2nd-order Markov approximation of the slot-occupancy pattern in a DQDB network

A methodology for approximating the slot-occupancy pattern process in a distributed queue dual bus (DQDB) network in underload conditions (i.e., aggregate offered load lower than the medium capacity) using a second-order discrete-time Markov process is presented. This methodology extends the authors´ previous work (1992), in which the slot-occupancy pattern process was approximated by a first-order discrete-time Markov process. Here the authors start from a simplified DQDB network that has a behavior close to the real DQDB in underload conditions. For the simplified DQDB, they derive the joint probability density function of the status (busy/empty) of three consecutive slots. From the joint probability density function, the parameters of a second-order discrete time Markov process are derived. The model is compared with the Bernoulli model that is often used in the literature to approximate the slot-occupancy-pattern process in the DQDB. The occupancy of the results is investigated through simulation