Queue Models With Time-varying Arrival Rates And Customers Loss

In the real life,due to the limitation of waiting space and other objective environmental factors,a large number of customers would loss in the process of queuing.With different time,the arrival rates of customers would also be different,so it is of great significance to study the queue model of time-varying arrival rates and customers loss under the limited waiting space.Firstly,this thesis studied the G/M/1/k queue model with constant-arrival rates and customers loss in the limited waiting space.By charactered the performance indexes of the queue system and applied the reflection mapping theorem as well as continuous mapping theorem,it got the limit expressions of queue length and customers loss number under the condition of high load.Furthermore,it extended to the multi-service station (?)/G/m/k queue model with the time-varying arrival rates and customers loss,and the queue model with the distribution of H₂^*service time.Secondly,this thesis studied the M _t/M/m/k queue model with customers loss.On the premise of considered the loss rate,it first discussed the M _t/M/m/k queue model without service interruption with time-varying arrival rates by martingale method,and got the martingale expression of the queue length.Then it studied the martingale expression of the service process and loss process in different states when the possibility of service interruption was p.According to the continuous mapping theorem and the properties of Brownian motion,the limit expression of the queue length was obtained.Finally,with the help of MATLAB software,this thesis took(?)/H ₂^*/m/k queue as an example.Through the established algorithm program,and simulated the effect chart of the queue length and the number of customers loss.Then analyzed the change law of the number about people lost in different situations,in the end gave reasonable suggestions combined with the data.