Summary: Scheduling parallel servers in the non-degenerate slowdown
diffusion regime: Asymptotic optimality results
November 21, 2011
We consider the problem of minimizing queue-length costs in a system with heterogenous
parallel servers, operating in a many-server heavy-traffic regime with non-degenerate slowdown.
This regime is distinct from the well-studied heavy traffic diffusion regimes, namely the (single
server) conventional regime and the (many-server) Halfin-Whitt regime. It has the distinguishing
property that waiting times and service times are of comparable magnitudes. We establish an
asymptotic lower bound on the cost and devise a sequence of policies that asymptotically attain
this bound. As in the conventional regime, the asymptotics can be described by means of a
Brownian control problem, the solution of which exhibits a state space collapse.
AMS subject classifications: 60K25, 60J60, 60F17, 90B22, 68M20
Keywords: The parallel server model, many-server queues, heavy traffic, diffusion limits,
asymptotically optimal control, non-degenerate slowdown regime
Many-server approximations are ubiquitous in the modeling of large-scale service systems. A preva-
lent mode of analysis in this context is the Halfin-Whitt heavy traffic diffusion regime , also called