Discrete Time Queueing System With Threshold And Vacations

In recent years,the discrete-time queue system plays a more and more important role in the field of communication equipment and wireless networks.For example,In the ATM network,computer communications system uses the fixed length of the cell as the basic unit to transmit messages.Using the discrete-time queuing system to establish models is fitter to the practical cases.At the same time,in the computer messages processing,we set the threshold to adjust and control the transfer of high speed and low speed service.It can not only reduce the cost of system immensely,but also improve the system's transfer efficiency.This paper improves the queue systems further on the basis of the existing literature about threshold policy and the detailed work is as follow:Firstly,this paper investigates a discrete time Geo/Geo/1 queue with single threshold and multiple working vacations.Using quasi birth and death chain and matrix-geometric solution method,we obtain the steady condition of queue length,the distribution of the conditional queue length and waiting time.Furthermore,we derived the result of stochastic decomposition of the queue length and waiting time.Secondly,this paper discusses a discrete time Geo/Geo/1 queue with double thresholds policy and vacations.Using the quasi birth and death chain and matrix-geometric solution method,we obtain the state transition probability matrix of the model.Then,the distribution of systems reliability and the steady number of customers and sojourn time are researched.Furthermore,conditional stochastic decomposition structures of the stationary length and waiting time are derived.Finally,we apply the queue to a virtual channel switching system and present various numerical experiments for the system.Finally,numerical results are offered to analysis the influence of thresholds on the performance.Finally,this paper considers the GI/Geo/1 queue with threshold and multiple working vacations.By using the two-dimensional Markov chain embedded in the time that the stationary queue length is obtained.Based on this,we get the system's stationary expected queue length and expected waiting time.In the end,the performance of the queue is presented with Matlab software.