Note on Effective Bandwidth of ATM Traffic 1 Costas Courcoubetis 2 and Jean Walrand 3 2 University of Crete, Heraklion 3 University of California at Berkeley ABSTRACT The objective of this note is to explore the existence of an effective bandwidth for ATM (asynchronous transfer mode) traffic. We show that such an effective bandwidth exists for a class of stationary Gaussian sources. We also show that the effective bandwidth cannot be defined for general non-stationary sources by providing an elemen- tary counter-example. 1. Introduction A number of recent papers have shown the existence of an effective bandwidth for some traffic models ([4], [5]). What this mean is that the set of acceptable numbers N i of sources of type i , for i = 1, 2, ..., J , that can go through a common buffer with service rate c is such that i =1 Σ J N i α i ≤ c. (1) Here, acceptable means that the resulting cell loss probability because of buffer overflow is less than some specified small value. Thus, the result says that one can consider that each source of type i uses a bandwidth α i . This result is somewhat surprising in that one might reasonably expect that the set of acceptable numbers N i would be characterized by a nonlinear expression. Thus, the question arises of identifying the generality of the concept of effective bandwidth. In terms of small loss probability, the effective bandwidth has been justified for the following two models. In [5], at each time n ≥ 1, a source of type i produces a random batch of X n i cells. The buffer has capacity B and it serves one cell per second. The X n i are independent and their distribution depends only on i . The buffer can then be viewed as a GI/GI/1 queue where the interarrival times are deterministic. It is shown in [5] that the probability that an arriving cell finds a queue length larger than some large B is smaller than a specified value if and only if (1) holds where α i = γ B logE{exp[ B γ X n i ]}. In [4] it is shown that if the sources are two-state Markov modulated fluid sources and if the buffer serves the fluid at a constant rate c , then an effective bandwidth can also be defined for each source. In this paper, we prove the existence of an effective bandwidth for a class of stationary Gaussian sources. We also show that, in general, sources do not have an effective bandwidth. We exhibit an ele- mentary counter-example in section 2. In section 3 we perform a simple calculation for i.i.d. Gaussian batches. This result, a particular case of that in [5], introduces the method that we will need for the next section. In section 4, we prove the existence of an effective bandwidth for a class of stationary Gaussian 1 Research supported in part by a Nato Grant, by a grant from Pacific Bell, and by a matching grant from the state of Cali- fornia. This research was performed while the second author was visiting the University of Crete.