2019/06/18 by Yutaka Sakuma, Sakuma, Yutaka, Hiroyuki Masuyama +3
Business, Management and Accounting · Health Professions · Social Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Healthcare Operations and Scheduling Optimization #Probability (math.PR) #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1906.07326
openalex publication_date 2019/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers a discrete-time single-server queue with a single acceptance period for a Poissonian population of homogeneous customers. Customers are served on a first-come first-served (FCFS) basis, and their service times are independent and identically distributed with a general distribution. We assume that each customer chooses her/his arrival-time slot with the goal of minimizing her/his expected waiting time in competition with other customers. For this queueing game, we derive a symmetric (mixed-strategy) Nash equilibrium; that is, an equilibrium arrival-time distribution of homogeneous customers, where their expected waiting times are identical. We also propose an agent-based model, which simulates the dynamics of customers who try to minimize their waiting times for service. Through numerical experiments, we confirm that this agent-based model achieves, in steady state, an arrival-time distribution similar to the equilibrium arrival-time distribution analytically obtained.