IN PROCEEDINGS OF IEEE INFOCOM ' 98 , SAN FRANCISCO , CA , MARCH 1998 . 1 SCED + : E cient Management of Quality of Service GuaranteesR

| Current proposals for the provision of deter-ministic quality of service guarantees in integrated services networks require per-session management of traac owing in network switches, raising scalability questions for practical implementation of high speed packet switching in large scale networks. At the same time, the end-to-end delay bounds associated with current proposals can be overly conservative , limiting the utility of the bounds to guide eecient resource allocation. In this paper, we introduce SCED+, a network scheduling algorithm that yields scalable provision of tight deterministic end-to-end delay bounds. These features are achieved through the use of aggregation and eecient statistical multiplexing between best-eeort and guaranteed traac. The SCED+ algorithm also supports statistical multiplexing between \guaranteed" traac streams, providing tight end-to-end delay bounds for traac streams which can tolerate non-zero packet loss rates. In order to facilitate the analysis of SCED+, we reene the so-called \network calculus" to address delay jitter, and introduce a simple and uniied approach to the analysis of output burstiness of traac departing from a general network element. O VER the past several years there has been great progress in the analysis and synthesis of scheduling algorithms for integrated services networks to support deterministic quality of service guarantees, e.g. The class of so-called \fair queueing" scheduling algorithms 12]]22]]2] is perhaps currently the most popular in the literature. In these algorithms, each session is allocated a guaranteed bandwidth. H. Zhang was apparently the rst to recognize the importance of the problem of an undesirable coupling between bandwidth and delay guarantees 31], which can limit the capacity of the scheduling algorithm to support many connections. Scheduling algorithms which overcome this undesirable coupling have appeared more recently 15]]16]]21]]25]]28]. In all of these scheduling algorithms, packets are time stamped accordingly and served in order of their time stamps. This requires sorting of packets, and as a result, implementation complexities which grow with the number of supported sessions. Since the number of sessions passing through a packet switch in a large scale network can be quite large, this has raised questions regarding the feasibility of implementing such scheduling algorithms in large high speed networks. Another problem associated with such scheduling algorithms in integrated services networks is the perceived \looseness" of the associated deterministic end-to-end delay bounds. Even if the end-to-end delay bounds are achievable by some traac arrival patterns, these arrival patterns may be rare. In the typical case the delay of …