Waiting time distribution of the MAP/D/k system in discrete time – a more efficient algorithm

We show that the discrete time MAP/D/k presented by Chaudhry et al. has a special structure which results in a simple and more efficient computational scheme than they have presented. Specifically, we show that the computational efforts for the matrix G at each iteration can be reduced from O(d³k³m³) to O(dk³m³) by rearranging the state space and then capitalizing on the resulting structure. This saving in computational effort is significant, especially when d is very large.