A ∑GIi/D/1/∞ queue with heterogeneous input/output slot times

In this paper, we present a ∑GIi/D/1/∞ queue with heterogeneous input/output slot times. This queueing model can be regarded as an extension of the ordinary GI/D/1/∞ model. For this ∑GIi/D/1/∞ queue, we assume that several input streams arrive at the system according to different slot times. In other words, there are different slot times for different input/output processes in the queueing model. The queueing model can therefore be used for an ATM multiplexer with heterogeneous input/output link capacities. Several cases of the queueing model are discussed to reflect different relationships among the input/output link capacities of an ATM multiplexer. In the queueing analysis, two approaches: the Markov model and the probability generating function technique, are adopted to develop the queue length distributions observed at different epochs. This model is particularly useful in the performance analysis of ATM multiplexers with heterogeneous input/output link capacities

A study of the generalised max–min fair rate allocation for ABR control in ATM

In the rate-based flow control for ATM Available Bit Rate service, fairness is an important requirement, i.e. each flow should be allocated a fair share of the available bandwidth in the network. Max–min fairness, which is widely adopted in ATM, is appropriate only when the minimum cell rates (MCRs) of the flows are zero or neglected. Generalised max–min (GMM) fairness extends the principle of the max–min fairness to accommodate MCR. In this paper, we will discuss the formulation of the GMM fair rate allocation, propose a centralised algorithm, analyse its bottleneck structure and develop an efficient distributed explicit rate allocation algorithm to achieve the GMM fairness in an ATM network. The study in this paper addresses certain theoretical and practical issues of the GMM fair rate allocation