This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed...This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed： 1） The probability that the server is in a ＂generalized busy period＂ at time n; 2） The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3） The expected number of service station failures during the time interval （0, hi, and the steady state failure frequency of the service station; 4） The expected number of service station breakdowns in a server＇s ＂generalized busy period＂. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.展开更多
This paper examines an M[x]/G/1 queueing system with an unreliable server and a delayed repair, in which the server operates a randomized vacation policy with multiple vacations. Whenever the system is empty, the serv...This paper examines an M[x]/G/1 queueing system with an unreliable server and a delayed repair, in which the server operates a randomized vacation policy with multiple vacations. Whenever the system is empty, the server immediately takes a,vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 -p. Whenever one or more customers arrive when the server is idle, the server immediately starts providing service for the arrivals. The server may also meet an unpredictable breakdown and the repair may be delayed. For such a system the authors derive the distributions of some important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the busy period initiation epoch, and the distribution of the idle period and the busy period. The authors perform a numerical analysis for changes in the system characteristics, along with changes in specific values of the system parameters. A cost effectiveness maximization model is constructed to explain the benefits of such a queueing system.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos. 71171138,70871084the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.200806360001
文摘This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed： 1） The probability that the server is in a ＂generalized busy period＂ at time n; 2） The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3） The expected number of service station failures during the time interval （0, hi, and the steady state failure frequency of the service station; 4） The expected number of service station breakdowns in a server＇s ＂generalized busy period＂. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.
文摘This paper examines an M[x]/G/1 queueing system with an unreliable server and a delayed repair, in which the server operates a randomized vacation policy with multiple vacations. Whenever the system is empty, the server immediately takes a,vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 -p. Whenever one or more customers arrive when the server is idle, the server immediately starts providing service for the arrivals. The server may also meet an unpredictable breakdown and the repair may be delayed. For such a system the authors derive the distributions of some important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the busy period initiation epoch, and the distribution of the idle period and the busy period. The authors perform a numerical analysis for changes in the system characteristics, along with changes in specific values of the system parameters. A cost effectiveness maximization model is constructed to explain the benefits of such a queueing system.
