This paper deals with a retrial queueing system M/M/C/K with exponential abandonment at which positive and negative primary customers arrive according to Poisson processes. This model is of practical interest: it permits to analyze the performance in call centers or multiprocessor computer systems. For model under study, we find the ergodicity condition and also the approximate solution by applying Value Extrapolation method which includes solving of some algebraic system of equations. To this end, we have resolved the algebraic system in question by different numerical methods. We present also numerical results to analyze the system performance.
Accepté le :
DOI : 10.1051/ro/2017059
Keywords: Multiserver retrial queue, abandonment, negative customer, ergodicity condition, value extrapolation, algebraic linear system of equations, invertible matrix, numerical method
Nesrine, Zidani 1 ; Pierre, Spiteri 1 ; Natalia, Djellab 1
@article{RO_2019__53_3_767_0,
author = {Nesrine, Zidani and Pierre, Spiteri and Natalia, Djellab},
title = {Numerical solution for the performance characteristics of the {M/M/C/K} retrial queue with negative customers and exponential abandonments by using value extrapolation method},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {767--786},
year = {2019},
publisher = {EDP Sciences},
volume = {53},
number = {3},
doi = {10.1051/ro/2017059},
mrnumber = {3973143},
zbl = {1423.60146},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2017059/}
}
TY - JOUR AU - Nesrine, Zidani AU - Pierre, Spiteri AU - Natalia, Djellab TI - Numerical solution for the performance characteristics of the M/M/C/K retrial queue with negative customers and exponential abandonments by using value extrapolation method JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 767 EP - 786 VL - 53 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2017059/ DO - 10.1051/ro/2017059 LA - en ID - RO_2019__53_3_767_0 ER -
%0 Journal Article %A Nesrine, Zidani %A Pierre, Spiteri %A Natalia, Djellab %T Numerical solution for the performance characteristics of the M/M/C/K retrial queue with negative customers and exponential abandonments by using value extrapolation method %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 767-786 %V 53 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2017059/ %R 10.1051/ro/2017059 %G en %F RO_2019__53_3_767_0
Nesrine, Zidani; Pierre, Spiteri; Natalia, Djellab. Numerical solution for the performance characteristics of the M/M/C/K retrial queue with negative customers and exponential abandonments by using value extrapolation method. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 3, pp. 767-786. doi: 10.1051/ro/2017059
, Analysis of multiserver retrial queueing system: a martingale approach and an algorithm of solution. Ann. Oper. 141 (2006) 19–52. | MR | Zbl | DOI
, , , and , Performance modeling of finite-source cognitive radio networks. Acta Cybernetica 22 (2016) 617–631. | MR | DOI
, G-networks: a versatile approach for work removal in queueing systems. EJOR 126 (2000) 233–249. | MR | Zbl | DOI
, Retrial queues: an algorithmic approach. J. Egyptian Math. Soc. 17 (2009) 83–101. | MR | Zbl
and , Retrial Queueing Systems: A Comput. Approach. Springer (2008). | Zbl | MR | DOI
, and , Analysis of multiserver queues with constant retrial rate. Eur. J. Oper. Res. 135 (2001) 569–581. | MR | Zbl | DOI
and , On the impact of customer balking, impatience and retrials in telecommunication systems, Comput. Math. Appl. 57 (2009) 217–229. | Zbl | DOI
and , Numerical calculation of the stationary distribution of the main multiserver retrial queue, Ann. Oper. Res. 116 (2002) 41–56. | MR | Zbl | DOI
and , Retrial networks with finite buffers and their application to internet data traffic. Probab. Eng. Inform. Sci. 22 (2008) 519–536. | MR | Zbl | DOI
, An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity. Appl. Math. Model. 34 (2010) 2272–2278. | Zbl | DOI
, Solution for a retrial queueing problem in cellular networks with the Fractional Guard Channel Policy. Math. Comput. Model. 53 (2011) 2059–2066. | Zbl | DOI
, and , An enhanced algorithm to solve multiserver retrial queueing systems with impatient customers. Comput. Industrial Eng. 65 (2013) 719–728. | DOI
, , , and , Generalized truncated methods for an efficient solution of retrial systems. Math. Probl. Eng. 2008 (2008) 183089. | MR | Zbl
, , , and , On the convergence of truncated processes of multiserver retrial queues. Math. Probl. Eng. 2010 (2010) 580349. | MR | Zbl
, A survey of retrial queues. Queueing Syst. 7 (1990) 127–168. | MR | Zbl | DOI
and , Retrial Queues. Chapman and Hall (1997). | Zbl | DOI
, Random neural networks with negative and positive signals and product form solution. Neural Comput. 1 (1989) 502–510. | DOI
, and , Queues with negative arrivals. J. Appl. Probab. 28 (1991) 245–250. | MR | Zbl | DOI
, , , and , Value extrapolation technique to solve retrial queues: a comparative perspective. ETRI J. 30 (2008) 492–494. | DOI
, Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts. J. App. Probab. 24 (1987) 486–494. | MR | Zbl | DOI
, Markov Processess for Stochastic Modeling. Elsevier, Elsevier Academic Press (2009). | MR | Zbl
and , Markov Chains, Theory and Applications. John Wiley Sons (1976). | MR | Zbl
and , On multiserver feedback retrial queues with balking and control retrial rate. Ann. Oper. Res. 141 (2006) 211–232. | MR | Zbl | DOI
, and , On multiserver feedback retrial queue with finite buffer. Appl. Math. Model. 33 (2009) 2062–2083. | MR | Zbl | DOI
, , Analyse numérique matricielle appliquée à l’art de l’ingénieur. Masson Tomes 1 and 2 (1986–1987). | MR | Zbl
and , An approximate method for calculating performance measures of Markov processes. Proc. Valuetools (2006). | DOI
and , Ergodicity, continuity and analyticity of countable Markov chains. Proc. Moscow Math. Soc. 39 (1979) 3–48. | MR | Zbl
, Computer solution of large linear systems. North Holland (1999). | MR | Zbl
and , Numerical investigation of a multiserver retrial model. Queueing Syst. 7 (1990) 169–190. | Zbl | DOI
, Some conditions for ergodicity and recurrence of Markov chains. Operat. Res. 17 (1969) 1058–1061. | MR | Zbl | DOI
, Multiserver retrial queues with two types of non persistent customers. Asia-Pacific J. Oper. Res. 31 (2014) 1440009. | MR | Zbl | DOI
, Asymptotic analysis for markovian queues with two types of non persistent retrial customers. Appl. Math. Comput. 265 (2015) 768–784. | MR | Zbl
and , Multiserver retrial queues with after-call work. Numer. Algebra, Control Optimiz. 1 (2011) 639–656. | MR | Zbl | DOI
and , Performance analysis of call centers with abandonment, retrial and after-call work. Performance Evaluation 80 (2014) 43–62. | DOI
, Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley Series in Probability and Statistics. Wiley (2008). | Zbl
, Iterative methods for sparse linear systems. PWS. Publishing Company (1996). | Zbl
, Markov models with retrials: the calculation of stationary performance measures based on the concept of truncation. Math. Comput. Model. 30 (1999) 207–228. | MR | Zbl | DOI
, Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. Math. Proc. Cambridge Philosoph. Soc. 78 (1975) 125–136. | MR | Zbl | DOI
and , A single server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule, Comput. Industrial Eng. 64 (2013) 84–93. | DOI
, and , The multi-server retrial system with Bernoulli feedback and starting failures. Inter. J. Comput. Math. 92 (2015) 954–969. | MR | Zbl | DOI
Cité par Sources :
