Queues with Delayed Information: Analyzing the Impact of the Choice Model Function

TL;DR

This paper investigates queueing systems with delayed information using a generalized multinomial logit choice model, analyzing how different functional forms affect critical delay and system behavior.

Contribution

It extends previous models by generalizing the choice model's functional form, providing new insights into delay effects and their dependence on model specifications.

Findings

Critical delay depends on the choice of functional form.

The functional form can be interpreted as an exponential model with uncertain rate.

Numerical experiments confirm theoretical predictions.

Abstract

In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is exponential. However, in this work we generalize this to different functional forms. In particular, we compute the critical delay and analyze how it depends on the choice of the functional form. We highlight how the functional form of the model can be interpreted as an exponential model where the exponential rate parameter is uncertain. Furthermore, the rate parameter distribution is given by the inverse Laplace-Stieltjes transform of the functional form when it exists. We perform numerous numerical experiments to confirm our theoretical insights.