We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digita...We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.展开更多
This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. U...This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n^+ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0^+, n^+] from any initial state. Meanwhile, the relationship among departure process, server's state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures,including the expected length of server busy period, server's actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N*for minimizing the system cost under a given cost structure.展开更多
文摘We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.
基金supported by the National Natural Science Foundation of China under Grant Nos.71571127and 71171138
文摘This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n^+ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0^+, n^+] from any initial state. Meanwhile, the relationship among departure process, server's state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures,including the expected length of server busy period, server's actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N*for minimizing the system cost under a given cost structure.
