Optimal Server Assignment in Multi-Server Queueing Systems with Random Connectivities

In this paper, we provide complementary results on delay-optimal server allocation in multi-queue multi-server (MQMS) systems with random connectivities. More specifically, we consider an MQMS system where each queue is limited to get service by at most one server during each time slot. It is known that maximum weighted matching (MWM) is a throughput-optimal server assignment policy for such a system. In this paper, using dynamic coupling argument we prove that for a system with i.i.d. Bernoulli arrivals and connectivities, MWM minimizes, in stochastic ordering sense, a range of cost functions of the queue lengths such as total queue occupancy (which implies minimization of average queueing delay). Finally, we propose a low complexity heuristic server assignment policy for MQMS systems namely least connected server first/longest connected queue (LCSF/LCQ) and through simulations we show that it performs very closely compared with the optimal policy in terms of average queueing delay.