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《Mathematics in Practice and Theory》 2008-11
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An M/G/1 Retrial Queue with Feedback,Second Optional Service and Bernoulli Vacation

CHEN Pei-shu,ZHU Yi-juan,XU Jie(Faculty of Science,Jiangsu University,Zhenjiang Jiangsu 212013,China)  
An M/G/1 retrial queue with feedback,second optional service and Bernoulli vacation schedules is considered.We assume that customers arrive to the system according to a Poisson process with rate λ.Assuming that only the customer at the head of the orbit has priority access to the server,and the retrial time is an arbitrary distribution.All demand the first ″essential″ service,whereas only some of them demand the second ″optional″ service.Just after completion of his service,a coustomer may leave the system or may opt to repeat his service,in which case this customer rejoins the orbit queue.Further,just after completion of a customer′s service the server may take a vacation of random length or may opt to continue staying in the system to serve the next customer.The necessary and sufficient condition for the system stability is derived through embedded Markov chain.The steady-state distributions of the number of customers in the system and orbit are obtained along with method of supplementary variables.We also derived the probability that the server is in idle when retrial,the probability that there is no one in orbit and other performance measures.A general decomposition law for this system is established on condition that the server idle time and vacation time is defined as generalized vacation.
【Fund】: 国家自然科学基金(70571030);; 江苏大学科研启动基金(04JDG11032)
【CateGory Index】: O226
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