Theoretical Analysis Of Two Types Of Queuing Model

Many scholars have also analyzed the queuing model established under vacation or repair deeply, and drawn the theoretical results and numerical analysis. But few studies queuing model with blocking in arrival process. And even analysis of queuing model with preparation is still a blank. Therefore, this research has important practical significance and theoretical significance.In this paper, two types of queuing systems are studied, namely M/M/c/N queuing model with blocking in arrival process and M/M/m/ +? queuing system with preparation of a probability p by customers. These are the new queuing models which are to promote classical queuing model. They are not only more flexible in the application, but also an innovative study of queuing theory. The main contents are as follows:The M/M/c/N queuing system with Blocking in Arrival process is considered. Based on the M/M/c/N queuing model, the random blocking process and the random smooth process are added to the arrival process. The Markov process method and state transition diagram are used to obtain the steady-state probability equations. Then we get the matrix solutions of steady-state probability equations. Some performance measures of the system are presented. Finally, numerical examples are given by using matlab software, and we discuss the impact of the random blocking process and the random smooth process on the system.Then Queuing system with preparation of a probability p by customers is considered in this paper.Customers arrive alone and every arriving customer queue a single queue. after queuing,customers either occupy servers and through the process of preparing before receiving services with a probability p or directly receive services with a probability 1-p.First, the Markov process method and state transition diagram are used to obtain the steady-state probability equations. Secondly, QBD process theory is used to get the stationary distribution conditions and the matrix geometric solution. Someperformance measures of the system are presented, such as the expected number of customers in the queue, the expected number of customers in the system, the probability without waiting. Finally the numerical solution of system metrics is obtained to analysis the system efficiency to provide a theoretical basis for the practical application.