This paper is concerned with a discrete-time queueing system with -policy and -optional services in which the service station may be subject to failures at random during serving the customers. All the arriving customers require the first essential service, whereas some of them may opt for a second service from the additional services with some probability. As soon as the system becomes empty, the server will not restart the service until the sum of the service times of the waiting customers in the system reaches or exceeds some given positive integer . Applying the total probability decomposition law, renewal theory, and probability generating function technique, the queueing indices and reliability measures are investigated simultaneously in our work. Both the probability generating function of the transient queue length distribution and the explicit formulas of the steady-state queue length distribution at time epoch are derived. Meanwhile, the stochastic decomposition property is presented for the proposed model. Various reliability indices, including the transient and steady-state unavailability, the expected number of breakdowns during , and the equilibrium failure frequency, are discussed. Finally, the optimum value of for minimizing the system cost is numerically discussed under a given cost structure.
Accepté le :
DOI : 10.1051/ro/2016006
Mots-clés : Discrete-time queue, D-policy, unreliable server, secondJ-optional service, cost optimization
@article{RO_2017__51_1_101_0, author = {Lan, Shaojun and Tang, Yinghui}, title = {Analysis of $D$-policy discrete-time {Geo/G/1} queue with second {J-optional} service and unreliable server}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {101--122}, publisher = {EDP-Sciences}, volume = {51}, number = {1}, year = {2017}, doi = {10.1051/ro/2016006}, zbl = {1360.60166}, mrnumber = {3590464}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2016006/} }
TY - JOUR AU - Lan, Shaojun AU - Tang, Yinghui TI - Analysis of $D$-policy discrete-time Geo/G/1 queue with second J-optional service and unreliable server JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 101 EP - 122 VL - 51 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016006/ DO - 10.1051/ro/2016006 LA - en ID - RO_2017__51_1_101_0 ER -
%0 Journal Article %A Lan, Shaojun %A Tang, Yinghui %T Analysis of $D$-policy discrete-time Geo/G/1 queue with second J-optional service and unreliable server %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 101-122 %V 51 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016006/ %R 10.1051/ro/2016006 %G en %F RO_2017__51_1_101_0
Lan, Shaojun; Tang, Yinghui. Analysis of $D$-policy discrete-time Geo/G/1 queue with second J-optional service and unreliable server. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 101-122. doi : 10.1051/ro/2016006. http://www.numdam.org/articles/10.1051/ro/2016006/
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