A gated service single vacation M/G/1 queue with setup and closedown periods,and different customer arrival rates,is studied in this paper.The probability generating function of the number of systems for customers who...A gated service single vacation M/G/1 queue with setup and closedown periods,and different customer arrival rates,is studied in this paper.The probability generating function of the number of systems for customers who are at the initial moment of service period is analyzed by using a total probability theorem,and the stability condition of the system is obtained.The stationary distribution of the queue length is solved by the regeneration cycle method.The stochastic decomposition of queue length in the steady state is calculated,and the service cycle is obtained.Moreover,classified discussions are established in order to solve the steady-state distribution for the waiting time.The variation of system performance indicators with parameters is analyzed by performing numerical experiments.展开更多
This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject ...This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service.We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution.Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.展开更多
基金supported by the National Natural Science Foundation of China(61973261)the Natural Science Foundation of Jilin Province(20210101151JC).
文摘A gated service single vacation M/G/1 queue with setup and closedown periods,and different customer arrival rates,is studied in this paper.The probability generating function of the number of systems for customers who are at the initial moment of service period is analyzed by using a total probability theorem,and the stability condition of the system is obtained.The stationary distribution of the queue length is solved by the regeneration cycle method.The stochastic decomposition of queue length in the steady state is calculated,and the service cycle is obtained.Moreover,classified discussions are established in order to solve the steady-state distribution for the waiting time.The variation of system performance indicators with parameters is analyzed by performing numerical experiments.
基金Supported by the National Natural Science Foundation of China(71571127)the Training Fund Program of Excellent Paper of Sichuan Normal University([2016]4-1)
文摘This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service.We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution.Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.
