Shape-controlled traffic patterns that maximize overflow probabilities in high-speed networks

We consider the problem of allocation of network resources for a Variable Bit Rate connection requiring a probabilistic bound on cell delay. We only make the standard assumption that the connection has a deterministically controlled shape as specified by a (σ, ρ) constraint, simultaneously with a (0, π) (or peak-rate) constraint. This paper settles one instance of this open problem raised by Doshi which is motivated by the need to obtain worst-case probabilistic bounds, and is particularly applicable to situations where no statistical descriptors of network traffic are available. In other words, instead of an approach based on traffic modeling and effective bandwidths, we describe an approach using `worst-case' bounds assuming only these deterministic constraints. In particular, we describe that traffic pattern (among all stationary-ergodic and deterministically constrained arrival processes) which maximizes the `overflow probability' P(Q₀>b), for a given buffer level b, where {Q_t} is the buffer occupancy process, in steady-state, when the service rate is some constant c between ρ and π. This result could be used for resource provisioning of connections or for performance evaluation of network devices.