As asynchronous transfer mode (ATM) becomes deployed as the basis for the telephone and telecommunications networks of the next 30 years, several issues will have to be addressed. ATM is based on the premise that, by using the natural burstiness of voice and data traffic, it is possible to have an almost twofold gain in bandwidth utilization. This gain is offset, however, by the demands of voice traffic that packets not be lost and that the delay between packets be predictable. As a result, congestion control is important to the quality of service in an ATM network. Congestion control is dependent on the arrival model used. It is evident that the arrival model, and therefore queueing models for these services, are important to the minute-by-minute operations of an ATM network.

The authors propose a means to combine the arrival models for sources to give an estimate of the total traffic that is arriving at the ATM. They produce from this a simple estimate of the blocking probabilities for broad classes of traffic. They suggest the use of their estimates as the means of congestion control within the ATM switch. They have greatly reduced the complexity that exists in some of the more detailed queueing models. The models they propose are generic and may not take into account some of the variations in arrival that can be expected. Their estimates have the distinct advantage, however, of being simple to compute in UAA form. This is an important quality when placing a computational algorithm in the midst of call processing, as is required by ATM congestion control.

The formulas give estimates of blocking probability for three regimes: overloaded, critical, and underloaded. The calculations involve at most looking up a value of the error function, when using the UAA version. The limitation of such simple calculations is that they are, at best, estimated upper bounds on admittance. This may mean that they will underestimate traffic load, leading to congestion that results in call drop while the call is in progress, or they will overestimate the load and waste bandwidth.

The models used by the authors may not be related to actual traffic on a large ATM network. It has been known for some time that in data networks, especially LANs (see Chen and Liu [1]), traffic sources are not Markovian in their behavior but are more self-similar in structure.

The authors provide a simple mathematical formula to estimate blocking that can be calculated in real time and thus used as admittance control within the ATM switch. They do not address how close to actual traffic these calculations are. This is to be expected, however, as they are for the most part simplifying the results of others. It is important as ATM networks are deployed that the actual behavior of traffic become understood. Several informal studies have shown that arrivals of many types of traffic are not Markovian. This difference may lead to unexpected and unwanted results.