Advanced search
Publication Cover
Stochastic Models Volume 20, 2004 - Issue 1
Submit an article Journal homepage
78
Views
19
CrossRef citations to date
0
Altmetric
Original Articles

The Waiting Time Distribution of a Type k Customer in a Discrete-Time MMAP[K]/PH[K]/c (c = 1, 2) Queue Using QBDs

B. Van Houdt# Department of Mathematics and Computer Science, Performance Analysis of Telecommunication Systems Research Group, University of Antwerp, Antwerp, Belgium; Department of Mathematics and Computer Science, Performance Analysis of Telecommunication Systems Research Group, University of Antwerp, Middelheimlaan 1, Antwerp, B-2020, BelgiumCorrespondence[email protected].
&
C. Blondia Department of Mathematics and Computer Science, Performance Analysis of Telecommunication Systems Research Group, University of Antwerp, Middelheimlaan 1, Antwerp, B-2020, Belgium
Pages 55-69 | Received 27 Feb 2003, Accepted 01 Jul 2003, Published online: 16 Feb 2007

Citations (19)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (3)

Ann M. Noblesse, Nikki Sonenberg, Robert N. Boute, Marc R. Lambrecht & Benny Van Houdt. (2022) A joint replenishment production-inventory model as an MMAP[K]/PH[K]/1 queue. Stochastic Models 38:3, pages 390-415.
Read now
J. Van Velthoven, B. Van Houdt & C. Blondia. (2005) Response Time Distribution in a D-MAP/PH/1 Queue with General Customer Impatience. Stochastic Models 21:2-3, pages 745-765.
Read now
Qi-Ming HE. (2004) Workload Process, Waiting Times, and Sojourn Times in a Discrete Time MMAP[K]/SM[K]/1/FCFS Queue. Stochastic Models 20:4, pages 415-437.
Read now

Articles from other publishers (16)

Sixiao Gao, Toyokazu Kobayashi, Akiko Tajiri & Jun Ota. (2021) Throughput analysis of conveyor systems involving multiple materials based on capability decomposition. Computers in Industry 132, pages 103526.
Crossref
Alexandre Brandwajn & Thomas Begin. (2019) First-come-first-served queues with multiple servers and customer classes. Performance Evaluation 130, pages 51-63.
Crossref
Peter Buchholz & Jan Kriege. (2017) Fitting correlated arrival and service times and related queueing performance. Queueing Systems 85:3-4, pages 337-359.
Crossref
Attahiru S. AlfaAttahiru S. Alfa. 2016. Applied Discrete-Time Queues. Applied Discrete-Time Queues 307 322 .
Bara Kim & Jeongsim Kim. (2015) A single server queue with Markov modulated service rates and impatient customers. Performance Evaluation 83-84, pages 1-15.
Crossref
Bara Kim & Jeongsim Kim. (2014) A batch arrival queue with impatient customers . Operations Research Letters 42:2, pages 180-185.
Crossref
Qi-Ming HeQi-Ming He. 2014. Fundamentals of Matrix-Analytic Methods. Fundamentals of Matrix-Analytic Methods 235 305 .
Saranga Menike, Pradeepa Yahampath, Athula Rajapakse & Attahiru Alfa. (2013) Queuing-theoretic modeling of a PMU communication network. Queuing-theoretic modeling of a PMU communication network.
Benny Van Houdt. (2012) Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience. European Journal of Operational Research 220:3, pages 695-704.
Crossref
Benny Van Houdt. (2012) A matrix geometric representation for the queue length distribution of multitype semi-Markovian queues. Performance Evaluation 69:7-8, pages 299-314.
Crossref
Qiming He. (2012) Analysis of a continuous time SM[K]/PH[K]/1/FCFS queue: Age process, sojourn times, and queue lengths. Journal of Systems Science and Complexity 25:1, pages 133-155.
Crossref
Juan F. Pérez & Benny Van Houdt. (2011) Quasi-birth-and-death processes with restricted transitions and its applications. Performance Evaluation 68:2, pages 126-141.
Crossref
Benny Van Houdt. (2010) A Phase-Type Representation for the Queue Length Distribution of a Semi-Markovian Queue. A Phase-Type Representation for the Queue Length Distribution of a Semi-Markovian Queue.
Juan F. Perez & Benny Van Houdt. (2009) Exploiting Restricted Transitions in Quasi-Birth-and-Death Processes. Exploiting Restricted Transitions in Quasi-Birth-and-Death Processes.
Qi-Ming He. (2005) Age Process, Workload Process, Sojourn Times, and Waiting Times in a Discrete Time SM[K]/PH[K]/1/FCFS Queue. Queueing Systems 49:3-4, pages 363-403.
Crossref
B. Van Houdt & C. Blondia. (2005) QBDs with marked time epochs: a framework for transient performance measures. QBDs with marked time epochs: a framework for transient performance measures.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.