This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service co...This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.展开更多
This paper studies a cold standby repairable system with working vacations and vacation interruption. The repairman's multiple vacations policy, the working vacations policy and the vacation interruption are consi...This paper studies a cold standby repairable system with working vacations and vacation interruption. The repairman's multiple vacations policy, the working vacations policy and the vacation interruption are considered simultaneously. The lifetime of components follows a phase-type(PH) distribution. The repair time in the regular repair period and the working vacation period follow other two PH distributions at different rates. For this system, the vector-valued Markov process governing the system is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying matrixanalytic methods. Finally, a numerical example is given to illustrate the results obtained.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11171019the Fundamental Research Funds for the Central Universities under Grant No.2011JBZ012the Program for New Century Excellent Talents in University under Grant No.NCET-11-0568
文摘This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.
基金supported by the National Natural Science Foundation of China(71371031)
文摘This paper studies a cold standby repairable system with working vacations and vacation interruption. The repairman's multiple vacations policy, the working vacations policy and the vacation interruption are considered simultaneously. The lifetime of components follows a phase-type(PH) distribution. The repair time in the regular repair period and the working vacation period follow other two PH distributions at different rates. For this system, the vector-valued Markov process governing the system is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying matrixanalytic methods. Finally, a numerical example is given to illustrate the results obtained.
