Equilibrium Analysis Of Queuing System With Capacity Constraints

Queuing theory,also known as stochastic service system theory,is one of the branches of operations research.It is a mathematical theory and method that mainly studies the phenomenon of stochastic dispersion and the working process of stochastic service system.Due to the constraints of system capacity,when the number of people in the system exceeds the capacity of the system,customers who subsequently arrive will not be able to enter the system to receive services.This will not only bring corresponding losses to the service system,but also lead to a decline in customer satisfaction,which will affect the sustainable development of service providers.The thesis analyzes the impact of the impatient characteristics of customers and -policy working vacation for queues with capacity constraints on the system.The main research contents are as follows:First,consider the problem of capacity-constrained queuing systems with balking and reneging.Among them,balking and reneging are two manifestations of the customer dissatisfaction queuing system.Balking means that the customer chooses to give up joining the queue because they cannot get service immediately after arriving at the queuing system;Reneging means that the customer chooses to withdraw from the queuing system halfway before accepting the service because he can not stand the longer waiting time after joining the queuing system.According to the different levels of information that customers observe when they arrive at the system,we discuss them in different situations and establish corresponding queuing system models.The Markov process theory is used to construct the system's steady-state probability equations,and the system performance indicators such as the expected sojourn time of a customer,the expected number of customers in the system and the expected social benefit per unit time are derived.Through numerical simulation experiments,the effects of different parameters of the system,such as arrival rate,service rate,number of servers,and system capacity,on the system performance are analyzed,which provides a basis for decision-making in improving customer satisfaction and social benefit of the service system.Then,in addition to considering the customer's impatient characteristics,this thesis also studies the capacity-constrained queuing system model with -policy working vacation mechanism.The so-called -policy working vacation mechanism means that the server starts to enter vacation when the queuing system is empty.When the number of customers in the system is not less than ,the system starts to change into normal working state until all customers in the system are served,the system will go on vacation again.The system server has a higher service rate in the normal working state and a lower service rate in the vacation state.According to the different levels of information that customers observe when they arrive at the system,it can be divided into almost unobservable situations and fully unobservable situations to study the problem.In the case of almost unobservable,the system equilibrium equations are set up by using Markov process theory,and the distribution expressions of the indexes such as the expected sojourn time of a customer,the expected number of customers in the system.In the case of fully unobservable,the influence of the changes of different system parameters on the system performance is analyzed through numerical simulation experiments,so as to provide the corresponding decision support for the service providers to set up the service system structure reasonably and keep the system running optimally,so as to realize the optimization of the resource utilization of the service system.