Deadline Aware Scheduling for Input Queued Packet Switches

We study the problem of designing scheduling algorithms for deadline-aware input-queued (IQ) packet switches. While most research on scheduling algorithms for IQ switches has focused on maximizing throughput, packet deadlines are a key consideration in the context of real-time applications like multimedia streaming and video telephony. We consider traffic streams associated with service profiles, which reflect the inter-packet deadline (IPD) constraints between packets constituting the stream, and are determined by application layer requirements. To make the NP-hard problem of scheduling with strict deadline constraints tractable, we use soft deadlines as a modeling tool, and study the scheduling problem with soft deadlines in a dynamic programming (DP) framework. Our objective is to design a scheduler which minimizes aggregate soft deadline violation, or equivalently, preserves the service profiles associated with each traffic stream as faithfully as possible. We establish the optimality of a myopic or greedy scheduling policy for the canonical 2× 2 crossbar switch, in a finite-horizon setting. For bigger switches, we demonstrate using a Lyapunov function technique that a myopic policy, even though not optimal, maximizes the admissible region of the switch when the inter-packet deadlines are geometrically distributed. We develop low-complexity approximations to the near-optimal myopic policy, one based on the notion of neighborhood search, and two others based on convex relaxations of an integer programming problem. We demonstrate the efficacy of the proposed policies via simulations, using goodput as a performance metric. A key feature of the proposed policies is that they do not require any knowledge of traffic statistics (for example, periodicity of traffic streams), rendering them robust and amenable to implementation. Index Terms Input-queued switches, Scheduling, Soft Deadlines, Dynamic Programming, Myopic policy, Convex optimization, Lyapunov technique.