| Title:
|
On transient queue-size distribution in the batch-arrivals system with a single vacation policy (English) |
| Author:
|
Kempa, Wojciech M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
126-141 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a ``usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of the original system on a single vacation cycle is brought to the study of the ``usual'' system. Finally, the renewal theory is used to derive the general result. Moreover, a numerical approach to analytical results is discussed and some illustrative numerical examples are given. (English) |
| Keyword:
|
batch Poisson arrivals |
| Keyword:
|
queue-size distribution |
| Keyword:
|
renewal theory |
| Keyword:
|
single vacation |
| Keyword:
|
transient state |
| MSC:
|
60K25 |
| MSC:
|
90B22 |
| idZBL:
|
Zbl 1288.90011 |
| idMR:
|
MR3195008 |
| DOI:
|
10.14736/kyb-2014-1-0126 |
| . |
| Date available:
|
2014-05-02T06:50:03Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143767 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[11] Kempa, W. M.: Characteristics of vacation cycle in the batch arrival queueing system with single vacations and exhaustive service..Internat. J. Appl. Math. 23 (2010), 4, 747-758. Zbl 1208.60096, MR 2731457 |
| Reference:
|
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| Reference:
|
[13] Kempa, W. M.: The virtual waiting time in a finite-buffer queue with a single vacation policy..Lecture Notes Comp. Sci. 7314 (2012), 47-60. 10.1007/978-3-642-30782-9_4 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[17] Tian, N., Zhang, Z. G.: Vacation Queueing Models. Theory and Applications..Springer, New York 2006. Zbl 1104.60004, MR 2248264 |
| . |
