Some Comparisons For Queue Length In Bulk Arrival And Bulk Service System

Bulk arrival and bulk service queuing model is one of the most important researchtopics in queuing theory, it is widely used in many areas such as communications,tra?c and transportation, management and service and other fields. The dependenciesbetween variables in bulk arrival and bulk service queuing system have been causedgreat attention among many authors, and a series of fruitful research results about oneservice window model have been derived in recent years. In this thesis, we will furtherdiscuss bulk arrival and bulk service queuing system with multi-window. Comparisonsfor queue lengths of M^X/G^Y/k, GI^X/G^Y/k, G^X/M^Y/k and G^X/GI^Y/k areobtained in the sense of increasing convex ordering.Vacation queuing model is another important research topic in queuing theory.It re?ects the objective facts that the service may be interrupted by some unexpectedevents, and provides an important theory and method to optimize device and to controloperation for queuing system. In recent years, some authors have made some importantprogress in the study of M/M/k and GI/M/k under di?erent vacation strategies, andderived the characterization of some steady-state index successfully. It obviously hasthe practical significance for enhancing service level or reducing service cost to introducethe vacation strategy in bulk arrival and bulk service queuing system. In this thesis,we will further investigate the asynchronous multiple vacation system of bulk arrivaland bulk service queuing system with multi-window. Comparisons for queue lengthsof G^X/GI^Y/k/AS, WV and GI^X/G^Y/k/AS, WV are obtained in the sense ofincreasing convex ordering.