Traffic Specification

Abstract

In this chapter, we address the parameterization problem for the constraint functions needed for deterministic traffic regulation and service guarantees. For efficient parameterization, one has to find a good “substitute” for the constraint function that can be represented by a set of parameters. In view of (2.15), the criteria for a good “substitute” for the constraint function are (i) the substitute must not be smaller than the constraint function, and (ii) no other functions not smaller than the constraint function are smaller than the substitute. These are in the same spirit as the requirements for the traffic specification (TSpec) in [183]. In [204], an algorithm is developed to find a substitute of the form $f\left( t \right) = {\min _{0 \leqslant i \leqslant n}}\left[ {{\sigma _i} + {\rho _i}t} \right].$ These functions are called Concave Piecewise Linear (CVPL) functions in [180] and they can be implemented by a concatenation of (σi,ρi)-leaky buckets,i = 1,…, n,as discussed in Section 2.2.2. In addition to the piecewise linear constraint functions, nonlinear functions have been found useful in [152] to characterize the Bellcore local area network traffic [140]. All these lead to the general parameterization problem for constraint functions.