Server assignment policies for maximizing the steady-state throughput of finite queueing systems

For a system of finite queues, we study how servers should be assigned dynamically to stations in order to obtain optimal (or near-optimal) long-run average throughput. We assume that travel times between different service facilities are negligible, that each server can work on only one job at a time, and that several servers can work together on one job. We show that when the service rates depend only on either the server or the station (and not both), then all nonidling server assignment policies are optimal. Moreover, for a Markovian system with two stations in tandem and two servers, we show that the optimal policy assigns one server to each station unless that station is blocked or starved (in which case the server helps at the other station), and we specify the criterion used for assigning servers to stations. Finally, we propose a simple server assignment policy for tandem systems in which the number of stations equals the number of servers, and we present numerical results that show that our policy appears to yield near-optimal throughput under general conditions.