M/M/n Queuing Process In Stochastic Environment

Queuing phenomenon is very common in the field of computer,service industry and communication,especially in the service industry,all service problems will involve queuing.Nowadays,the service industry accounts for an increasing proportion in the national economy,and it is also an important indicator to measure the development situation in one country,and therefore,to study the queue phenomena can be better to management decision making,to provide a better theory support for the development of service industry of the future.In recent decades,and scholars of different service system were studied,and put forward a lot of theoretical results.At the same time,to the study of stochastic process in random environment and into a new stage,and the theoretical innovation is the result of Cogburn environmental factors to be included in the markov chain are discussed,and then by the further research of scholars both at home and abroad,to get the fruitful theoretical results.But for the study of stochastic process in random environment steps will not stop,and there are still many difficulties and work needs to be done.This paper mainly studied the poisson process in random environment,M/M/n queuing process,and its main contents can be divided into the following two aspects:1.Models of Poisson processes in stochastic environments:The Poisson process model in random environment is introduced,and its transition probability is derived.The special relations between the Poisson process and the uniform distribution and ? distribution are discussed respectively.It is proved that the Poisson process in random environment is a special kind of Markov process in random environment when the environmental process is a coordinate process.Finally,the stochastic Kolmogorov equation of the process is given.2.M/M/n Queuing process in stochastic environment:The definition of M/M/n queuing process in stochastic environment is given,the equilibrium condition of M/M/n queuing process in stochastic environment P{?*??*|?(?*)<1}=1.the expressions of L(?*),Lq(?*),K(?*)and their relations are given,finally the random Kolmogorov forward and backward equations of p(?*,t;i,j)of system state process X*are given.