2023/10/16 by Wouter J. E. C. van Eekelen, Grani A. Hanasusanto, van Eekelen, Wouter J. E. C. +5
Business, Management and Accounting · Computer Science · Health Professions · #Advanced Queuing Theory Analysis #Cognitive Radio Networks and Spectrum Sensing #FOS: Mathematics #Healthcare Operations and Scheduling Optimization #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2310.09995
openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an M/M/s queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we establish for this setting tight bounds for the expected waiting time. These bounds correspond to an arrival rate that takes only two values. The proofs crucially depend on the fact that the expected waiting time, as function of the arrival rate, has a convex derivative. We apply the novel tight bounds to a rational queueing model, where arriving individuals decide to join or balk based on expected utility and only have partial knowledge about the market size.