Departure processes and busy periods of a tandem network

Consider a single-server tandem queueing network with a Markovian arrival process (MAP) to the first station and exponential service times. Using the dimension-reduction and expanding blocks (DREB) scheme, we formulate the joint queue length process into a single-dimensional level-dependent quasi-bi...

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Bibliographic Details
Published inOperational research Vol. 11; no. 3; pp. 245 - 257
Main Authors Lian, Zhaotong, Zhao, Ning
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.11.2011
Springer Nature B.V
Subjects
Business and Management
Communications networks
Computational Intelligence
Management Science
Markov analysis
Operations Research
Operations Research/Decision Theory
Original Paper
Queuing
Studies
IMAP
Level-dependent QBD
Tandem network
Departure process
Busy period
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Summary:Consider a single-server tandem queueing network with a Markovian arrival process (MAP) to the first station and exponential service times. Using the dimension-reduction and expanding blocks (DREB) scheme, we formulate the joint queue length process into a single-dimensional level-dependent quasi-birth-death (LDQBD) process with expanding blocks. This allows us to show that the departure process from each station is a MAP with infinite phases or an IMAP, which implies that the departure process of any IMAP / M /1 is an IMAP. It also allows us to study the inter-departure time and the busy period in each station easily.
ISSN:1109-2858
1866-1505
DOI:10.1007/s12351-010-0076-0