A MODEL OF INTERACTION OF TRAVELERS, PARKING AGENCY AND AUTHORITIES FOR OPTIMIZATION FREE AND PAID PARKING
Keywords:
parking behavior, parking policy, parking fee, parking space, urban transportation, land use planning, game theory
Abstract
The system of two parking lots is researched: paid and free. The task of the city authorities is to determine part of the land for parking agency. The agency selects the best parking fee, and travelers determine which parking to choose. The goals of each participant are different: passengers attempt to minimize the loss of time and parking fees, the agency maximizes profits, and the city thinks about the public good (in this case, about all travelers). The mutual dependence of participants leads to the need to apply game theory to describe their interaction. The mathematical model defines restrictions on the parameters for existence Nash equilibrium. The numerical example that does not contradict the existing picture of the world is considered.
References
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26. Litman, T. A. (2006) Parking taxes: evaluating options and impacts. Victoria transport policy institute, from https://www.vtpi.org/parking_tax.pdf
27. Mingardo, G., Van Wee, B., & Rye, T. (2015) Urban parking policy in Europe: A conceptualization of past and possible future trends. Transportation Research Part A: Policy and Practice, 74, p. 268-281, from https://doi.org/10.1016/j.tra.2015.02.005
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31. He, F., Yin, Y., Chen, Z., & Zhou, J. (2015) Pricing of parking games with atomic players. Transportation Research Part B: Methodological, 73, p. 1-12, from https://doi.org/10.1016/j.trb.2014.12.003
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34. Wenbo, F., & Khan, M. B. (2012) Modeling the parking pricing of multiple parking facilities under different operation regimes. Journal of Transportation Technologies, 2(03), p. 260, from http://dx.doi.org/10.4236/jtts.2012.23028
35. Inci, E., & Lindsey, R. (2015) Garage and curbside parking competition with search congestion. Regional Science and Urban Economics, 54, p. 49-59, from https://doi.org/10.1016/j.regsciurbeco.2015.07.003
36. Arnott, R. On the optimal target curbside parking occupancy rate. Economics of Transportation, 2014, 3(2), p. 133-144, from https://doi.org/10.1016/j.ecotra.2014.07.001
37. Benenson, I., Martens, K., & Birfir, S. (2008) PARKAGENT: An agent-based model of parking in the city. Computers, Environment and Urban Systems, 32(6), p. 431-439, from https://doi.org/10.1016/j.compenvurbsys.2008.09.011
38. Tsai, M. T., & Chu, C. P. (2012)Evaluating parking reservation policy in urban areas: An environmental perspective. Transportation Research Part D: Transport and Environment 17(2), p. 272-272, from https://doi.org/10.1016/j.trd.2011.10.006
39. Dowling, C., Fiez, T., Ratliff, L., & Zhang, B. (2018) How Much Traffic is Searching for Parking? Simulating Curbside Parking as a Network of Finite Capacity Queues., from https://www.thetalkingmachines.com/sites/default/files/feeds/2018/02/22/12/1702.06156.pdf
40. Balijepalli, N. C., Shepherd, S. P., & Kant, P. (2015) Calibration and validation of parking search-time function. In Proceedings of the Institution of Civil Engineers-Transport, Thomas Telford Ltd, 168(1), p. 3-14, from http://eprints.whiterose.ac.uk/82751/
41. Arnott, R., Inci, E., & Rowse, J. (2015) Downtown curbside parking capacity. Journal of Urban Economics, 86, p. 83-97, from https://doi.org/10.1016/j.jue.2014.12.005
42. Koryagin, M. E. (2008) Competition of public transport flows. Automation and Remote Control, 69(8), p.1380-1389, from https://doi.org/10.1134/S0005117908080109
2. Vuchic, V. R. (1999) Transportation for livable cities. Center for urban policy research press, Rutgers University, Brunswick, N.J..
