In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of ...In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.展开更多
In this paper,we consider a GI/M/1 queue operating in a multi-phase service environment with working vacations and Bernoulli vacation interruption.Whenever the queue becomes empty,the server begins a working vacation ...In this paper,we consider a GI/M/1 queue operating in a multi-phase service environment with working vacations and Bernoulli vacation interruption.Whenever the queue becomes empty,the server begins a working vacation of random length,causing the system to move to vacation phase 0.During phase 0,the server takes service for the customers at a lower rate rather than stopping completely.When a vacation ends,if the queue is non-empty,the system switches from the phase 0 to some normal service phase i with probability qi,i=1,2,⋯,N.Moreover,we assume Bernoulli vacation interruption can happen.At a service completion instant,if there are customers in a working vacation period,vacation interruption happens with probability p,then the system switches from the phase 0 to some normal service phase i with probability qi,i=1,2,⋯,N,or the server continues the vacation with probability 1−p.Using the matrix geometric solution method,we obtain the stationary distributions for queue length at both arrival epochs and arbitrary epochs.The waiting time of an arbitrary customer is also derived.Finally,several numerical examples are presented.展开更多
This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline. Customers arrive according to a semi-Markov arrival process and the service times...This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual types of customers have PH-distributios. A GI/M/1 type Markov process for a generalized age process of batches of customers is constructed. The stationary distribution of the GI/M/1 type Markov process is found explicitly and, consequently, the distributions of the age of the batch in service, the total workload in the system, waiting times, and sojourn times of different batches and different types of customers are obtained. The paper gives the matrix representations of the PH-distributions of waiting times and sojourn times. Some results are obtained for the distributions of queue lengths at departure epochs and at an arbitrary time. These results can be used to analyze not only the queue length, but also the composition of the queue. Computational methods are developed for calculating steady state distributions related to the queue lengths, sojourn times, and waiting times.展开更多
文摘In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.
基金the National Natural Science Foundation of China(No.61773014)。
文摘In this paper,we consider a GI/M/1 queue operating in a multi-phase service environment with working vacations and Bernoulli vacation interruption.Whenever the queue becomes empty,the server begins a working vacation of random length,causing the system to move to vacation phase 0.During phase 0,the server takes service for the customers at a lower rate rather than stopping completely.When a vacation ends,if the queue is non-empty,the system switches from the phase 0 to some normal service phase i with probability qi,i=1,2,⋯,N.Moreover,we assume Bernoulli vacation interruption can happen.At a service completion instant,if there are customers in a working vacation period,vacation interruption happens with probability p,then the system switches from the phase 0 to some normal service phase i with probability qi,i=1,2,⋯,N,or the server continues the vacation with probability 1−p.Using the matrix geometric solution method,we obtain the stationary distributions for queue length at both arrival epochs and arbitrary epochs.The waiting time of an arbitrary customer is also derived.Finally,several numerical examples are presented.
基金This research is supported by the Provincial Natural Science Foundation of Jiangsu under Grant No.BK97047The Education Bureau Foundation of Jiangsu Province under Grant No. 00KJT11003.
基金Supported by the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318204 （国家重点基础研究发展规划（973）） the Cisco Academic Research Project of China （思科教育科研资助项目）
文摘This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual types of customers have PH-distributios. A GI/M/1 type Markov process for a generalized age process of batches of customers is constructed. The stationary distribution of the GI/M/1 type Markov process is found explicitly and, consequently, the distributions of the age of the batch in service, the total workload in the system, waiting times, and sojourn times of different batches and different types of customers are obtained. The paper gives the matrix representations of the PH-distributions of waiting times and sojourn times. Some results are obtained for the distributions of queue lengths at departure epochs and at an arbitrary time. These results can be used to analyze not only the queue length, but also the composition of the queue. Computational methods are developed for calculating steady state distributions related to the queue lengths, sojourn times, and waiting times.
基金Supported by National Science Foundation of China(10801124,11171321,10801188)the Fundamental Research Funds for the Central Universities(WK2040170006)
基金The National Natural Science Foundation of China under Grant No.60975027,60903100the Natural Science Foundation of Ningbo of China under Grant No.2009A610080~~
