# Strategic Arrivals to Queues Offering Priority Service

## TL;DR

This paper analyzes strategic customer behavior in queue systems with fixed start times and priority levels, characterizing equilibria and optimizing revenue through pricing and priority structuring.

## Contribution

It introduces a model for strategic arrivals with heterogeneous customers and multiple priority levels, providing equilibrium analysis and revenue optimization strategies.

## Key findings

- Unique Nash equilibria for heterogeneous arrivals are characterized.
- Customers naturally divide into priority intervals at equilibrium.
- Near-maximum revenue achieved with only three priority queues.

## Abstract

We consider strategic arrivals to a FCFS service system that starts service at a fixed time and has to serve a fixed number of customers, e.g., an airplane boarding system. Arriving early induces a higher waiting cost (waiting before service begins) while arriving late induces a cost because earlier arrivals take the better seats. We first consider arrivals of heterogeneous customers that choose arrival times to minimize the weighted sum of waiting cost and and cost due to expected number of predecessors. We characterize the unique Nash equilibria for this system. Next, we consider a system offering L levels of priority service with a FCFS queue for each priority level. Higher priorities are charged higher admission prices. Customers make two choices - time of arrival and priority of service. We show that the Nash equilibrium corresponds to the customer types being divided into L intervals and customers belonging to each interval choosing the same priority level. We further analyze the net revenue to the server and consider revenue maximizing strategies - number of priority levels and pricing. Numerical results show that with only three queues the server can attain near maximum revenue.