Storage requirements in ATM switching elements with correlated arrivals and independent uniform routing

An ATM switching element with a finite number of independent and identical traffic sources (users), and an equally high number of destinations is considered. The sources are assumed to be bursty, and the burstiness of the sources is modeled by describing both their active periods (during which users generate one cell per slot) and their passive periods (during which users do not generate data) as geometric random variables. Arriving cells are assumed to be routed to their destinations in a uniform and independent way. As a result, a correlated-arrivals queueing model for the switch is obtained, which is analyzed in this paper by purely analytical means. Specifically, closed-form expressions for the mean and the variance of the buffer contents, and an accurate analytic approximation for the tail probabilities of the buffer contents are derived.