Critically Loaded Time-Varying Multi-Server Queues: Computational Challenges and Approximations

In this paper, we consider time-varying multi-server queues with abandonment and retrials. For their performance analysis, fluid and diffusion limits utilizing strong approximations have been widely used in the literature. Although those limits are asymptotically exact, they may not accurately approximate performance of multi-server queues even if the number of servers is large. To address that concern, this paper focuses on developing a methodology by taking fluid and diffusion limits in a non-traditional fashion. We show that our approximation is significantly more accurate and also asymptotically true. We illustrate the effectiveness of our methodology by performing several numerical experiments. Key words: transient analysis; multi-server queues; nearly critically loaded; uniform acceler-ation; strong approximations 1