Replications in Stochastic Traffic Flow Models: Incremental Method to Determine Sufficient Number of Runs

Summary

This paper tackles the issues of the minimal and sufficient number of replication needed to evaluate correctly the mean value of a stochastic simulation results but also the shape of the results’ distribution. Indeed, stochasticity is more and more widespread in traffic flow models.

On one hand, microscopic models try to reproduce inter-vehicular deviation through stochastic algorithm. Distributions are sources of randomness. Even if many articles discuss the need for a certain number of simulations to obtain reliable results, they seldom if ever suggest a way to determine this number. Different simulations runs can produce various results due to a randomly assignment of desired speed of each car for example.

On other hand macroscopic models have no individual parameter. This can prevent them from representing some traffic phenomena as roundabout insertion; lane-changing; various desired speed…Stochasticity can overcome those weaknesses. Recently [1] presents a microscopic Lagrangian solution of LWR model allowing individual fundamental diagram.

Thereby, numerous runs have to be computed to estimate the mean value of a measure of effectiveness (MOE) but also to test if the results come from a particular stochastic process. The knowledge of the whole distribution allows us to determine every percentile needed (for example the 5% worse situations).

The aim of this paper is to propose a way to identify such distributions and to estimate the minimal number of replications that one should make to obtain a given confidence level.

We will focus on car-following component of models while lane changing, insertion (ramps, roundabout), and assignment will not be considered. However the proposed methodology can be applied to any components of traffic models.