The constrained gravity model with power function as a cost function

Abstract

A gravity model for trip distribution describes the number of trips between two zones, as a product of three factors, one of the factors is separation or deterrence factor. The deterrence factor is usually a decreasing function of the generalized cost of traveling between the zones, where generalized cost is usually some combination of the travel, the distance traveled, and the actual monetary costs. If the deterrence factor is of the power form and if the total number of origins and destination in each zone is known, then the resulting trip matrix depends solely on parameter, which is generally estimated from data. In this paper, it is shown that as parameter tends to infinity, the trip matrix tends to a limit in which the total cost of trips is the least possible allowed by the given origin and destination totals. If the transportation problem has many cost-minimizing solutions, then it is shown that the limit is one particular solution in which each nonzero flow from an origin to a destination is a product of two strictly positive factors, one associated with the origin and other with the destination. A numerical example is given to illustrate the problem.

A social network perspective on ICT and urban travel

“…They are often used as input for calibration of trip distribution models by comparing the observed TLFD with the modelled one (Bureau of Public Roads, 1965). This way, it is tried to determine the travel pattern between traffic zones and to identify the extent to which generalized costs (distance) are considered by people when travel decisions are made (Arasan and Wermuth, 1996;Samanta and Mazumder, 2006).…”

Balancing mass transit ridership through land use development

“…The deterrence factor is the generalized function of travel costs with the parameters for calibration, described as an impedance to the interaction among two points in space and directly influences the trip distribution as it represents the disincentive to There are many researches that estimate trip distribution by employing the gravity model with different functions of deterrence factors, each one of which takes advantage of its function with the situation of model application. Samanta and Mazumder (2006) employed the gravity model with the cost deterrence described by the power function for estimating a trip distribution matrix. Moreover, the gravity model with an exponential deterrence function proves that the deterrence function is particularly useful for exhibiting the probabilistic trip behavior, it is also consistent with the cost-efficiency principle.…”