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Reliability indices of a geo/G/1/1 erlang loss system with active breakdowns under bernoulli schedule / Zaiming Liu in International journal of management science and engineering management, Vol. 5 N° 6 (Décembre 2010) 

Public ISBD [article]  in International journal of management science and engineering management > Vol. 5 N° 6 (Décembre 2010) . - pp.433-438 Titre : Reliability indices of a geo/G/1/1 erlang loss system with active breakdowns under bernoulli schedule Type de document : texte imprimé Auteurs : Zaiming Liu, Auteur ; Shan Gao, Auteur Année de publication : 2011 Article en page(s) : pp.433-438 Note générale : Management Langues : Anglais (eng) Mots-clés : Erlang  loss  system  Unreliable  server  Bernoulli  schedule  Supplementary  variable  technique Résumé : This paper deals with a discrete-time Erlang loss system, in which breakdowns occur randomly at any instant while the server is serving the customers. As soon as breakdown occurs, the server is sent to repair directly, the customer being served before server breakdown decides, with probability 1−q, to depart the system (impatient customer) and, with complementary probability q(0≤q≤1), to wait for the server to complete his remaining service (patient customer). Additionally, Bernoulli vacation schedule is introduced into this model: after completion of each repair without interrupted customer waiting there or after completion of service, the server either goes for a vacation with probability θ(0≤θ≤1) or may wait for serving the next customer with complementary probability 1 −θ. Firstly, we obtain the z-transforms of the probabilities of server state by using a new type discrete supplementary variable technique. Secondly, we present some performance measures of this model, such as the steady-state availability, failure frequency of the system, mean time to the first failure and the probabilities when the server is idle, busy, down or on vacation. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system. DEWEY : 658 ISSN : 1750-9653 En ligne : http://www.ijmsem.org/OnlineJournal.do/?161.html [article] Reliability indices of a geo/G/1/1 erlang loss system with active breakdowns under bernoulli schedule [texte imprimé] / Zaiming Liu, Auteur ; Shan Gao, Auteur . - 2011 . - pp.433-438. Management Langues : Anglais (eng) in International journal of management science and engineering management > Vol. 5 N° 6 (Décembre 2010) . - pp.433-438 Mots-clés : Erlang  loss  system  Unreliable  server  Bernoulli  schedule  Supplementary  variable  technique Résumé : This paper deals with a discrete-time Erlang loss system, in which breakdowns occur randomly at any instant while the server is serving the customers. As soon as breakdown occurs, the server is sent to repair directly, the customer being served before server breakdown decides, with probability 1−q, to depart the system (impatient customer) and, with complementary probability q(0≤q≤1), to wait for the server to complete his remaining service (patient customer). Additionally, Bernoulli vacation schedule is introduced into this model: after completion of each repair without interrupted customer waiting there or after completion of service, the server either goes for a vacation with probability θ(0≤θ≤1) or may wait for serving the next customer with complementary probability 1 −θ. Firstly, we obtain the z-transforms of the probabilities of server state by using a new type discrete supplementary variable technique. Secondly, we present some performance measures of this model, such as the steady-state availability, failure frequency of the system, mean time to the first failure and the probabilities when the server is idle, busy, down or on vacation. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system. DEWEY : 658 ISSN : 1750-9653 En ligne : http://www.ijmsem.org/OnlineJournal.do/?161.html