Paper Info
Title
Strategic Arrivals To A Queue With Service Rate Uncertainty
Abstract
We study the problem of strategic choice of arrival time to a single-server queue with opening and closing times when there is uncertainty regarding service speed. A Poisson population of customers choose their arrival time with the goal of minimizing their expected waiting times and are served on a first-come first-served basis. There are two types of customers that differ in their beliefs regarding the service-time distribution. The inconsistent beliefs may arise from randomness in the server state along with noisy signals that customers observe. Customers are aware of the two types of populations with differing beliefs. We characterize the Nash equilibrium dynamics for exponentially distributed service times and show how they substantially differ from the model with homogeneous customers. We further provide an explicit solution for a fluid approximation of the game. For general service-time distributions we provide an algorithm for computing the equilibrium in a discrete-time setting. We find that in equilibrium customers with different beliefs arrive during different (and often disjoint) time intervals. Numerical analysis further shows that the mean waiting time increases with the coefficient of variation of the service time. Furthermore, we present a learning agent-based model (ABM) in which customers make joining decisions based solely on their signals and past experience. We numerically compare the long-term average outcome of the ABM with that of the equilibrium and find that the arrival distributions are quite close if we assume (for the equilibrium solution) that customers are fully rational and have knowledge of the system parameters, while they may greatly differ if customers have limited information or computing abilities.
Year
DOI
Venue
2021
10.1007/s11134-020-09683-7
QUEUEING SYSTEMS
Keywords
DocType
Volume
Queueing game, Strategic arrival times, Service rate uncertainty, Agent-based model, Delay estimation and learning
Journal
97
Issue
ISSN
Citations 
3-4
0257-0130
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Liron Ravner100.34
Yutaka Sakuma200.34