  We study the problem of assigning $K$ 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 during each
time slot. Such a queueing model has been used in addressing resource
allocation problems in wireless networks. It has been previously proven that
Maximum Weighted Matching (MWM) is a throughput-optimal server assignment
policy for such a queueing system. In this paper, we prove that for a 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
such as total queue occupancy (which implies minimization of average queueing
delays). Then, we extend the model by considering imperfect services where it
is assumed that the service of a scheduled packet fails randomly with a certain
probability. We prove that the same policy is still optimal for the extended
model. We finally show that the results are still valid for more general
connectivity and arrival processes which follow conditional permutation
invariant distributions.
