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.