35 - Comparison of Static Maximum Likelihood Origin-destination Formulations

Abstract

Initially, the two basic formulations for estimating the most likely origin-destination (O-D) demand (as defined by the maximum entropy/minimum information) are presented and discussed in terms of logic behind each of the formulations. These formulations include the maximum entropy/minimum information associated with the O-D matrix (termed the trip formulation) and the maximum entropy/minimum information associated with the link flows (termed the volume formulation). These formulations are described in terms of how they are derived and any simplifying assumptions that were made in order to analytically solve the basic formulation. After presenting the alternative formulations for solving the synthetic O-D problem and the associated simplifying assumptions, the following section investigates the consistency of the two formulations (trip and volume formulation) for two simple hypothetical networks, one that ensures a constant total demand and another that presents a variable total demand. The reason for selecting these simple networks is to be able to enumerate the solution space in formulation. Furthermore, the various formulations are tested for a number of cases including (1) the impact of seed O-D scaling on the final solution; (2) the impact of the seed O-D feasibility on the final O-D table estimate; and (3) the impact of the lack of flow continuity on the final solution. This paper presented the various maximum likelihood static O-D estimation formulations. The various formulations and solution algorithms for solving the synthetic O-D problem were compared considering the routes are know a priori under a number of conditions: (1) when the total number of trips is constant versus variable; (2) when the seed matrix is feasible versus infeasible; and (3) when flow continuity is or is not satisfied, and finally conclusions are presented.