Queues With Impatient Policy And Different Arrival Rates

The paper researches queues with impatient policy and different arrival rates.Queues with impatient policy and queues with different arrival rates have been studied by many researchers and many results have been obtained.But queues combining different arrival rates and impatient policy has not been studied.We first time study queueing model with different arrival rates and impatient policy.Firstly,we study a queue M/G/1 with impatient policy and with different arrival rates multiple vacations and set-up times;secondly,we make a further research about this model on the base and study a queue M~X/G/1 with impatient policy and with different arrival rates multiple adaptive vacations and setup times.In the two models,the necessary and sufficient condition were provided in which the queueing system is positive recurrent,and generating function of the steady-state queue length and steady-state waiting time distribution,at the same time,their stochastic decomposition results were also given,moreover,we show the generating function of the busy period,vacation period,set-up period and idle period,then the probability which the server was in various states in the steady-state situation was shown,respectively.At last,we study a queue M~X/G/1 combining different arrival rates, impatient policy,N-policy and set-up time.By the method of supplementary variable,the author solve the state equations and give the form of Z transformation of steady-state queue length distribution,departure time queue length distribution and the system busy beginning time queue length distribution,at the same time,we also give queue indexes such as conditional waiting probability and so on.