Moments of the first passage time to overload for a buffered statistical multiplexer

We consider the first passage to overload for a buffered statistical multiplexer loaded with N identical binary on-off sources. First passage times to overload are related to the characterization of congestion imminence which in turn is crucial in the design of effective congestion control algorithms for delay sensitive services in broadband wide area networks. We give the moments of the first passage time to overload as solutions of a set of linear first order ordinary differential equations. Furthermore, adapting the methodology developed by Anick, Mitra and Sondhi (1982) we express the moments of the first passage time to overload in a spectral expansion form, involving the system´s eigenvalues. Numerical results for the first two moments are presented