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 .

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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
Mots-clés : Queueing models, matrix analytic method, performance measures, cost model, optimisation 
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     title = {A matrix geometric solution of a multi-server queue with waiting servers and customers' impatience under variant working vacation and vacation interruption},
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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 . https://geodesic-test.mathdoc.fr/item/YJOR_2023_33_3_a3/