Analysis Of Queueing System Of Multi-server For Customer Classification Service

Queueing theory is a discipline specializing in the study of congestion phenomenon.Through the study of various factors in the queueing process of various service systems,the optimal design of service system is obtained and the optimal management strategy is proposed for operators.In recent years,the establishment of service rules is a hot issue in the study of queueing theory.Different queueing rules have direct influence on the operating efficiency of queueing system and customer satisfaction.This paper mainly studies the queueing system of two identical server based on the theory of single server and multi-server.Specific work is as follows:Firstly,based on the queueing model of M/M/1,M/M/2,this paper studies the index of the queueing system of two same server for customer classification service.Using the theory of birth and death process,the main queueing indexes such as the average length of the system under steady state and the average waiting time of customers under steady state are obtained.Further,the paper analyzes the arrival rate and service rate of customers in two kinds of service modes,classified service and non-classified service,and finds that there are obvious differences in the system operation indicators of different service modes through numerical comparison.Under reasonable classification strategy,customer classification service can improve the operating efficiency of the system.Secondly,based on the queueing model of GI/M/c,the index of the queueing system of two same server of classified services are analyzed.The main queueing indexes such as the average length of the system under steady state and the average waiting time of customers under steady state are obtained by using the embedded Markov chain,the theory of stationary distribution and Laplace transform.The paper also analyzes the arrival rate and service rate of customers under the two service modes of classified service and non-classified service.Through the comparison of numerical experiments,it is found that under different service modes,the system operation indicators are significantly different,and different classification strategies have a significant impact on the operating efficiency of the system.Overall,for the queuing system of two same service stations,the advantages and disadvantages of different service modes are not absolute.Under the classified service mode,its classification standard also has a significant impact on the operation index of the system.In practical application,the choice of service mode and the determination of customer classification principle and classification standard must proceed from the reality.The analysis of this paper provides a calculation comparison and decision analysis method for the operation design and optimization of similar systems in practice.