The Research and Application of M/M/1/N Queuing Model with Variable Input Rates, Variable Service Rates and Impatient Customers
How to maintain the service speeds for the business
to make the biggest profit is a problem worthy of study, which is
discussed in this paper with the use of queuing theory. An M/M/1/N
queuing model with variable input rates, variable service rates and
impatient customers is established, and the following conclusions
are drawn: the stationary distribution of the model, the relationship
between the stationary distribution and the probability that there are n
customers left in the system when a customer leaves (not including
the customer who leaves himself), the busy period of the system,
the average operating cycle, the loss probability for the customers
not entering the system while they arriving at the system, the mean
of the customers who leaves the system being for impatient, the
loss probability for the customers not joining the queue due to the
limited capacity of the system and many other indicators. This paper
also indicates that the following conclusion is not correct: the more
customers the business serve, the more profit they will get. At last,
this paper points out the appropriate service speeds the business
should keep to make the biggest profit.
[1] Yu-min LIU ; LI Xiao-fen; WANG Wen-xia; An Ordinary Differential
Equation on the M/M/n Model with Variable Import Rate ; Journal of
Taiyuan University of Science and Technology 2006,27(6):438-440.
[2] Wen-zhi TAI; An explanation of M/M/1 queuing model with variable
input rate; Journal of Southwest University for Nationalities(Natural
Science Edition; 2009,35:485-488
[3] Wen-zhi TAI; GAO Shi-ze; A M/M/1 Queuing Model with Variable Input
Rate; Journal of Chongqing Normal University(Natural Science; 2009,
26:69-72
[4] Chang TAN; M/M/1 Queuing System of Changeable Input Rates -The
probabiltic is k=1/k; Journal of Guizhou University(Natural Science);
2008, 25(5):445-448
[5] Guanghui Xu ; Stochastic Service System; Science Press; 1984,9
[6] S.M.Ross"Application Probability Models with Optimization
Application"Holden-Day. San Francisco,USA 1970
[1] Yu-min LIU ; LI Xiao-fen; WANG Wen-xia; An Ordinary Differential
Equation on the M/M/n Model with Variable Import Rate ; Journal of
Taiyuan University of Science and Technology 2006,27(6):438-440.
[2] Wen-zhi TAI; An explanation of M/M/1 queuing model with variable
input rate; Journal of Southwest University for Nationalities(Natural
Science Edition; 2009,35:485-488
[3] Wen-zhi TAI; GAO Shi-ze; A M/M/1 Queuing Model with Variable Input
Rate; Journal of Chongqing Normal University(Natural Science; 2009,
26:69-72
[4] Chang TAN; M/M/1 Queuing System of Changeable Input Rates -The
probabiltic is k=1/k; Journal of Guizhou University(Natural Science);
2008, 25(5):445-448
[5] Guanghui Xu ; Stochastic Service System; Science Press; 1984,9
[6] S.M.Ross"Application Probability Models with Optimization
Application"Holden-Day. San Francisco,USA 1970
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64237", author = "Quanru Pan", title = "The Research and Application of M/M/1/N Queuing Model with Variable Input Rates, Variable Service Rates and Impatient Customers", abstract = "How to maintain the service speeds for the business
to make the biggest profit is a problem worthy of study, which is
discussed in this paper with the use of queuing theory. An M/M/1/N
queuing model with variable input rates, variable service rates and
impatient customers is established, and the following conclusions
are drawn: the stationary distribution of the model, the relationship
between the stationary distribution and the probability that there are n
customers left in the system when a customer leaves (not including
the customer who leaves himself), the busy period of the system,
the average operating cycle, the loss probability for the customers
not entering the system while they arriving at the system, the mean
of the customers who leaves the system being for impatient, the
loss probability for the customers not joining the queue due to the
limited capacity of the system and many other indicators. This paper
also indicates that the following conclusion is not correct: the more
customers the business serve, the more profit they will get. At last,
this paper points out the appropriate service speeds the business
should keep to make the biggest profit.", keywords = "variable input rates, impatient customer, variable servicerates, profit maximization.", volume = "5", number = "3", pages = "499-4", }