Geodesic
A matrix geometric solution of a multi-server queue with waiting servers and customers' impatience under variant working vacation and vacation interruption
Yugoslav journal of operations research, Tome 33 (2023) no. 3, p. 389 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided
Classification : 60K25, 68M20, 90B22
Keywords: Queueing models, matrix analytic method, performance measures, cost model, optimisation 
@article{YJOR_2023_33_3_a3,
     author = {Ines Ziad and Vijaya P Laxmi and E Girija Bhavani and Amina Angelika Bouchentouf and Shakir Majid},
     title = {A matrix geometric solution of a multi-server queue with waiting servers and customers' impatience under variant working vacation and vacation interruption},
     journal = {Yugoslav journal of operations research},
     pages = {389 },
     year = {2023},
     volume = {33},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2023_33_3_a3/}
}
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Ines Ziad; Vijaya P Laxmi; E Girija Bhavani; Amina Angelika Bouchentouf; Shakir Majid. A matrix geometric solution of a multi-server queue with waiting servers and customers' impatience under variant working vacation and vacation interruption. Yugoslav journal of operations research, Tome 33 (2023) no. 3, p. 389 . http://geodesic.mathdoc.fr/item/YJOR_2023_33_3_a3/