In this paper we present a dynamic model for access control mechanism used in computer communication network. This model represents a substantial improvement over the models developed in the previous works [1] [2]. The model is governed by a system of discrete nonlinear difference equations. In the dynamic model, token buckets police incoming traffic and one multiplexor serving all the token pools multiplexes conforming traffic using round robin scheme. For performance evaluation of the system, we construct traffic models which exhibit both short-range dependence (SRD) and long-range dependence (LRD) properties. These traffic models capture the salient features of existing network traffic characteristics such as self-similarity and long range dependence. They are constructed using homogeneous and non homogeneous Poisson processes and doubly stochastic Poisson (Cox) process driven by Fractional Brownian motion. Using the proposed dynamic model, we study several issues related to network performance corresponding to different stochastic inputs. All these are illustrated by numerical result.