(A) unified analysis of BMAP/G/1 queues with generalized vacations

Abstract

In this dissertation, both a class of continuous-time BMAP/G/1 queues with generalized vacations and a class of discrete-time BMAP/G/1 queues with generalized vacations are considered. This dissertation aims at presenting a unified analysis of these systems that have applications in various areas such as computer, communication, manufacturing and other stochastic systems. To this end, this dissertation presents explicit forms of matrix decomposition for the queue length distributions, for the workload distribution, and for the joint distribution of the queue length and the remaining service time in these systems. The significance of these decompositions is that the analysis of any continuous- and discrete-time BMAP/G/1 vacation queue is reduced to characterizing the conditional vector generating function of the queue length at an arbitrary epoch given that the server is on a vacation period. This is demonstrated by deriving the queue length distributions of various continuous- and discrete-time BMAP/G/1 vacation queues based on the decomposition presented in this dissertation. Also, these decompositions provide qualitative insight that is not obvious in the detailed matrix analytic treatment. Further, it is shown that queue length distributions are easily derived compared to standard procedures (e.g. matrix analytic method and supplementary variable technique) if these decompositions are used. Finally, general recursions for the factorial moments of the queue length and the workload are presented as application of these decompositions. The results in this dissertation would be beneficial not only to queueing theorists but also to practitioners who try to optimize his/her queueing systems.