Strong approximation for a single-station multiserver queue

Based on the background of large call center in life, a single-station multi-server queue is studied in the paper. The performance analysis of large call center is transferred to the established queueing model. Different from others, this paper analyze the model by stochastic limit methods in almost surely convergence queueing regime. Specifically, strong limit theorem is used to obtain the strong approximation of queue length and the total weighted cumulative idle time processes under traffic intensity p ≥ 1 . As a result, the original discrete queueing system is transferred into a continuous Brown Motion (BM), which offers a basis for further research. In words, the results on strong approximation asymptotically describe the original system.