We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the exter...We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.展开更多
In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operati...In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.展开更多
An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimi...An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimize the joint cost,the optimal appointment schedule of the fixed number of customers is studied.The joint cost function is composed of customers expected delay time and service availability time.The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time.Furthermore,the effect of impatience on the optimal schedule as well as the total operating cost is studied.The results show that as the impatience rate increases,the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle.In addition,impatient behaviors can increase the joint cost.展开更多
基金Supported by the National Natural Science Foundation of China(No.11671404)the Fundamental Research Funds for the Central Universities of Central South University 2016zzts014
文摘We study M/M/c queues （c =1, 1 〈 c 〈 ∞ and c =∞） in a Markovian environment with impa- tient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.
文摘In this paper,we develop an M/M/c queueing system in a Markovian environment with waiting servers,balking and reneging,under both synchronous single and multiple working vacation policies.When the system is in operative phase j,j=1,K¯,customers are served one by one.Once the system is empty,the servers have to wait a random period of time before leaving,causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate.Using the method of the probability generating functions,we establish the steady-state analysis of the system.Special cases of the queueing model are presented.Then,explicit expressions of the useful system characteristics are derived.In addition,a cost model is constructed to define the optimal values of service rates,simultaneously,to minimize the total expected cost per unit time via a quadratic fit search method.Numerical examples are provided to display the impact of different system characteristics.
基金The National Natural Science Foundation of China(No.71671036)the Scientific Innovation Research of Graduate Students in Jiangsu Province(No.KYLX_0211)
文摘An appointment scheduling problem is studied with the consideration of customer impatience.On the assumption that both the time of leaving queue and the time of service are exponentially distributed,in order to minimize the joint cost,the optimal appointment schedule of the fixed number of customers is studied.The joint cost function is composed of customers expected delay time and service availability time.The expected delay time of each customer in the queue is recursively computed in terms of customer interarrival time.Furthermore,the effect of impatience on the optimal schedule as well as the total operating cost is studied.The results show that as the impatience rate increases,the optimal interarrival time becomes shorter and the interarrival time of the last few customers gradually approaches that of the customers in the middle.In addition,impatient behaviors can increase the joint cost.
