Leaky-bucket (LB) based traffic parameters are widely used for traffic declaration and monitoring (enforcing) in asynchronous transfer mode (ATM) networks. For such a system, every traffic source is policed by an LB enforcer before entering the access node at the edge of the network. In this article, we investigate the characteristics of the model that such traffic sources are multiplexed together by a multiplexer in the edge node. Based on the worst case performance, we derive the upper bound and the lower bound of queue length at the multiplexer as functions of the LB parameters and number of connections. In particular, we also take the peak cell rate, which is an important parameter, into consideration. We also modify the well-known Little's formula which is derived based on long-term average, to be suitable for a complete busy period. It helps us to derive bounds on average waiting time by way of average queue length.
