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 proce ss that models the status of consecutive slots traveling on the forwar d 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 Ist and 2nd-or der 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 met hodology developed for such chains by Neuts and the recursion algorith m of Ramaswami to derive the steady-state probabilities. We investigat e special features of the Markov chain that induce a significant compl exity reduction of the algorithm for its solution. From the steady-sta te probabilities, we obtain the network configurations and the workloa d conditions for which the simplified DQDB is close to real DQDB. The accuracy of our results was tested by simulation. Finally, through a h ybrid analytic/simulation approach we study the influence of the slot- occupancy-pattern model on the access delay experienced by users in a DQDB network.