In many practical queuing situations reneging and balking can only occur if the number of customers in the system is greater than a certain threshold value. Therefore, in this paper we study a single server Markovian queuing model having customers’ impatience (balking and reneging) with threshold, and retention of reneging customers. The transient analysis of the model is performed by using probability generating function technique. The expressions for the mean and variance of the number of customers in the system are obtained and a numerical example is also provided. Further the steady-state solution of the model is obtained. Finally, some important queuing models are derived as the special cases of this model.
Mots-clés : Transient analysis, steady-state analysis, customers’ impatience, threshold retention
@article{RO_2019__53_5_1861_0, author = {Sharma, Sapana and Kumar, Rakesh and Ammar, Sherif Ibrahim}, title = {Transient and steady-state analysis of a queuing system having customers{\textquoteright} impatience with threshold}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {1861--1876}, publisher = {EDP-Sciences}, volume = {53}, number = {5}, year = {2019}, doi = {10.1051/ro/2018106}, mrnumber = {4021874}, zbl = {1431.90050}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2018106/} }
TY - JOUR AU - Sharma, Sapana AU - Kumar, Rakesh AU - Ammar, Sherif Ibrahim TI - Transient and steady-state analysis of a queuing system having customers’ impatience with threshold JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 1861 EP - 1876 VL - 53 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018106/ DO - 10.1051/ro/2018106 LA - en ID - RO_2019__53_5_1861_0 ER -
%0 Journal Article %A Sharma, Sapana %A Kumar, Rakesh %A Ammar, Sherif Ibrahim %T Transient and steady-state analysis of a queuing system having customers’ impatience with threshold %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 1861-1876 %V 53 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018106/ %R 10.1051/ro/2018106 %G en %F RO_2019__53_5_1861_0
Sharma, Sapana; Kumar, Rakesh; Ammar, Sherif Ibrahim. Transient and steady-state analysis of a queuing system having customers’ impatience with threshold. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1861-1876. doi : 10.1051/ro/2018106. http://www.numdam.org/articles/10.1051/ro/2018106/
The busy period of an M/M/1 queue with balking and reneging. Appl. Math. Model. 37 (2013) 9223–9229. | DOI | MR | Zbl
, and ,Transient analysis of a two-heterogeneous servers queue with impatient behavior. J. Egypt. Math. Soc. 22 (2014) 90–95. | DOI | MR | Zbl
,Transient analysis of M/M/1 queue with impatient behavior and multiple vacations. Appl. Math. Comput. 260 (2015) 97–105. | DOI | MR | Zbl
,Some queuing problems with balking and reneging I. Oper. Res. 11 (1963) 88–100. | DOI | MR | Zbl
and ,Some queuing problems with balking and reneging II. Oper. Res. 11 (1963) 928–937. | DOI | MR | Zbl
and ,M/M/1 queue with impatient customers of higher priority. Queue. Syst. 38 (2001) 49–66. | DOI | MR | Zbl
, and ,Queueing with balking. Biometrika 44 (1957) 360–369. | DOI | MR | Zbl
,Queueing with reneging. Metrika 2 (1959) 186–197. | DOI | MR | Zbl
,Transient solution of M/M/1 queue with balking. Queue. Syst. 13 (1993) 441–448. | DOI | MR | Zbl
, and ,A catastrophic-cum-restorative queuing problem with correlated input and impatient customers. Int. J. Agile Syst. Manage. 5 (2012) 122–131. | DOI
,M/M/1/N queuing system with retention of reneged customers. Pak. J. Stat. Oper. Res. 8 (2012) 859–866. | DOI | MR | Zbl
and ,An M/M/1/N queueing model with retention of reneged customers and balking. AJOR 2 (2012) 1–5.
and ,Transient solution of a two-heterogeneous servers’ queuing system with retention of reneging customers. Bull. Malays. Math. Sci. Soc. 4 (2017) 1–18. | MR
and ,Transient analysis of M/M/c queuing system with balking and retention of reneging customers. Comm. Stat. Theory Methods 47 (2018) 1318–1327. | DOI | MR | Zbl
and ,Geo/Geo/1/N queue with retention of reneging customers. World J. Res. Rev. 4 (2017) 20–21.
,A computationally oriented analysis of the G/M/1 queue. Opsearch 19 (1982) 67–83. | MR | Zbl
and ,Transient behaviour of an M/M/1/N queue. Stochastic Process. Appl. 13 (1982) 327–331. | DOI | MR | Zbl
and ,M/M/s queue with impatient customers and retrials. Appl. Math. Model. 33 (2009) 2596–2606. | DOI | MR | Zbl
and ,Queueing models with balking, reneging and interruptions. Oper. Res. 13 (1965) 596–608. | DOI | MR | Zbl
,Queueing models with balking and reneging in M/G/1 system. Metrika 2 (1967) 173–188. | DOI | MR | Zbl
,Introduction to the Theory of Queues. Oxford University Press, London (1962). | MR | Zbl
,M/D/1 feedback queueing models with retention of reneged customers. IJSR 5 (2016) 405–408. | DOI
, and ,Impatient customer queue with Bernoulli schedule vacation interruption. Comput. Oper. Res. 56 (2015) 1–7. | DOI | MR | Zbl
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