Abstract
This paper presents a more general class ofMAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element. The model is analyzed by applying matrix analytic methods for the underlying quasi birth death process. The main result of the paper is the probability-generating function of the number of jobs in the system. Finally, a numerical example provides an insight into the behavior of the model.
| Original language | English |
|---|---|
| Title of host publication | Advances in Intelligent Systems and Computing |
| Publisher | Springer Verlag |
| Pages | 19-27 |
| Number of pages | 9 |
| Volume | 383 |
| ISBN (Print) | 9783319222660 |
| DOIs | |
| Publication status | Published - 2016 |
| Event | 10th International Conference on Queueing Theory and Network Applications, QTNA 2015 - Ha Noi, Ha Long, Viet Nam Duration: Aug 17 2014 → Aug 20 2014 |
Publication series
| Name | Advances in Intelligent Systems and Computing |
|---|---|
| Volume | 383 |
| ISSN (Print) | 21945357 |
Other
| Other | 10th International Conference on Queueing Theory and Network Applications, QTNA 2015 |
|---|---|
| Country | Viet Nam |
| City | Ha Noi, Ha Long |
| Period | 8/17/14 → 8/20/14 |
Keywords
- Dependent arrival and service process
- MAP
- Matrix analytic methods
- QBD
- Stationary analysis
- Vacation queue
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science(all)
Cite this
Exhaustive vacation queue with dependent arrival and service processes. / Horváth, Gábor; Saffer, Zsolt; Telek, M.
Advances in Intelligent Systems and Computing. Vol. 383 Springer Verlag, 2016. p. 19-27 (Advances in Intelligent Systems and Computing; Vol. 383).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Exhaustive vacation queue with dependent arrival and service processes
AU - Horváth, Gábor
AU - Saffer, Zsolt
AU - Telek, M.
PY - 2016
Y1 - 2016
N2 - This paper presents a more general class ofMAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element. The model is analyzed by applying matrix analytic methods for the underlying quasi birth death process. The main result of the paper is the probability-generating function of the number of jobs in the system. Finally, a numerical example provides an insight into the behavior of the model.
AB - This paper presents a more general class ofMAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element. The model is analyzed by applying matrix analytic methods for the underlying quasi birth death process. The main result of the paper is the probability-generating function of the number of jobs in the system. Finally, a numerical example provides an insight into the behavior of the model.
KW - Dependent arrival and service process
KW - MAP
KW - Matrix analytic methods
KW - QBD
KW - Stationary analysis
KW - Vacation queue
UR - http://www.scopus.com/inward/record.url?scp=84946434755&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84946434755&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-22267-7_2
DO - 10.1007/978-3-319-22267-7_2
M3 - Conference contribution
AN - SCOPUS:84946434755
SN - 9783319222660
VL - 383
T3 - Advances in Intelligent Systems and Computing
SP - 19
EP - 27
BT - Advances in Intelligent Systems and Computing
PB - Springer Verlag
ER -