Skip to content
Open access

DOUBLY CONSTRAINED GRAVITY MODEL FOR ORIGIN-DESTINATION TRIP DISTRIBUTION: A PYTHON-BASED FOUR-ZONE CASE STUDY

Aug 2026 · International Journal of Science and Research Archive · Vol 20, pp. 685-689 · 0 citations

Abstract

This study presents a reproducible implementation of a doubly constrained gravity model for origin-destination trip distribution. The formulation preserves prescribed trip productions and attractions while representing the effect of generalized travel cost through an exponential deterrence function. A four-zone numerical case is implemented in Python 3.12.7 using iterative balancing of origin and destination factors. For the baseline case, with β = 0.10, the model converges in 16 balancing cycles to a maximum marginal relative error below 10^-10, producing an OD matrix whose row and column totals match the target trip ends simultaneously. A sensitivity analysis for β values from 0.05 to 0.20 shows that stronger cost sensitivity reduces the flow-weighted mean travel cost from 10.25 to 6.79 cost units and increases the intrazonal share from 37.54% to 61.82%. The results demonstrate the practical importance of explicit convergence checks and parameter calibration in gravity-based demand modelling. The paper provides a compact computational framework suitable for model verification, teaching, and as a transparent baseline for larger empirical transport-planning applications.

Read PDF

Similar papers

Open access Oct 2026

A Direct Calibration Framework for Gravity-Based Trip Distribution Using ICT Travel Time Data Types

This study aims to enhance the gravity-based trip distribution calibration framework through the use and adaptation of Information and communication technologies (ICT)-based travel time data types, such as the origin–destination (O-D) travel time matrix (TTM) and partial route (PAR) travel time vector (TTV). The bi-lev...

Kemal Yasin Göka, Halim Ceylan · 0 citations
Open access Aug 2026

Occupancy-Aware High-Speed Rail Pricing with Aggregate Data: A Case Study in China

Aggregate origin–destination data and summary load factors do not identify train-specific flows; imposing each load factor as an exact margin can therefore overstate precision. We develop an auditable high-speed rail pricing framework combining pooled passenger-kilometer entropy completion, an occupancy-aware pivot log...

Yu Wang, Zhen-Zhong Guan, Jia-Ning Liu et al. · 0 citations
Open access Sep 2026

Do Station-Level Ridership Models Travel Through Time? Conditional Transferability and New-Station Limits in Kaohsiung MRT

Station-level direct-demand models relate observed station use to network role, location, service, and catchment attributes. They are used to benchmark station demand and, when an external systemwide forecast is available, to allocate that total across stations. This study examines the temporal stability and conditiona...

Wil Martens, D. Andersson, Hsin-Kun Su · 0 citations
Review Open access Aug 2026

Introducing a tourist tax in a mature destination: Evidence from a beta-binomial model

This study analyzes tourists’ stated willingness to pay (WTP) for a tourist tax using a beta-binomial model. WTP responses take discrete bounded values between €0 and €4 per night, which standard count models with unbounded support cannot accommodate. Our framework allows flexible dispersion patterns and incorporates c...

E. Gómez–Déniz, J. Cazorla-Artiles, C. González-Martel · 1 citation · ⚡1
Preprint Sep 2026

Estimate then Predict: Convex Formulation for Travel Demand Forecasting

Travel demand forecasting is essential for evaluating large-scale infrastructure projects, yet the traditional sequential four-step process can produce inconsistencies across trip distribution, mode choice, and traffic assignment. Although combined models address these inconsistencies, their practical use has been limi...

Youngseo Kim, Gioele Zardini, S. Samaranayake et al. · 6 citations · ⚡1
Review Sep 2026

Travel Mode- and Purpose-Specific Origin-Destination Matrices for England and Wales from Fused Travel Survey and Mobile Network Data

Origin-destination (OD) matrices sit behind much of quantitative transport planning, from model calibration and accessibility analysis to the appraisal of new services and development. The increasing emphasis on place-based solutions requires mobility data that can support decision-making not only at the strategic leve...

Bo-Wen Zhang, Chen Zhong, M. Ma et al. · 0 citations

We use cookies to run the site and, with your consent, for analytics and to show ads. See our Cookie Policy.