Paper Info
Title
Quasi-birth-and-death Markov processes with a tree structure and the MMAP[K]/PH[K]/N/LCFS non-preemptive queue
Abstract
This paper studies a multi-server queueing system with multiple types of customers and last-come-first-served (LCFS) non-preemptive service discipline. First, a quasi-birth-and-death (QBD) Markov process with a tree structure is defined and some classical results of QBD Markov processes are generalized. Second, the MMAP[K]/PH[K]/N/LCFS non-preemptive queue is introduced. Using results of the QBD Markov process with a tree structure, explicit formulas are derived and an efficient algorithm is developed for computing the stationary distribution of queue strings. Numerical examples are presented to show the impact of the correlation and the pattern of the arrival process on the queueing process of each type of customer.
Year
DOI
Venue
2000
10.1016/S0377-2217(98)00396-8
European Journal of Operational Research
Keywords
Field
DocType
Queueing theory,Matrix analytic methods,Tree structure,Last-come-first-served,Quasi-birth-and-death Markov process
M/M/1 queue,Kendall's notation,Discrete mathematics,Mathematical optimization,Bulk queue,M/M/c queue,M/G/1 queue,M/G/k queue,M/D/c queue,Mathematics,Markov renewal process
Journal
Volume
Issue
ISSN
120
3
0377-2217
Citations 
PageRank 
References 
3
1.25
1
Authors
1
Name
Order
Citations
PageRank
Qi-Ming He123034.21