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.

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.

DOI : 10.1051/ro/2018106
Classification : 90B22
Mots-clés : Transient analysis, steady-state analysis, customers’ impatience, threshold retention
Sharma, Sapana 1 ; Kumar, Rakesh 1 ; Ammar, Sherif Ibrahim 1

1 
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     title = {Transient and steady-state analysis of a queuing system having customers{\textquoteright} impatience with threshold},
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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://archive.numdam.org/articles/10.1051/ro/2018106/

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