  In this paper, we investigate the problem of assignment of $K$ identical
servers to a set of $N$ parallel queues in a time slotted queueing system. The
connectivity of each queue to each server is randomly changing with time; each
server can serve at most one queue and each queue can be served by at most one
server per time slot. Such queueing systems were widely applied in modeling the
scheduling (or resource allocation) problem in wireless networks. It has been
previously proven that Maximum Weighted Matching (MWM) is a throughput optimal
server assignment policy for such queueing systems. In this paper, we prove
that for a symmetric system with i.i.d. Bernoulli packet arrivals and
connectivities, MWM minimizes, in stochastic ordering sense, a broad range of
cost functions of the queue lengths including total queue occupancy (or
equivalently average queueing delay).
