A new approach to an N/G/1 queue

We propose a new approach that gives a one-step computational algorithm to directly obtain the queue length distribution of an N/G/1 queueing system. The new approach is based on the supplementary variable method and the matrix–analytic method. We shall show that this approach enables us to derive the joint distribution of the queue length and the elapsed service time. This revised version was published online in June 2006 with corrections to the Cover Date.