Queue-length Variations In A Two-Restaurant Problem

TL;DR

This study investigates the distribution of queue-length ratios in a two-restaurant model with preferential attachment, revealing robust fixed point distributions and power-law variations under different agent strategies.

Contribution

It introduces a numerical analysis of queue-length ratios in a two-restaurant model, highlighting the emergence of power-law dynamics and fixed point distributions.

Findings

Distribution of fixed points is robust across scenarios.

Queue-length ratios can follow a power-law distribution.

Agent strategy variations influence queue dynamics.

Abstract

This paper attempts to find out numerically the distribution of the queue-length ratio in the context of a model of preferential attachment. Here we consider two restaurants only and a large number of customers (agents) who come to these restaurants. Each day the same number of agents sequentially arrives and decides which restaurant to enter. If all the agents literally follow the crowd then there is no difference between this model and the famous `P\'olya's Urn' model. But as agents alter their strategies different kind of dynamics of the model is seen. It is seen from numerical results that the existence of a distribution of the fixed points is quite robust and it is also seen that in some cases the variations in the ratio of the queue-lengths follow a power-law.