A generalized processor sharing approach to flow control in integrated services networks: the multiple node case

Worst-case bounds on delay and backlog are derived for leaky bucket constrained sessions in arbitrary topology networks of generalized processor sharing (GPS) servers. The inherent flexibility of the service discipline is exploited to analyze broad classes of networks. When only a subset of the sessions are leaky bucket constrained, we give succinct per-session bounds that are independent of the behavior of the other sessions and also of the network topology. However, these bounds are only shown to hold for each session that is guaranteed a backlog clearing rate that exceeds the token arrival rate of its leaky bucket. A much broader class of networks, called consistent relative session treatment (CRST) networks is analyzed for the case in which all of the sessions are leaky bucket constrained. First, an algorithm is presented that characterizes the internal traffic in terms of average rate and burstiness, and it is shown that all CRST networks are stable. Next, a method is presented that yields bounds on session delay and backlog given this internal traffic characterization. The links of a route are treated collectively, yielding tighter bounds than those that result from adding the worst-case delays (backlogs) at each of the links in the route. The bounds on delay and backlog for each session are efficiently computed from a universal service curve, and it is shown that these bounds are achieved by "staggered" greedy regimes when an independent sessions relaxation holds. Propagation delay is also incorporated into the model. Finally, the analysis of arbitrary topology GPS networks is related to Packet GPS networks (PGPS). The PGPS scheme was first proposed by Demers, Shenker and Keshav (1991) under the name of weighted fair queueing. For small packet sizes, the behavior of the two schemes is seen to be virtually identical, and the effectiveness of PGPS in guaranteeing worst-case session delay is demonstrated under certain assignments.>