Hassan Halabian

Hassan Halabian, Ioannis Lambadaris, Chung-Horng Lung

In this paper, we characterize the network stability region (capacity region) of multi-queue multi-server (MQMS) queueing systems with stationary channel distribution and stationary arrival processes. The stability region is specified by a finite set of linear inequalities. We first show that the stability region is a polytope characterized by the finite set of its facet defining hyperplanes. We explicitly determine the coefficients of the linear inequalities describing the facet defining hyperplanes of the stability region polytope. We further derive the necessary and sufficient conditions for the stability of the system for general arrival processes with finite first and second moments. For the case of stationary arrival processes, the derived conditions characterize the system stability region. Furthermore, we obtain an upper bound for the average queueing delay of Maximum Weight (MW) server allocation policy which has been shown in the literature to be a throughput optimal policy for MQMS systems. Using a similar approach, we can characterize the stability region for a fluid model MQMS system. However, the stability region of the fluid model system is described by an infinite number of linear inequalities since in this case the stability region is a convex surface. We present an example where we show that in some cases depending on the channel distribution, the stability region can be characterized by a finite set of non-linear inequalities instead of an infinite number of linear inequalities.

Hassan Halabian, Ioannis Lambadaris, Chung-Horng Lung

In this paper, we characterize the stability region of multi-queue multi-server (MQMS) queueing systems with stationary channel and packet arrival processes. Toward this, the necessary and sufficient conditions for the stability of the system are derived under general arrival processes with finite first and second moments. We show that when the arrival processes are stationary, the stability region form is a polytope for which we explicitly find the coefficients of the linear inequalities which characterize the stability region polytope.

Hassan Halabian, Ioannis Lambadaris, Chung-Horng Lung

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).