Extremal behaviour and bounds for a network buffer fed by deterministically shaped random processes

Allocation of resources is a challenging issue in the design and control of broadband ISDN networks because different network connections require different kinds of quality-of-service (QoS). Here, we consider the case of a VBR connection modelled as a random process but with deterministic shaping constraints. These constraints are known ahead of time and are typically specified by the simultaneous imposition of a (σ,ρ) and a (0,π) constraint, i.e., a π-peak-rate constraint. Since the actual statistics of the process may be unknown, it is desirable to obtain estimates of packet delay or buffer occupancy in the “worst-case”. One can therefore interpret the results in terms of “capacities” of the VBR channels described