# Computational schemes for two exponential servers where the first has a finite buffer

RAIRO - Operations Research - Recherche Opérationnelle (2011)

- Volume: 45, Issue: 1, page 17-36
- ISSN: 0399-0559

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topHaviv, Moshe, and Zlotnikov, Rita. "Computational schemes for two exponential servers where the first has a finite buffer." RAIRO - Operations Research - Recherche Opérationnelle 45.1 (2011): 17-36. <http://eudml.org/doc/275090>.

@article{Haviv2011,

abstract = {We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to the second queue. Second, we observe that given that the second server is busy, the two queue lengths are independent. Third, we develop two computational schemes for the stationary distribution of the two-dimensional Markov process underlying this model, one with a complexity of $O(n \log \delta ^\{-1\})$, the other with a complexity of $O(\log n \log ^2\delta ^\{-1\})$, whereδ is the tolerance criterion.},

author = {Haviv, Moshe, Zlotnikov, Rita},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {memoryless queues; quasi birth and death processes; matrix geometric; queueing; performance evaluation; scheduling; queues and service},

language = {eng},

number = {1},

pages = {17-36},

publisher = {EDP-Sciences},

title = {Computational schemes for two exponential servers where the first has a finite buffer},

url = {http://eudml.org/doc/275090},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Haviv, Moshe

AU - Zlotnikov, Rita

TI - Computational schemes for two exponential servers where the first has a finite buffer

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 1

SP - 17

EP - 36

AB - We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to the second queue. Second, we observe that given that the second server is busy, the two queue lengths are independent. Third, we develop two computational schemes for the stationary distribution of the two-dimensional Markov process underlying this model, one with a complexity of $O(n \log \delta ^{-1})$, the other with a complexity of $O(\log n \log ^2\delta ^{-1})$, whereδ is the tolerance criterion.

LA - eng

KW - memoryless queues; quasi birth and death processes; matrix geometric; queueing; performance evaluation; scheduling; queues and service

UR - http://eudml.org/doc/275090

ER -

## References

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