Customers' abandonment strategy in an M/G/1 queue

TL;DR

This paper analyzes customer abandonment behavior in an M/G/1 queue, deriving Nash equilibrium strategies based on queue observations and exploring how service time distributions influence equilibrium properties.

Contribution

It introduces a novel threshold-based model for customer abandonment in M/G/1 queues and characterizes the equilibrium conditions and their dependence on service time distributions.

Findings

Nash equilibrium characterized by two threshold sequences

Equilibrium existence and uniqueness depend on service time distribution

Threshold strategies are based on observed queue length and history

Abstract

We consider an M/G/1 queue in which the customers, while waiting in line, may renege from it. We study the Nash equilibrium profile among customers, and show that it is defined by two sequences of thresholds. For each customer, the decision is based on the observed past (which determines from what sequence the threshold is taken), and the observed queue length (which determines the appropriate element in the chosen sequence). We construct the a of equations that has the Nash equilibrium as its solution, and discuss the relationships between the properties of the service time distribution and the properties of the Nash equilibrium, such as uniqueness and finiteness.