Research On Several Double-Ended Matched Queueing Systems With Inputs’ Behavior Characteristics

With the rapid development of our country in various aspects,the social industrial structure is constantly changing,and various service industries relying on the Internet are increasingly emerging.Matching services in the form of one-to-one,one-to-many and many-to-many for customers with different needs are coming into view,such as online commodity trading systems,maintenance service systems and other service platforms that provide personalized services.With the continuous improvement of the service industry,customer behavior has received more and more attention.In recent years,many scholars have conducted research on this topic.Against the above background,this dissertation is devoted to the research on the double-ended matched queueing systems with inputs’ behavior characteristics.The main structure of this dissertation is arranged as follows:In Chapter 2,a multi-priority one-to-one matched queueing system with delaysensitive heterogeneous input streams is studied.We mainly analyze the strategic behaviors of the input groups and their effects on the system.The asymmetric queueing game problem in this model is studied with the end of customers as the target end.Through analysis,a two-stage equilibrium strategy for each customer composed of payment strategy and probability joining strategy is obtained.Among them,both of the continuous and discrete types of customers are discussed by using the sequential approachm,and it is found that the forms of customers’ equilibrium strategies under the two types are different.Finally,based on the performance indicators obtained,the total social revenue model is constructed and discussed,and the particle swarm optimization algorithm is applied to obtain the optimal combination of two-end basic charges and the optimal total social revenue.In Chapter 3,we study a one-to-many matched queueing system with boundedly rational customers under impatient service mechanism.Considering a situation where one server can match multiple customers,the matching behavior of the server may be triggered in advance due to its impatient matching mechanism.In addition,customers are not accurate in estimating their own sojourn time due to their cognitive bias.In this regard,we develop and discuss the logit model for customers,from which the actual ratio of joining customers is obtained.We find that the trend of the actual ratio of joining customers with respect to the degree of irrationality depends on the expected utility when the customers are completely rational.To solve the steady-state probability,we apply the probability generating function method and the G-matrix method jointly.Then the performance indicators such as the expected queue length and the expected sojourn time of the customers are obtained.Finally,the profit model is constructed and the algorithm is used to solve the optimization of the profit.In Chapter 4,we study the limited service source matched queueing system based on the many-to-many matching mechanism.This chapter extends the matching mechanism of the previous two chapters by considering the matching between multiple customers and multiple servers.In order to characterize the limited service capacity of the actual matching service platform,the number of servers is assumed to be limited and fixed.In this paper,regular and strategic customers are discussed separately,where the former model is the basis of the latter.In the model of regular customers,the mean drift rule is used to determine the necessary and sufficient condition for the existence of the steady state.Subsequently,we use matrix censoring tool and RG-factorization to obtain the steady-state probability,which leads to some performance indicators such as the expected queue length.Further,the conditional expected sojourn time of customers is obtained with the help of LST(Laplace-Stieltjes Transform).In the model of strategic customers,the queue length at both ends can be observed before the customer enters the queue.Through the backward induction,the subgame perfect equilibrium of the system is obtained.The state space of Markov chain under equilibrium presents a finite-dimensional form.Then the steady-state probabilities,along with performance indicators such as the loss probability of customers,are obtained similarly.In both models,we obtain the PH representation and expected value of the conditional clearing time by constructing a Markov chain with absorption states.Finally,several numerical examples are given to illustrate the effect of the parameters on the performance indicators.The numerical results show that the customers’ strategies lead to a shorter expected queue length compared to the regular customers case.In Chapter 5,we study the limited service sources many-to-many matched queueing system with impatient customers and impatient service mechanism.To portray the impatience of customers and the early occurrence of batch matching in actual matching systems,this chapter introduces the impatient customers and the impatient matching mechanism on the basis of the regular customers model in Chapter 4.In terms of methodology,by constructing an infinite-dimensional non-homogeneous quasi birth-and-death process,and using the method of truncated Markov chain to solve the steady-state probability of the system.The expression of the matrix G at any truncation point is given,and a detailed algorithm is provided on how to determine an appropriate truncation point.From this,important performance indicators such as the expected queue length of customers and the probability of the loss probability of customers are obtained.In addition,by reconstructing the two-dimensional and threedimensional Markov chains,the distribution of system clearing time and waiting time for matching,as well as their expected values are obtained.Finally,several numerical examples are conducted to reveal the effects of different parameters on performance indicators.