A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue ...A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.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
This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times ...This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times and inter-retrial times are all exponentially distributed. If the number of customers in orbit is equal to or less than a certain threshold, the service rate is set in a low value and it also can be switched to a high value once this number exceeds the threshold. The stationary distribution and two performance measures are obtained through the partial generating functions. It is shown that this state-dependent service policy degenerates into a classic retrial queueing system without control policy under some conditions. In order to achieve the social optimal strategies, a new reward-cost function is established and the global numerical solutions, obtained by Canonical Particle Swarm Optimization algorithm, demonstrate that the managers can get more benefits if applying this state-dependent service policy compared with the classic model.展开更多
文摘A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.71571014 and 71390334
文摘This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times and inter-retrial times are all exponentially distributed. If the number of customers in orbit is equal to or less than a certain threshold, the service rate is set in a low value and it also can be switched to a high value once this number exceeds the threshold. The stationary distribution and two performance measures are obtained through the partial generating functions. It is shown that this state-dependent service policy degenerates into a classic retrial queueing system without control policy under some conditions. In order to achieve the social optimal strategies, a new reward-cost function is established and the global numerical solutions, obtained by Canonical Particle Swarm Optimization algorithm, demonstrate that the managers can get more benefits if applying this state-dependent service policy compared with the classic model.
