We study the problem of assigning @math identical servers to a set of @math 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.
In contrast to the single-server system (where LCQ was both throughput-optimal and delay-optimal), in MQMS-Type1 system the MW policy is not necessarily delay-optimal. More specifically, in @cite_29 it was also shown that although MW policy is throughput-optimal, even for a system with i.i.d. Bernoulli arrivals and connectivity processes, MW policy in its general form, is not delay-optimal.
@cite_29
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Network capacity region of multi-queue multi-server queueing system with random connectivities and stationary arrival processes is studied in this paper. Specifically, the necessary and sufficient conditions for the stability of the system are derived under general arrival processes with finite first and second moments. In the case of stationary arrival processes, these conditions establish the network capacity region of the system. It is also shown that AS LCQ (Any Server Longest Connected Queue) policy stabilizes the system when it is stabilizable. Furthermore, an upper bound for the average queue occupancy is derived for this policy.