Research Of Queueing Systems With Impatient Customers And PH Distributed Vocation Policy

In recent years,with the development of the society and the progress of technology,queueing phenomenon gradually aroused people's concern in the communication systems,transport systems,computer systems,production management systems and many other fields.So,the research of queueing systems become more and more important.Along with the deeper and development of study on queueing systems,queueing system with impatient customers and vacations has attracted many attentions of researchers.The main purpose of this paper is to study the problem of queueing system with impatient customers and phase type distributed vacation policy.By constructing appropriate level dependent quasi-birth-and-death process and using truncation method,the problem of queueing system with impatient customers and phase type distributed vacation policy is studied.The steady state probability and some key performance measures are obtained.The main results of this paper are as follows:Firstly,a M/M/1 queueing system with impatient customers and phase type distributed vacation policy is studied.The model as a level dependent quasi-birth-and-death process will be formulated.The steady state probability and some key performance measures are obtained by using finite truncation method.The effects of parameters on the some system performance measures is analyzed by giving a numerical example.Then,a M/PH/1 queueing system with impatient customers and phase type distributed vacation policy is studied.A level dependent quasi-birth-and-death process is developed.The steady state probability and some key performance measures are obtained by using finite truncation method.The effects of parameters on the some system performance measures is analyzed by giving a numerical example.When service time has an exponential distribution,an Erlang distribution and a hyperexponential distribution respectively.Finally,a PH/PH/1 queueing system with impatient customers and phase type distributed vacation policy is studied.Using the level dependent quasi-birth-and-death process and finite truncation method,we get the steady state probability and some key performan-ce measures.