IDEAS home Printed from https://ideas.repec.org/a/sae/envirb/v39y2012i6p978-990.html

The Implications of Using a Gravity Model to Determine Territory in a Circular Domain

Author

Listed:
  • Hidenori Tamagawa

    (Department of Urban System Science, Graduate School of Urban Environmental Sciences, Tokyo Metropolitan University, Hachioji, 192-0397, Tokyo, Japan)

Abstract

This paper uses a gravity model to determinate the territory of two facilities on a two-dimensional plane and aims to discover its new implications. The recursive process is installed to the model in such a way that the future scale of a facility reflects the present amount of territory. And the facilities can be located in a two-dimensional circular domain so that the hinterland effect is incorporated. As a result, firstly, an ordinary tendency—the so-called weak-to-the-wall phenomenon—is observed. The smaller the distance-decay parameter, the more frequently this monopolization occurs. On the other hand, peculiar variations in the model's behavior are also found with changes in parameter values. A reversal of the facility scale, the coexistence of two facilities even with a small distance-decay parameter, and other novel phenomena also occur with some cases of facility locations and initial scale conditions.

Suggested Citation

  • Hidenori Tamagawa, 2012. "The Implications of Using a Gravity Model to Determine Territory in a Circular Domain," Environment and Planning B, , vol. 39(6), pages 978-990, December.
    • Handle: RePEc:sae:envirb:v:39:y:2012:i:6:p:978-990
    DOI: 10.1068/b38023
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/b38023
    Download Restriction: no
    File URL: https://libkey.io/10.1068/b38023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. David L. Huff, 1963. "A Probabilistic Analysis of Shopping Center Trade Areas," Land Economics, University of Wisconsin Press, vol. 39(1), pages 81-90.
    2. Rijk, F. J. A. & Vorst, A. C. F., 1983. "Equilibrium points in an urban retail model and their connection with dynamical systems," Regional Science and Urban Economics, Elsevier, vol. 13(3), pages 383-399, August.
    3. Fleming, Euan M. & Thiemann, Franziska & Mueller, Rolf A.E., 2011. "Information and Communication Technology and the Global Flow of Wine: A Gravity Model of ICT in Wine Trade," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114353, European Association of Agricultural Economists.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Minoru Osawa & Takashi Akamatsu & Yuki Takayama, 2017. "Harris And Wilson (1978) Model Revisited: The Spatial Period‐Doubling Cascade In An Urban Retail Model," Journal of Regional Science, Wiley Blackwell, vol. 57(3), pages 442-466, June.
    2. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Most likely retail agglomeration patterns: Potential maximization and stochastic stability of spatial equilibria," Papers 2011.06778, arXiv.org, revised Aug 2025.
    3. Sohyun Park & Keumsook Lee, 2021. "Examining the Impact of E-Commerce Growth on the Spatial Distribution of Fashion and Beauty Stores in Seoul," Sustainability, MDPI, vol. 13(9), pages 1-20, May.
    4. Dong, Xiaojing & Ben-Akiva, Moshe E. & Bowman, John L. & Walker, Joan L., 2006. "Moving from trip-based to activity-based measures of accessibility," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(2), pages 163-180, February.
    5. Wieland, Thomas, 2015. "Nahversorgung im Kontext raumökonomischer Entwicklungen im Lebensmitteleinzelhandel: Konzeption und Durchführung einer GIS-gestützten Analyse der Strukturen des Lebensmitteleinzelhandels und der Nahversorgung in Freiburg im Breisgau [Local retail ," MPRA Paper 77145, University Library of Munich, Germany.
