Multi-stage Adaptive With Different Arrival Rates And Impatient Customers Leave M / G / 1 Gate Service Systems

Based on the gated queuing system, this paper studies the queuing system with the different arrival rates and impatient waiting customers, and the server takes the multi-level adaptive vacation in the model. By the approach of regenerative-cycle method, the paper obtains the indicators of the system:the stochastic decomposition of queue-length and the waiting-time of a customer on the steady state, the length of the system cycle and the probability of the system in each state respectively.