Analysis of discrete-time M/G/1-type queueing models

Abstract

We analyze three complex queueing models. The models considered in this dissertation have many applications in computer and telecommunication networks including IP (Internet Protocol) and ATM (Asynchronous Transfer Mode) networks which provide multimedia services. In view of this, we deal with discrete-time priority queue with generalized vacations and structured batch arrivals, multiserver queue with deterministic service time and correlated arrivals, and finite-capacity queue with general bulk (batch) service rules and correlated arrivals. Three queues considered in this dissertation are sufficiently complex and generalized queueing models. We develop simple approaches for the three complex queues. First, we show the invariant relation of the queue waiting time between two priority queues. With this relation, one does not have to analyze two models separately as did in the traditional queueing theory. Second, the waiting time distribution of multiserver queue with constant service time is given through investigating a property inherent in the multiserver queue with constant service time. With the property, we can get the waiting time distribution of multiserver queue from those of single server queue. Third, we investigate generalized . bulk service queues. We derive the relation between departure epoch- and random epoch-probability of the number of customers using the concept of the mean sojourn time of the phase of underlying Markov chain of D-BMAP (discrete-time batch Markovian arrival process) so that we can avoid using the lengthy approach of the supplementary variable technique.