| With the continuous improvement of infrastructure and the continuous progress of technology,transportation,medical,multimedia services,production and manufacturing,information technology and other industries are characterized by a gradual expansion in size,a gradual increase in the number of institutions,and a diversification of functions.However,along with the rapid development of each industry,some accompanying problems cannot be ignored.For example,in the transportation industry,the problem of uneven distribution of demand between cabs,short-distance buses and passengers will occur during peak hours such as weekdays and holidays when people are waiting for cars,and during non-peak hours when cars are waiting for people;in the medical industry,the number of patients in hospitals is predominantly high while medical resources are scarce,especially during the COVID-19;in the computer and communication networks,streaming media technologies such as video conferencing,tele-shopping,distance learning,etc.often have a situation where the audio and video transmissions are out of sync at a particular time when the network load is high;In the production manufacturing industry,the supply chain is unstable and insecure due to multiple factors such as COVID-19,Sino US trade war and Ukraine war,etc.,the production plan cannot be delivered on time;in the industries involved in the sharing economy,the supply and demand sides of shared resources cannot be precisely matched,etc.These different application scenarios and practical fields have a common feature: the precise matching problem between resource suppliers and resource demanders,both of which show strong randomness.Therefore,it is of great theoretical significance and practical value to study the precise matching problem of random supply and demand for resource matching in many practical industries.The previous double-ended matching queuing systems have investigated the doubleended Poisson inputs and 1:1 matching structure,while this dissertation studies the matching queuing problems that are closer to the reality,such as the non-Poisson Markov arrival process,the m:n batch matching structure,the matching structure between various types of customers,and a stochastic model of the sharing economy platforms based on the double-ended matching queuing systems.In this dissertation,RG-factorization,matrix geometric solution method and quasi-birth and death(QBD)process are used to study these practical systems,and system performance evaluation methods are given,and effective numerical calculation techniques and related algorithms are developed.The main findings of this dissertation are as follows.(1)Studing a double-ended queue under Markovian arrival process inputs and customers’ impatient behavior.This system can be expressed as a level-dependent QBD process with bidirectional infinite sizes.Firstly,some stable conditions for the double-ended queues are obtained by using mean drift technique.Then,the stationary probability vector of the bilateral QBD process is given by using RG-factorization of Markov process.Based on the stationary probability vector,probability distribution of the queue length and average stationary queue lengths are obtained.Moreover,a Markov process with an absorption state is built for analyzing the sojourn time of any arriving customer in the system,and the average sojourn time is obtained by using the technique of the first passage times and the phase-type(PH)distribution.Finally,some numerical examples are used to illustrate how the performance measures are influenced by some key system parameters.(2)Studing a matched queue with matching batch pair(m,n)and two types of impatient customers,where the two types of customers arrive according to two independent Poisson processes.Once m A-customers and n B-customers are matched as a group,the m+n customers immediately leave the system.Firstly,this matched queue can be expressed as a bidirectional level-dependent QBD process and the stable condition for the double-ended queues is given by using mean drift technique.Then,the stationary probability vector of the bilateral QBD process is given by using RG-factorization of Markov process.Based on the stationary probability vector,probability distribution of the queue length and average stationary queue lengths are obtained.Moreover,to calculate the sojourn time of any customer in the system,the expression for the average sojourn time is given by using the first passage times and the PH distribution.Finally,some numerical examples are used to illustrate how the performance measures are influenced by some key system parameters.(3)Considering a double-ended queue with two types at each side and impatient behaviors.The customers at each side are divided into two types,one of which can match both types at the other side and the other can only match one type at the other side.The customer at one side waits in the queue until the match is completed,while the customer at the other side leaves the system immediately if the match is unsuccessful.Firstly,such a system can be expressed as a level-dependent QBD process with infinitely many phases.The stability condition of the queueing system is given by using the average drift technique.Then,to deal with the level-dependent QBD process,the matrix geometric solution is applied to obtain stationary probability vectors.Based on this,the queue size distributions and the average stationary queue lengths are given.Furthermore,an effective method is given to discuss the sojourn time of any arriving customer and to compute the average sojourn time by using the technique of the first passage times and the PH distribution.Finally,some numerical examples are employed to illustrate how the performance measures are influenced by key system parameters.(4)Based on the above three double-ended queueing models,this dissertation describes and analyzes a stochastic model of sharing economy platforms,in which the resource suppliers in the system are finite,the demand side arrives according to a Markovian arrival process,and the matching rate between the demand and supply sides depends on the number of idle supply sides.Firstly,the stochastic model of sharing economy platforms can be expressed as a level-independent QBD process.Based on this,the matrix-geometric solution is applied to provide a detailed analysis for the queueing model of service platforms,including the system stability,the average stationary numbers of demand sides and of idle supply sides,the average sojourn time of an arriving demand side,and the expected revenues for both the service platform and each supply side.Specifically,a new effective method is proposed for computing the average sojourn time of any demand side by means of the first passage times and the PH distribution.Finally,some numerical examples are employed to verify theoretical results,and demonstrate how the performance measures of the service platform are influenced by some key system parameters.(5)Studing the types of sharing economy platforms and providing an empirical analysis.Firstly,in order to reflect the universality of the general queuing model of the sharing economy platform proposed in this dissertation,the operation process is given for specific online car hailing platforms,bike sharing platforms,car sharing platforms,medical platforms,food delivery platforms,home accommodation platforms,freight platforms,online printing platforms,shared manufacturing platforms,second-hand platforms and sharing elderly care service platforms,and the corresponding contents of each element in the sharing economy queuing model are pointed out.Then,taking the representative and well-developed online car platform as an example,the model is instantiated by obtaining the order data from the actual drops of travel.The matrix-geometric solution is applied to provide a detailed analysis for the stochastic model of online car platforms,including the system stability,the average stationary numbers of idle vehicles and of passengers waiting for receiving services,the average sojourn time of any arriving passenger,and the expected revenues for both the online car platform and each idle vehicle. |
PDF Full Text Request