Stability, queue length and delay. II. Stochastic queueing networks

For Pt.I, see ibid., vol.1, pp.999-1004. The notions of linear EP (envelope process), MEP (minimum envelope process), and MER (minimum envelope rate) developed previously are extended to stochastic processes. The notion of MER might be of practical importance in communication networks. It is shown that the MERs are equivalent to the notion of effective bandwidths in communication networks when restricting oneself to two-state Markov modulated arrival processes. Since the present definition of MER is fairly general and does not require a preset mathematical model, the proposed approach can be used to obtain the effective bandwidths for other real-time traffic, e.g., video. Moreover, the tool for computing the bounds and approximations of the tail distributions of delays at each queue in a network is already available in the present analysis once the MERs are obtained