With Leave Latency Queuing System Performance Analysis And Its Applications

Considering power saving for portable devices of communication wireless networks, we present a new trigger mechanism of vacation.Even if the equipment has completed all servers,it does not immediately enter doze state.Only when there is no new service during idle period,equipment begin to sleep.The vacation starts at the end of idle,we call it a queueing system with vacation delay.In this paper, firstly,the classic conclusions of Markov chains of GI/M/1 type are reminded,and using these conclusions to discuss M/M/1 queue with vacation delay in the third chapter.A sufficient and necessary condition of system ergodicity is obtained.The generating function of steady state queue length and mean queue length are derived, and Laplace Stieltjes of steady state waiting time and mean waiting time of this system are also given.The results show that stochastic decomposition of the steady state queue length and the steady state waiting time are existence.Considering a specific application of wireless communication networks,we study MAP/PH/1 queuing system with vacation delay,and obtain a sufficient and necessary condition of system ergodicity in the forth chapter.Meanwhile,the stationary distribution and mean queue length are also discussed.Finally,in the fifth chapter we sum up this paper and put forward a series of new researches.