Queue Models With Time-Varying Arrival Rates And Simulations

The law of customer arrival is one of the important factors affecting the queue,and the queue models with time-varying arrival rates are widely applied in different fields.Therefore,it is of great value in theory and practice to study the queue models with time-varying arrival rates.Firstly,the single-server queue modelG_t/GI/1 and multi-server queue model G_t/GI/s with time-varying arrival rates under the condition of heavy traffic are studied.Secondly,the restriction condition about customer abandonment is added to the multi-server queue model G_t/GI/s.Then the queue model G_t/GI/s+M with time-varying arrival rates and customer abandonment is studied.According to the performance indicators of the queue model(including the customer number of arrived,served and abandoned,the queue length and the virtual waiting time etc.).Based on the relationships among the performance indicators of the queue model,the corresponding expressions are constructed.By giving the convergence limit of arrival process and the fluid scale and diffusion scale of each performance index function,the functional weak laws of large numbers and functional central limit theorems of the queue model are established.Then the heavy traffic limits of the performances indicators of the queue model are obtained by applying continuous mapping theorem.And the convergence limits of the performances indicators of the queue model M_t/GI/s+GI in discrete time are obtained by using the knowledge about risk rate function of service time and abandonment time distributions.Furthermore,the multi-server network queue with customer transfer is studied.Finally,some simulations about the queue model G_t/M/s+M with customer abandonment are done by MATLAB software.Given the arrival rate function of the queue model and the distributions of service time and endurance time,the simulation results of waiting time,residence time,queue length and number of abandoned customers are simulated.