L-Infinity Norm Model for Handling Traffic Count Inconsistencies in Path Flow Estimator

Path Flow Estimator (PFE) is a one-stage network observer proposed to estimate path flows, path travel times, origin-destination (O-D) flows, etc., from traffic counts in a transportation network. Although PFE does not require traffic counts to be collected on all network links when inferring unmeasured traffic conditions, it requires all available counts to be consistent. This requirement is difficult to fulfill in most of real applications due to the errors inherited in data collection and processing. The original PFE handles this issue by specifying appropriate error bounds on the traffic counts. This method enhances the flexibility of PFE by allowing the user to incorporate local knowledge about the network conditions into the estimation process. However, specifying appropriate error bounds for all measured links in a real network application is laborious. In addition, improper specification of the error bounds could lead to biased estimates of the O-D demand. This paper therefore presents an L∞-norm model in PFE capable of internally handling the inconsistency problem within the estimation process. Numerical results are also presented to illustrate the features and applicability of the proposed L∞-norm PFE model.