# Revenue maximization with access and information pricing schemes in a partially-observable queueing game

## TL;DR

This paper analyzes customer behavior in an unobservable queueing system, derives equilibrium strategies, and explores revenue-maximizing pricing schemes, showing how customer sensitivity influences optimal pricing policies.

## Contribution

It provides a novel analysis of strategic customer decisions and revenue optimization in partially observable queueing systems, including equilibrium computation and heuristic solutions.

## Key findings

- Equilibrium strategies are proven to exist and be unique.
- Pricing policy depends on customer sensitivity to waiting time.
- Charging for information becomes optimal when customers are highly sensitive.

## Abstract

Today's queueing network systems are more rapidly evolving and more complex than those of even a few years ago. The goal of this paper is to study customers' behavior in an unobservable Markovian M/M/1 queue where consumers have to choose between two strategic decisions about information acquisition before joining or not the queue. According to their decision, customers decide to give up the service (balk the system) or to join the queue. We study the Nash equilibrium strategies: we compute the equilibrium and we prove its existence and uniqueness. Based on this result, we consider the problem of revenue maximization where the provider has to choose between two charging mechanisms: to charge the access to the system or to charge the queue length information to new incoming customers. We propose an heuristic algorithm to solve the considered problem and numerical experiments have been conducted in order to illustrate the result. We show that, depending on the sensitivity of customers to their waiting time, the provider will change the pricing policy used. Particularly, when customers are more sensitive then the provider will charge the information instead of the access.