Queueing systems modeled by Level-dependent Quasi-Birth-and-Death processes

Abstract

Queueing theory is applied to mathematical modeling and analysis of computer systems, telecommunication systems and other systems which appear in industrial engineering. Especially, Quasi-Birth-and-Death(QBD) processes are widely used in modeling of telecommunication systems and inventory systems, and matrix geometric method is one of the best methods to analyze QBD processes. In this dissertation, we model a system with the splitting channel scheme in multimedia UMTS network and a (s,S) continuous inventory system of perishable items with repeated demands and random lead times by level-dependent QBD process, and analyze the performance of the systems by matrix analytic method. We also investigate MAP/M/c queue with constant impatient time by using the minimal nonnegative solutions of two matrix quadratic equations which appear in the analysis of QBD processes by matrix analytic method. In chapter 3, we present a splitting channel scheme with threshold control in multimedia cellular networks supporting two class of services, narrowband and wideband, where wideband calls split their channels to originating call and handoff call under two threshold control. We model our scheme by level-dependent finite QBD queueing system and analyze the call level performance of our system by matrix analytic method. The packet level performance of the handoff scheme is also studied. Comparisons are made to the performance of the non-splitting handoff scheme and the well known guard channel handoff scheme. In chapter 4, we consider an (s,S) continuous inventory model of perishable items with repeated demands and random lead times. The replenishment lead times of orders are i.i.d. with a phase-type distribution. Demands occurring when there are no items in the inventory may leave the system forever or enter the retrial group to try again for their demand in random order and at random interval. The repeating demand in the retrial group operates in the geometric loss system. We repr...