S. Andradottir et al., Server assignment policies for maximizing the steady-state throughput of finite queueing systems, MANAG SCI, 47(10), 2001, pp. 1421-1439
For a system of finite queues, we study how servers should be assigned dyna
mically to station's in order to obtain optimal (or near-optimal) long-run
average throughput. We assume that travel times between different service f
acilities are negligible, that each server can work on only one job at a ti
me, and that several servers can work together on one job. We show that whe
n the service rates depend only on either the server or the station (and no
t both), then all nonidling server assignment policies are optimal. Moreove
r, for a Markovian system with two stations in tandem and two servers, we s
how 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 statio
ns. Finally, we propose a simple server assignment policy for tandem system
s in which the number of stations equals the number of servers, and we pres
ent numerical results that show that our policy appears to yield near-optim
al throughput under general conditions.