Delay Optimal Server Assignment to Symmetric Parallel Queues with Random Connectivities

TL;DR

This paper proves that in symmetric parallel queue systems with random connectivities, the Maximum Weighted Matching policy optimally minimizes various queue length cost functions, including average delay.

Contribution

It establishes that MWM not only is throughput optimal but also minimizes queue length-related costs in symmetric systems with stochastic connectivities.

Findings

MWM minimizes total queue occupancy in symmetric systems.

MWM is proven to be delay optimal among all policies.

The results apply to systems with i.i.d. Bernoulli arrivals and connectivities.

Abstract

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).