Reneging in a batch arrival two phases queue with random feedback and Coxian-2 vacation
RAIRO - Operations Research - Recherche Opérationnelle, Special issue - Advanced Optimization Approaches and Modern OR-Applications, Tome 50 (2016) no. 4-5, pp. 909-920.

In this system we consider a batch arrival Poisson input with two phases of heterogeneous service with random feedback in each servivce. The first phase of service is essential for all customers, but with a probability tagged customer chose second phase, feedback to tail of original queue or leave the system. Also, after completion of the second phase, with a probability the customer leaves the system, or feedback to tail of original queue. At each service completion epoch, the server may apt to take a vacation with a probability or continue to be available in the system for the next service. The service times are assumed to be general. The vacation period of the server has two heterogeneous phases with Coxian-2 distribution. The vacation times are assumed to be general. When the server goes for vacation, service become unavailable and customers may decide to renege at each vacation times. We assume reneging follow exponential distribution. All stochastic processes involved in this system (service and vacation times) are independent of each other. We derive the PGF’s of the system and by using them the performance measures are obtained. Some numerical approch are examined the validity of results.

DOI : 10.1051/ro/2016001
Classification : 90B22
Mots-clés : Mx/G/1queue, random feedback, reneging, Coxian-2 vacation, mean queue size, mean response time
Zadeh, Abdolrahim Badamchi 1

1 Department of Statistics, Allameh Tabataba’i University, Tehran, Iran.
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Zadeh, Abdolrahim Badamchi. Reneging in a batch arrival two phases queue with random feedback and Coxian-2 vacation. RAIRO - Operations Research - Recherche Opérationnelle, Special issue - Advanced Optimization Approaches and Modern OR-Applications, Tome 50 (2016) no. 4-5, pp. 909-920. doi : 10.1051/ro/2016001. http://www.numdam.org/articles/10.1051/ro/2016001/

I. Adan, A. Economou and S. Kapodistria, Synchronized reneging in queueing systems with vacations. Queueing Systems 62 (2009) 1–33. | DOI | MR | Zbl

E. Altman and U. Yechiali, Analysis of customers’ impatience in queues with server vacations. Queueing Systems 52 (2006) 261–279. | DOI | MR | Zbl

A. Badamchizadeh and G.H. Shahkar, A Two Phases Queue System with Bernoulli Feedback and Bernoulli Schedule Server Vacation. Int. J. Inform. Manag. Sci. 19 (2008) 329–338. | MR | Zbl

A. Badamchizadeh. A Batch Arrival Queue System with Coxian-2 Server Vacations and Admissibility Restricted. Am. J. Ind. Business Manage. 2 (2012) 47–54.

M. Baruah and K. Madan and T. Eldabi, A batch arrival queue with second optional service and reneging during vacation periods. Rev. Investig. Oper. 34 (2013) 244–258. | MR | Zbl

M. Baruah and K. Madan and T. Eldabi, A two stage batch arrival queue with reneging during vacation and breakdown periods. Am. J. Oper. Res. 3 (2013) 570–580.

D.Y. Barrer, Queueing with impatient customers and indifferent clercks. Operat. Res. 5 (1957) 650–656. | DOI | MR | Zbl

D.Y. Barrer, Queueing with impatient customers and ordered service. Operat. Res. 5 (1957) 650–656. | DOI | MR | Zbl

A. Choudhury and P. Medhi, Balking and Reneging in MultserverMarkovian Queueing Systems. Int. J. Math. Oper. Res. 3 (2011) 377–394. | DOI | MR | Zbl

G. Choudhury and M. Paul, A two phase queueing system with Bernoulli feedback. Inform. Manag. Sci. 16 (2005) 35–52. | MR | Zbl

S. Dimou, A. Economou and D. Fakinos The single server vacation queueing model with geometric abandonments. J. Statist. Plann. Infer. 141 (2011) 2863–2877. | DOI | MR | Zbl

F.A. Haight, Queueing with Renaging. Metrika 2 (1959) 180-197. | DOI | MR | Zbl

K.C. Madan and G. Choudhury, A single server queue with two phases of heterogenous service under Bernoulli schedule and a general vcation time. Inform. Manag. Sci. 16 (2005) 1–16. | MR | Zbl

P. Medhi and A. Choudhury, Reneging in Queues Without Waiting Space. Int. J. Appl. Nat. Soc. Sci. 1 (2013) 111–124.

M.R. Salehirad and A. Badamchizadeh, On the multi-phase M/G/1 queueing system with random feedback Cent. Eur. J. Oper. Res. 17 (2009) 131–139. | DOI | MR | Zbl

G.H. Shahkar, A. Badamchizadeh, On M/(G 1 ,G 2 ,...,G k )/V/1/(BS). Far. East. J. Theo. Stat. 20 (2006) 151–162. | MR | Zbl

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