2023/08/09 by Young Myoung Ko, Ko, Young Myoung, Jamol Pender +3
Business, Management and Accounting · #Advanced Queuing Theory Analysis #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2308.04684
openalex publication_date 2023/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the number of customers that overlap or coincide with a virtual customer in an Erlang-A queue. Our study provides a novel approach that exploits fluid and diffusion limits for the queue to approximate the mean and variance of the number of overlapping customers. We conduct a detailed analysis of the fluid and diffusion limit differential equations to derive these approximations. We also construct new accurate approximations for the mean and variance of the waiting time in the Erlang-A queue by combining fluid limits with the polygamma function. Our findings have important implications for queueing theory and evaluating the overlap risk of more complicated service systems.