In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quas...In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quasi-birth-anddeath(QBD)process with countably phases.Using the operator-geometric solution method,we first give the expression of the operator and the joint stationary distribution.Then we obtain the probability generating function(PGF)for stationary queue length distribution and sojourn time distribution,respectively.展开更多
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
基金This work was supported by the National Natural Science Foundation of China(No.61174160)Post-Doctoral Science Foundation of Central South University(No.125011)The authors are grateful to the three anonymous referees and the editor for their careful reading and invaluable comments and suggestions,which are helpful to improve the paper.This research completed when the first author was a post-doctoral fellow in School of Mathematics,Central South University。
文摘In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quasi-birth-anddeath(QBD)process with countably phases.Using the operator-geometric solution method,we first give the expression of the operator and the joint stationary distribution.Then we obtain the probability generating function(PGF)for stationary queue length distribution and sojourn time distribution,respectively.
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.
