Scheduling algorithms for arbitrary communication networks

Abstract

We consider the problem of designing scheduling schemes for networks with arbitrary topology and scheduling constraints. We address the optimality of scheduling schemes for packet networks in terms of throughput, delay and fairness. Specifically, we design two scheduling schemes. The first one achieves simultaneous throughput and delay optimization. The second scheme provides fairness. We design a scheduling scheme that guarantees a per-flow average delay bound of O(number of hops), with a constant factor loss of throughput. We derive the constants for a network operating under primary interference constraints. Our scheme guarantees an average delay bound of ... is the number of hops and pj is the effective loading along flow j. This delay guarantee comes at a factor 5 loss of throughput. We also provide a counter-example to prove the essential optimality of our result. For the fair scheduling scheme, we define a packet-based notion of fairness by establishing a novel analogy with the ranked election problem. The election scheme of Goodman and Markowitz (1952) [14] yields a maximum weight style scheduling algorithm. We then prove the throughput optimality of the scheme for a single-hop network. Standard methods for proving the stability of queuing systems fail us and hence we introduce a non-standard proof technique with potential wider applications.