Generalized Processor Sharing Networks with Exponentially Bounded Burstiness Arrivals

Abstract

We consider virtual circuit packet switching communication networks that employ processor sharing type service disciplines and study their stability when the offered traffic to the network has exponentially bounded burstiness (EBB). The advantages of processor sharing switching techniques both in terms of service flexibility and the potential capability to guarantee certain grades of service, were emphasized in [7]. The study presented there assumes that the traffic offered to the network is flow-controlled by the leaky-bucket mechanism, and the performance of both generalized processor sharing (GPS) and packet-by-packet generalized processor sharing (PGPS) is analyzed.In this paper we employ an exponential characterization (EBB) introduced in [11] to analyze this type of systems in a stochastic setting. We first examine the GPS and PGPS servers in isolation, and demonstrate their superiority to a general server in the stochastic environment. We then show that a network of servers, that are all either GPS or PGPS, is stable whenever the service rate of each node is larger than the total arrival rate to it. In addition, we provide exponential upper bounds to the traffic flows within the network links, and to the backlogs of each session in the various nodes on its path.