Strategic Bidding in an Accumulating Priority Queue: Equilibrium Analysis

TL;DR

This paper analyzes strategic priority bidding in an accumulating priority queue, deriving equilibrium behaviors and proposing a pricing mechanism to improve efficiency in both homogeneous and heterogeneous customer scenarios.

Contribution

It provides explicit equilibrium solutions for homogeneous customers, characterizes equilibria for heterogeneous cases, and introduces a pricing scheme that aligns priority rates with a $C ext{mu}$ rule.

Findings

Explicit Nash equilibrium for homogeneous customers.

Characterization of equilibria in heterogeneous cases.

Pricing mechanism that improves efficiency and enforces priority order.

Abstract

We study the strategic purchasing of priorities in a time-dependent accumulating priority M/G/$1$ queue. We formulate a non-cooperative game in which customers purchase priority coefficients with the goal of reducing waiting costs in exchange. The priority of each customer in the queue is a linear function of the individual waiting time, with the purchased coefficient being the slope. The unique pure Nash equilibrium is solved explicitly for the case with homogeneous customers. A general characterisation of the Nash equilibrium is provided for the heterogeneous case. It is shown that both avoid the crowd and follow the crowd behaviours are prevalent, within class types and between them. We further present a pricing mechanism that ensures the order of the accumulating priority rates in equilibrium follows a $C\mu$ type rule and improves overall efficiency.