A calculus for network delay. I. Network elements in isolation

Abstract

A calculus is developed for obtaining bounds on delay and buffering requirements in a communication network operating in a packet switched mode under a fixed routing strategy. The theory developed is different from traditional approaches to analyzing delay because the model used to describe the entry of data into the network is nonprobabilistic. It is supposed that the data stream entered into the network by any given user satisfies burstiness constraints. A data stream is said to satisfy a burstiness constraint if the quantity of data from the stream contained in any interval of time is less than a value that depends on the length of the interval. Several network elements are defined that can be used as building blocks to model a wide variety of communication networks. Each type of network element is analyzed by assuming that the traffic entering it satisfies bursting constraints. Under this assumption, bounds are obtained on delay and buffering requirements for the network element; burstiness constraints satisfied by the traffic that exits the element are derived.