Cost optimization analysis for an MX/M/c vacation queueing system with waiting servers and impatient customers

Amina Angelika Bouchentouf ^[1] ; Abdelhak Guendouzi ^[2]
1. [1] Universidad Djillali Liabes de Sidi Bel Abbes
2. [2] Universidad de Saida
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 76, Nº. 2, 2019, págs. 309-341
Idioma: inglés
DOI: 10.1007/s40324-018-0180-2
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Resumen
- This paper deals with the study of an MX/M/c Bernoulli feedback queueing system with waiting servers and two different policies of synchronous vacations (single and multiple vacation policies). During vacation period, the customers may leave the system (reneging), and using certain customer retention mechanism, the reneged customers may be retained in the system. The probability generating function (PGF) has been used to obtain the steady state probabilities of the model. Various performances measures of the system are derived. Then, a cost model is developed. Further, a cost optimization problem is considered using quadratic fit search method. Finally, a variety of numerical illustrations are discussed for the applicability of the model.