We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle...We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle,a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions,the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.展开更多
This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediatel...This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the jth vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability （l-p）. For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds （N＊,J＊） that minimize the cost function. Some numerical examples are also presented.展开更多
文摘We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle,a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions,the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.
文摘This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the jth vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability （l-p）. For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds （N＊,J＊） that minimize the cost function. Some numerical examples are also presented.
