Paper Info
Title
Analysis of generalized QBD queues with matrix-geometrically distributed batch arrivals and services
Abstract
Abstract In a quasi-birth–death (QBD) queue, the level forward and level backward transitions of a QBD-type Markov chain are interpreted as customer arrivals and services. In the generalized QBD queue considered in this paper, arrivals and services can occur in matrix-geometrically distributed batches. This paper presents the queue length and sojourn time analysis of generalized QBD queues. It is shown that, if the number of phases is N, the number of customers in the system is order-N matrix-geometrically distributed, and the sojourn time is order-\(N^2\) matrix-exponentially distributed, just like in the case of classical QBD queues without batches. Furthermore, phase-type representations are provided for both distributions. In the special case of the arrival and service processes being independent, further simplifications make it possible to obtain a more compact, order-N representation for the sojourn time distribution.
Year
DOI
Venue
2016
10.1007/s11134-015-9467-5
Queueing Systems: Theory and Applications
Keywords
Field
DocType
Matrix-analytic methods,Age process,Batch arrival,Batch service,Queue length analysis,Sojourn time analysis,60K25,68M20
Time distribution,Mathematical optimization,Matrix (mathematics),Computer science,Queue,Markov chain,Real-time computing,Queue management system,Special case
Journal
Volume
Issue
ISSN
82
3-4
1572-9443
Citations 
PageRank 
References 
0
0.34
5
Authors
1
Name
Order
Citations
PageRank
Gábor Horváth121035.47