Analysis Of The Queuing Strategy Of M/G/1 Queueing Systems With Purchase Priority

With the rapid development of social economy and the improvement of people's quality of life,the high quality of service is needed to meet people's requirement.In general,in the service systems with first-come-first-served rule,impatient customers are less satisfied because of the long waiting time.In order to meet people's needs,customers may choose whether to buy priority when they enter the random queuing system.The customers who buy priority need to pay for it and enjoy the priority at the same time.This paper studies the optimal strategy of M /G/ 1 queuing system with non-preemptive priority.First of all,we study the individual team entry strategy and the social optimal strategy in the fully visible situation.The fully visible situation refers to that the arriving customers have the complete information of the system,that is,the priority queue,the number of customers in the common queue and the status of the server can be obtained by arriving customers.In the case of complete visibility,the individual entry strategy is the behavior that customers choose whether to enter the priority queue according to their own income function under the complete information.By analyzing the individual income function of the priority queue,we get the threshold value of the customer entering the priority queue in the fully visible situation.The behavior of the customer entering the priority queue under this threshold is the individual strategy.The social optimal strategy in the fully visible situation is the behavior that the service provider pursues the best profit under the complete information.By analyzing the social benefit function of unit time,we get the system threshold which makes the social benefit optimal in the fully visible situation.The behavior of reaching the threshold by which customers enter the system is the social optimal strategy.Secondly,we study the individual strategy and the social optimal strategy in the completely invisible situation.The completely invisible situation refers to the situation that the arriving customers do not have the complete information of the system,that is,the arriving customers can't get the priority queue,the number of customers in the common queue,and the status of the server,so as to enter the priority queue with probability.In the case of no visible situation,the individual strategy is the behavior of customers entering the priority queue with probability according to theirown profit function without any information.By analyzing the individual income function of the priority queue,we get the probability that the customer chooses to enter the priority queue according to the price of the purchase priority when it is completely invisible.The behavior that the customer enters the priority queue with this probability is the dominant strategy as well as the individual strategy.The social optimal strategy in the completely invisible situation is the behavior that the service provider pursues the best profit without any information.By analyzing the social benefit function of unit time,we can get the probability of customers entering the priority queue when the benefit and waiting cost of priority queue and common queue are different,and the behavior of arriving customers entering the priority queue with this probability is the best social strategy.