In this paper, we study a single server queueing system with Coxian-2 service. In Particular, we study M/C-2/M/1 queue with Coxian-2 service and exponential vacation. We assume that units (customers) arrive at t...In this paper, we study a single server queueing system with Coxian-2 service. In Particular, we study M/C-2/M/1 queue with Coxian-2 service and exponential vacation. We assume that units (customers) arrive at the system one by one in a Poisson process and the server provides one-by-one service based on first in first out (FIFO) rule. We obtained the steady state queue size distributions in terms of the probability generating functions, the average number of customers and their average waiting time in the system as well as in the queue.展开更多
For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions...For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.展开更多
An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately ...An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.展开更多
文摘In this paper, we study a single server queueing system with Coxian-2 service. In Particular, we study M/C-2/M/1 queue with Coxian-2 service and exponential vacation. We assume that units (customers) arrive at the system one by one in a Poisson process and the server provides one-by-one service based on first in first out (FIFO) rule. We obtained the steady state queue size distributions in terms of the probability generating functions, the average number of customers and their average waiting time in the system as well as in the queue.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11571052,11731012)the Natural Science Foundation of Hunan Province(Grant Nos.2018JJ2417,2019JJ50405)+3 种基金the Outstanding Youth Foundation of Hunan Province Department of Education(Grant No.18B401)the China Scholarship Council(Grant No.201808430239)Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(Grant No.2018MMAEZD02)the Doctoral Scientific Research Project of Hunan University of Arts and Science.
文摘For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.
基金Supported by the National Natural Science Foundation of China(No.61173119)
文摘An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.
