Delay optimal server assignment to symmetric parallel queues with random 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 [1], [2]. 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).

Stability analysis and optimal control of multi-server wireless queueing systems

“…In fact, the random ness of th e connectivities between the queues and the servers in the studied systems is modeling the tim e variability of the wireless channels in realistic wireless systems. The system studied in Section 3.1 of C hapter 3 can be applied for modeling th e tra n sm itte r allo cation problem in a satellite node [62], The multi-server systems studied in Sections 3.2 and 3.3 of C hapter 3 and in Chapters 4 and 5 can be applied in m odeling th e dynamic resource allocation in wireless access networks (See [3,5,[11][12][13][14][15]18,[62][63][64][65][66][67][68][69][70]).…”