A discrete-time queueing model of an atm ´leaky bucket´ policing mechanism.

The International Telephone and Telegraph Consultative Committee (CCITT) have adopted Asynchronous Transfer Mode (ATM) as the transfer technique for future Broadband Integrated Services Digital Networks (B-ISDNs). ATM networks have no node-by-node traffic flow control. However, to protect the quality of service, traffic flow is controlled at the source by ´policing mechanisms´. A policing mechanism ensures that the user doesn´t send more traffic onto the network than allowed. The so-called ´leaky bucket´ mechanism seems the most favoured of the proposed policing mechanisms. From the point of view of cell loss probabilities (one of the measures of quality of service) the leaky bucket can be modelled exactly as a G/D/1/N queue. The problem with this model is the general arrival pattern of such a queue. Previously proposed models have made large and unrealistic assumptions about the arrival pattern, for example assuming that arrivals are exponentially distributed. This paper proposes the GGeo/GGeo/l/N discrete-time queue solved using the principle of maximum entropy as a much more realistic model. The suitability of this model is twofold. ATM traffic consists of individual cells and is essentially discrete which makes discrate-lime modelling appropriate. Secondly, ATM traffic is very bursty in nature and capturing this burstiness is essential for an accurate model. Moreover the generalised geometric (GGeo) distribution is uniquely described by its first two moments hence the model captures much of the variability of the arrival process caused by this bursty nature. The model is validated using simulation and some numerical results are compared to real data concluding that the model is indeed accurate as well as very computationally efficient.