An M/G/1 type approach to the approximation of the slot-occupancy pattern in a DQDB network

In a previous paper, we presented a method for approximating the process that models the status of consecutive slots traveling on the forward bus in a DQDB network (slot-occupancy-pattern process) in underload conditions. That method models the slot-occupancy-pattern process of a simplified DQDB network, which behaves similarly to DQDB, by using an nth-order discrete-time Markov process. Because of its computational complexity, the method was applied only to evaluate the 1st and 2nd-order approximations. By noting that the nth-order discrete-time Markov process is a Markov chain of M/G/1 type, here we exploit the basic methodology developed for such chains by Neuts and the recursion algorithm of Ramaswami to derive the steady-state probabilities. We investigate special features of the Markov chain that induce a significant complexity reduction of the algorithm for its solution. From the steady-state probabilities, we obtain the network configurations and the workload conditions for which the simplified DQDB is close to real DQDB. The accuracy of our results was tested by simulation. Finally, through a hybrid analytic/simulation approach we study the influence of the slot-occupancy-pattern model on the access delay experienced by users in a DQDB network.