    6. Rickard Enström & Olof Netzell, 2008. "Can Space Syntax Help Us in Understanding the Intraurban Office Rent Pattern? Accessibility and Rents in Downtown Stockholm," The Journal of Real Estate Finance and Economics, Springer, vol. 36(3), pages 289-305, April.
    7. Liwei Zhao & Qiaobing Yue & Junhong Liang & Shiyi Cheng, 2025. "Evaluation of Rural Livability Considering Social Interactions and Implications for Rural Revitalization: A Case Study of Ezhou City, China," Sustainability, MDPI, vol. 17(9), pages 1-20, April.
    8. Yang, Xiping & Fang, Zhixiang & Xu, Yang & Yin, Ling & Li, Junyi & Lu, Shiwei, 2019. "Spatial heterogeneity in spatial interaction of human movements—Insights from large-scale mobile positioning data," Journal of Transport Geography, Elsevier, vol. 78(C), pages 29-40.
    9. Paul Cheshire & Christian Hilber & Piero Montebruno & Rosa Sanchis-Guarner, 2018. "Take Me to the Centre of Your Town! Using Micro-geographical Data to Identify Town Centres," CESifo Economic Studies, CESifo Group, vol. 64(2), pages 255-291.
    10. Eacott, Scott, 2024. "School provision, workforce distribution, housing, and the staffing of schools: The case of Sydney, Australia," International Journal of Educational Development, Elsevier, vol. 109(C).
    11. Chang-i Hua & Frank Porell, 1979. "A Critical Review of the Development of the Gravity Model," International Regional Science Review, , vol. 4(2), pages 97-126, December.
    12. Zhuoran Shan & Xuehan Shen & Man Yuan, 2022. "Exploring the Relationship between the Clustering Degree of Children’s Business Formats and the Attractiveness of Commercial Centers in Wuhan by Modifying the Classic Retail Model," Land, MDPI, vol. 11(8), pages 1-21, July.
    13. Lin, Jie & Cromley, Gordon, 2023. "Using the transportation problem to build a congestion/threshold constrained spatial accessibility model," Journal of Transport Geography, Elsevier, vol. 112(C).
    14. Baruch A. Kipnis, 1977. "Center-Hinterland Interrelationships in a Nodal Region: An Input-Output Analysis," Urban Studies, Urban Studies Journal Limited, vol. 14(3), pages 347-351, October.
    15. Weinhold, Ines & Wende, Danny & Schrey, Christopher & Militzer-Horstmann, Carsta & Schang, Laura & Sundmacher, Leonie, 2022. "Assessing patients’ acceptable and realised distances to determine accessibility standards for the size of catchment areas in outpatient care," Health Policy, Elsevier, vol. 126(11), pages 1180-1186.
    16. Jiahui Qin & Shijia Luo & Disheng Yi & Heping Jiang & Jing Zhang, 2022. "Measuring Cluster-Based Spatial Access to Shopping Stores under Real-Time Travel Time," Sustainability, MDPI, vol. 14(4), pages 1-21, February.
    17. Wieland, Thomas, 2014. "Räumliches Einkaufsverhalten und Standortpolitik im Einzelhandel unter Berücksichtigung von Agglomerationseffekten: Theoretische Erklärungsansätze, modellanalytische Zugänge und eine empirisch-ökonometrische Marktgebietsanalyse anhand eines Fallbeisp," MPRA Paper 77163, University Library of Munich, Germany.
    18. Cho, Clare & Volpe, Richard J., "undated". "Independent Grocery Stores in the Changing Landscape of the U.S. Food Retail Industry," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258517, Agricultural and Applied Economics Association.
    19. Jing Yao & Alan T. Murray, 2014. "Locational Effectiveness of Clinics Providing Sexual and Reproductive Health Services to Women in Rural Mozambique," International Regional Science Review, , vol. 37(2), pages 172-193, April.
    20. Vladimir Marianov & H. A. Eiselt & Armin Lüer-Villagra, 2020. "The Follower Competitive Location Problem with Comparison-Shopping," Networks and Spatial Economics, Springer, vol. 20(2), pages 367-393, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:envirb:v:39:y:2012:i:6:p:978-990. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.