Research On The Influence Of Balking,Queue Jumping And Reneging On The Performance Of Priority Queuing System

Queuing phenomena is very common in daily life.There will be a series of queuing problems during the queuing process,such as the congestion and paralysis of the service system caused by too many customers waiting in line,and the conflicts caused by customers choosing to cut the queue to reduce the queue time during the queuing process,etc.,these problems have brought a negative impact on the normal operation of the service system that cannot be ignored.The queuing problem is actually caused by the unreasonable allocation of system resources and the imbalance of public resources.When studying the actual queuing problem,only by in-depth analysis of customer behavior can we better put forward opinions and suggestions for the system,and really play a role in optimizing the system and resource allocation.Therefore,based on the diversity of customer behavior in the queuing system,this thesis studies the influence of customers'balking'queue jumping and reneging behaviors on the performance of the priority queuing system.First of all,this thesis selects the most common behaviors of balking,queue jumping and reneging in the actual queuing,based on the queuing model proposed by Wang Qiangqiang,a multi-service desk queuing model with segmented input rate and service rate is constructed.Among them,the input rate is divided into three stages,the service rate is divided into four stages,and the segment threshold is determined by the income-cost structure function.Then we analyze the model,derive the system steady-state probability and main performance index formulas at different threshold stages according to the birth and death process,and conduct numerical experiments.Through the analysis of the numerical results,the steady-state probability distribution of the system at different threshold stages is consistent with the actual queuing system situation.In the actual queuing system,by adjusting the number of service desks in the system,the gap between the calculated main performance index value and the expected performance index value can be narrowed to achieve optimal control of the system.Secondly,this thesis combines the multi-service-desk queuing model with customer's balking,queue jumping and reneging behavior and the queuing system with preemptive priority to study the multi-service preemptive priority queuing system with balking,queue jumping and reneging.Among them,there are two types of customers in the queuing system:priority customers and ordinary customers,and priority customers have priority over ordinary customers.In this thesis,the quasi birth and death process is used to model the problem and the matrix analysis method is used to solve the model.The steady-state probability expression of the queuing system is deduced and the relevant performance indicators are calculated.Numerical experiments on the queuing system and sensitivity analysis of related parameters show that the average queue length of ordinary customers is positively correlated with the arrival rate of priority customers,and negatively correlated with the reneging rate and the service rate of priority customers.In addition,the three behaviors of customers balking,queue jumping and reneging have a significant impact on the performance indicators of the queuing system.Therefore,this thesis proposes to limit the number of people to enter the system in time periods and formulate service plans for priority customers,streamline the service process to adjust the system's queue length,improve the service efficiency of the system,and achieve the purpose of system optimization.Finally,this thesis summarizes and prospects.Based on the actual queuing process,this thesis considers various factors to construct a model to make it fit the actual situation as much as possible.However,the model research only conducts theoretical analysis and numerical analysis,and actual cases can be selected for analysis in subsequent research.And the model only considers the two-level priority customer type,and it is the case of preemptive priority.In the future,it can be promoted in the direction of multi-priority,non-preemptive priority.