Comparation of Impedance Functions for Modelling Student Trip Distribution at Surabaya Senior High Schools

Citto Pacama Fajrinia, Nina Saraswati, Verdy Ananda Upa, Anik Budiati

Abstract

Student travel from home to school is an important component of urban mobility because it generates concentrated travel demand during school arrival and dismissal periods. This study compared the Negative Power, Negative Exponential, and Tanner impedance functions in representing student trip-length distributions at four public senior high schools in Surabaya, Indonesia. Primary data were collected through questionnaire-based surveys involving 262 students. Home-to-school travel distances were grouped into 3-km intervals, and the proportion of trips within each interval was calculated for each school. The three functions were calibrated using the observed distributions and evaluated using the Sum of Squared Error (SSE) and Mean Absolute Percentage Error (MAPE). The Tanner function produced the lowest SSE values at all study sites, indicating the smallest aggregate deviation between observed and estimated distributions. In contrast, the Negative Exponential function produced the lowest MAPE values at each school, indicating the lowest relative prediction error. Practically, the findings provide an initial empirical basis for identifying dominant student travel-distance ranges and selecting an impedance function according to the analytical objective. This information can support school accessibility planning, traffic management around school areas, the determination of school service zones, and student transportation planning in Surabaya. The Tanner function is more suitable for representing the aggregate distribution shape, whereas the Negative Exponential function is more appropriate when relative accuracy is prioritised. Detailed planning applications still require additional data on travel modes, travel times, traffic volumes, and road-network conditions.

Keywords

Gravity Model; Impedance Functions; Negative Exponential; Tanner; Trip Distribution

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References

X. Ji, H. Guan, M. Lu, F. Chen, and W. Qin, “International Research Progress in School Travel and Behavior: A Literature Review and Bibliometric Analysis,” Sustainability, vol. 14, no. 14, Art. no. 8857, 2022.

C. Liao and T. Dai, “Is ‘Attending Nearby School’ Near? An Analysis of Travel-to-School Distances of Primary Students in Beijing Using Smart Card Data,” Sustainability, vol. 14, no. 7, Art. no. 4344, 2022.

S. AlQuhtani, “Factors Affecting Active Commuting to School in Sprawled Cities: The Case of Najran City, Saudi Arabia,” Sustainability, vol. 15, no. 12, Art. no. 9562, 2023.

S. Chen, M. Hong, and W. Wei, “A Study of the Influencing Mechanism of Travel Mode Choice for Primary School Students: A Case Study in Wuhan,” Buildings, vol. 15, no. 5, Art. no. 700, 2025.

J. de D. Ortúzar and L. G. Willumsen, Modelling Transport, 4th ed. Chichester, U.K.: John Wiley & Sons, 2011.

I. H. Naser, M. B. Mahdi, F. H. Meqtoof, and H. A. Etih, “Modelling Trip Distribution Using the Gravity Model and Fratar’s Method,” Mathematical Modelling of Engineering Problems, vol. 8, no. 2, pp. 230–236, 2021.

J. O. Rum, Syafi’i, and S. J. Legowo, “Estimasi Parameter Model Gravity dengan Metode Penaksiran Kuadrat Terkecil dan Fungsi Hambatan Eksponensial-Negatif (Studi Kasus Kabupaten Sukoharjo),” Matriks Teknik Sipil, vol. 9, no. 2, pp. 84–90, 2021.

N. D. Pramesti, W. L. Wulandari, B. Riyanto, and K. H. Basuki, “Analisis Distribusi Perjalanan Menggunakan Model Gravitasi Dua Batasan dengan Optimasi Fungsi Hambatan: Studi Kasus Kota Semarang dan Kota Surakarta,” Jurnal Karya Teknik Sipil, vol. 3, no. 1, pp. 228–239, 2014

W. Herijanto and N. Thorpe, “Developing the Singly Constrained Gravity Model for Application in Developing Countries,” Journal of the Eastern Asia Society for Transportation Studies, vol. 6, pp. 1708–1723, 2005.

R. J. Hyndman and A. B. Koehler, “Another Look at Measures of Forecast Accuracy,” International Journal of Forecasting, vol. 22, no. 4, pp. 679–688, 2006.

S. Kim and H. Kim, “A New Metric of Absolute Percentage Error for Intermittent Demand Forecasts,” International Journal of Forecasting, vol. 32, no. 3, pp. 669–679, 2016.

DOI: https://doi.org/10.31284/j.jtm.2026.v7i2.9185

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