Scheduling in parallel queues with randomly varying connectivity and switchover delay

Abstract

We consider a dynamic server control problem for two parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot the server decides either to stay with the current queue or switch to the other queue based on the current connectivity and the queue length information. The introduction of switchover time is a new modeling component of this problem, which makes the problem much more challenging. We develop a novel approach to characterize the stability region of the system by using state-action frequencies, which are stationary solutions to a Markov Decision Process (MDP) formulation of the corresponding saturated system. We characterize the stability region explicitly in terms of the connectivity parameters and develop a frame-based dynamic control (FBDC) policy that is shown to be throughput-optimal. In fact, the FBDC policy provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple Myopic policies that achieve more than 96% of the stability region. Finally, simulation results show that the Myopic policies may achieve the full stability region and are more delay efficient than the FBDC policy in most cases.