Multi stage unreliable retrial Queueing system with Bernoulli vacation

[摘要] In this work we considered the Bernoulli vacation in group arrival retrial queues with unreliable server. Here, a server providing service in k stages. Any arriving group of units finds the server free, one from the group entering the first stage of service and the rest are joining into the orbit. After completion of the ith, (i=1,2,...k) stage of service, the customer may go to (i+1)thstage with probability θi, or leave the system with probability qi= 1 - θi, (i = 1,2,...k - 1) and qi= 1, (i = k). The server may enjoy vacation (orbit is empty or not) with probability v after finishing the service or continuing the service with probability 1-v. After finishing the vacation, the server search for the customer in the orbit with probability θ or remains idle for new arrival with probability 1-θ. We analyzed the system using the method of supplementary variable.

[发布机构] Department of Mathematics, School of Advanced Sciences, VIT University, Vellore; 632014, India^1

[效力级别] 工业技术

[关键词] Bernoulli vacations;Multi stage;Retrial queue;Retrial queueing systems;Supplementary variables;Unreliable servers