Bounds for performance measures of token rings

In polling systems that have been studied in the literature, one usually asserts independent Poisson arrivals. This assumption is, however, unrealistic when dealing with many applications, e.g., local area networks (LANs) using token-ring protocols. The arrival processes there may be quite irregular, highly bursty, and correlated. We use the new approach for modeling such arrival streams proposed by Cruz (1991), to obtain strict upper bounds on several performance measures. It is based on characterizing the inputs by bounds on the average arrival rate and the burstiness, and is especially useful in describing the arrival streams that are filtered (policed) by leaky buckets. We first obtain bounds for the gated, exhaustive, and globally-gated service disciplines, and then consider timed token rings (such as the FDDI). The results for the first three disciplines improve the general bounds obtained by Altman, Foss, Riehl and Stidham (see Proceedings of the 14th International Teletraffic Congress, France, p.811-20, June 1994). We further obtain improved exponential bounds of the type introduced by Chang (see IEEE Trans. Automat. Contr., vol.34, no.5, p.913-31, 1994), and Yaron and Sidi (see ibid., vol.1, no.3, p.372-85, 1993) for the globally-gated discipline.