Dual Scheduling Algorithm In A Generalized Switch: Asymptotic Optimality And Throughput Optimality

Generalized switch is a model of a queueing system where parallel servers are interdependent and have time-varying service capabilities. It includes as special cases the model of data scheduling in a wireless network and the input-queued cross-bar switch model. A finite set S of queues (users) are served in discrete time by a switch. Switch state h follows a discrete-time, finite-state Markov chain. At each time slot t, the switch can choose a scheduling decision m from a finite set M , which captures the interdependency among the servers specifying which subsets of servers can be active simultaneously. Each scheduling decision has the associated vector of service rates r̃(h(t)) at which queues are served, where h(t) denotes the switch state at time t. This article considers the dual scheduling algorithm that uses rate control and queuelength based scheduling to allocate resources for a generalized switch. We first consider a saturated system in which each user has infinite amount of data to be served. We prove the asymptotic optimality of the dual scheduling algorithm for such a system, which says that the vector of average service rates of the scheduling algorithm maximizes some aggregate concave utility functions. As the fairness objectives can be achieved by appropriately choosing utility functions, the asymptotic optimality establishes the fairness properties of the dual scheduling algorithm. We next consider a system with exogenous arrivals, i.e., data flows of finite size arrive at the system randomly. For such a system, we propose a modified dual scheduling algorithm that stabilizes the system whenever the input rates are within the feasible rate region and is then throughput-optimal, i.e., achieves 100% throughput. The dual scheduling algorithm motivates a new architecture for scheduling, in which an additional queue is introduced to interface the user data queue and the time-varying server and to modulate the scheduling process, so as to achieve different performance objectives. Further research would include scheduling with Quality of Service guarantees with the dual scheduler, and its application and implementation in various versions of the generalized switch model.