The stability of join-the-shortest-queue models with general input and output processes

Admission control can be employed to avoid congestion in queueing networks subject to overload. In distributed networks the admission decisions are often based on imperfect measurements on the network state. This paper studies how the lack of complete state information affects the system performance by considering a simple network model for distributed admission control. The stability region of the network is characterized and it is shown how feedback signaling makes the syst...

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 f...

We consider a single-hop switched queueing network. Amongst a plethora of applications, these networks have been used to model wireless networks and input queued switches. The MaxWeight scheduling policies have proved popular, chiefly, because they are throughput optimal and do not require explicit estimation of arrival rates. In this article, we prove the same throughput optimality property for a generalization of the MaxWeight policy called the MaxWeight-({\alpha},g) poli...

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...

Join the shortest queue (JSQ) refers to networks whose incoming jobs are assigned to the shortest queue from among a randomly chosen subset of the queues in the system. After completion of service at the queue, a job leaves the network. We show that, for all non- idling service disciplines and for general interarrival and service time distributions, such networks are stable when they are subcritical. We then obtain uniform bounds on the tails of the marginal distributions of ...

In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other servers. Under a stronger assumption, that the departure rates are proportional to the queue length in each server, we obtain a characterization of the stability region through a system of equations. We start by defining the mathematical mode...

We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and strong stability. We then consider networks of queues with random events and control actions that can be implemented over time to affect arrivals and service at the queues. The control actions also generate a vector of additional network att...

Stability with respect to a given scheduling policy has become an important issue for wireless communication systems, but it is hard to prove in particular scenarios. In this paper two simple conditions for stability in broadcast channels are derived, which are easy to check. Heuristically, the conditions imply that if the queue length in the system becomes large, the rate allocation is always the solution of a weighted sum rate maximization problem. Furthermore, the change o...

The fundamental problem in the study of parallel-server systems is that of finding and analyzing `good' routing policies of arriving jobs to the servers. It is well known that, if full information regarding the workload process is available to a central dispatcher, then the {\em join the shortest workload} (JSW) policy, which assigns jobs to the server with the least workload, is the optimal assignment policy, in that it maximizes server utilization, and thus minimizes sojour...

We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes jobs which have been least routed through the network. We show that the network is globally stable under this policy if there exists an appropriate quadratic local Lyapunov function that provides a negative drift with respect to nominal load...