  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.
