horizon server. The cyclic polling server moves in one direction, even if no requests are waiting, and stops whenever it encounters a request. The greedy server selects the nearest request for its next service. At any station the greedy server can reverse its direction if a new request arrives nearby, and if no requests are waiting the greedy server does not move. The horizon server, with parameter d, ignores all requests for service from a distance farther than d,. Within its horizon (≤ d) it acts like the greedy server. Analytical solutions for N = 2 and 3 and numerical results for N≤ 6 show that the horizon server, with the optimum value of d, outperforms the polling and the greedy servers.