3. Gärling, T., & Schuitema, G. (2007) Travel demand management targeting reduced private car use: effectiveness, public acceptability and political feasibility. Journal of Social Issues, 63(1), p. 139-153, from https://doi.org/10.1111/j.1540-4560.2007.00500.x
4. Shoup, D. C. (1997) The high cost of free parking. Journal of planning education and research, 17(1), p. 3-20, from https://doi.org/10.1177/0739456X9701700102
5. Te Brömmelstroet, M., Bertolini, L. (2008) Developing land use and transport PSS: meaningful information through a dialogue between modelers and planners. Transport policy, 15(4), p. 251–259, from https://doi.org/10.1016/j.tranpol.2008.06.001
6. Balijepalli, N.C., Shepherd, S.P., May, A.D. (2008) Modelling the Choice of Car Parks in Urban Areas and Managing the Demand for Parking. In: 87th Annual Meeting of the Transportation Research Board, 13th-17th January 2008, Washington D.C, from https://core.ac.uk/download/pdf/51657.pdf
7. Larson, R. C., Sasanuma, K. (2010) Urban Vehicle Congestion Pricing: A Review. Journal of Industrial and Systems Engineering, 3(4), p. 227-242, from http://www.jise.ir/article_4013.html
8. Marsden, G.R. (2014) Parking Policy. In Parking Issues and Policies. Transport and Sustainability, Emerald Group Publishing Limited, p. 11 - 32, from https://doi.org/10.1108/S2044-994120140000005016
9. Zhang, X., Huang, H. J., & Zhang, H. M. (2008) Integrated daily commuting patterns and optimal road tolls and parking fees in a linear city. Transportation Research Part B: Methodological, 42(1), p. 38-56, from https://doi.org/10.1016/j.trb.2007.06.001
10. Bates, J., Leibling, D. (2012) Spaced Out, Perspectives on parking policy, London: RAC Foundation, from http://www.racfoundation.org/assets/rac_foundation/content/ downloadables/spaced_out-bates_leibling-jul12.pdf
11. Lam, W. H., Li, Z. C., Huang, H. J., & Wong, S. C. (2006) Modeling time-dependent travel choice problems in road networks with multiple user classes and multiple parking facilities. Transportation Research Part B: Methodological, 40(5), p. 368-395, from https://doi.org/10.1016/j.trb.2005.05.003
12. Guo, L., Huang, S., Zhuang, J., & Sadek, A. W. (2013) Modeling parking behavior under uncertainty: a static game theoretic versus a sequential neo-additive capacity modeling approach. Networks and Spatial Economics, 13(3), p. 327-350, from https://link.springer.com/article/10.1007%2Fs11067-012-9183-1
13. van Nieuwkoop, R. H., Axhausen, K. W., & Rutherford, T. F. (2016) A traffic equilibrium model with paid-parking search. Journal of Transport Economics and Policy (JTEP), 50(3), p. 262-286, from https://www.jstor.org/stable/jtranseconpoli.50.3.0262
14. Shoup, D. C. (2006) Cruising for parking. Transport Policy, 13(6), p. 479-486, from https://doi.org/10.1016/j.tranpol.2006.05.005
15. Calthrop, E., & Proost, S. (2006) Regulating on-street parking. Regional Science and Urban Economics, 36(1), p. 29-48, from https://doi.org/10.1016/j.regsciurbeco.2005.04.002
16. Zheng, N., Geroliminis, N. (2016) Modeling and optimization of multimodal urban networks with limited parking and dynamic pricing. Transportation Research Part B: Methodological, 83, p. 36-58, from https://doi.org/10.1016/j.trb.2015.10.008
17. Rye, T. (2010) Parking management: a contribution towards liveable cities, Module 2c (Sustainable transport: a sourcebook for policy-makers in developing cities). Eschborn, Germany, from http://sutp.transport-nama.org/files/contents/documents/resources/A_Sourcebook/SB2_Land-Use-Planning-and-Demand-Management/GIZ_SUTP_SB2c_Parking-Management_EN.pdf
18. Hollander, Y., Prashker, J. N., & Mahalel, D. (2006) Determining the desired amount of parking using game theory. Journal of urban planning and development, 132(1), p. 53-61, from https://doi.org/10.1061/(ASCE)0733-9488(2006)132:1(53)
19. Millard-Ball, A., Weinberger, R. R., & Hampshire, R. C. (2014) Is the curb 80% full or 20% empty? Assessing the impacts of San Francisco’s parking pricing experiment. Transportation Research Part A: Policy and Practice, 63, p. 76-92, from https://doi.org/10.1016/j.tra.2014.02.016
20. Bagloee, S. A., Asadi, M., & Richardson, L. (2012) Methodology for parking modeling and pricing in traffic impact studies. Transportation research record, 2319(1), p. 1-12, from https://doi.org/10.3141/2319-01
21. Hsu, C. I., & Lin, F. S. (1997) Demand distribution and operating strategies of airport remote and terminal parking facilities. Transportation Planning and Technology, 20(3), p. 219-234 Available from: https://doi.org/10.1080/03081069708717590
22. De Borger, B., & Russo, A. (2017) The political economy of pricing car access to downtown commercial districts. Transportation Research Part B: Methodological, 98, p. 76-93, from https://doi.org/10.1016/j.trb.2016.12.012
23. Zhao, C., Li, S., Wang, W., Li, X., & Du, Y. (2018) Advanced Parking Space Management Strategy Design: An Agent-Based Simulation Optimization Approach. Transportation Research Record, 2672(8), p. 901-910, from https://doi.org/10.1177/0361198118758671
24. Litman, T. (2018) Parking pricing implementation guidelines. Victoria transport policy institute, from https://vtpi.org/parkpricing.pdf
25. Qian, Z. S., Xiao, F. E., & Zhang, H. M. (2011) The economics of parking provision for the morning commute. Procedia-Social and Behavioral Sciences, 17, p. 612-633, from https://doi.org/10.1016/j.sbspro.2011.04.535
26. Litman, T. A. (2006) Parking taxes: evaluating options and impacts. Victoria transport policy institute, from https://www.vtpi.org/parking_tax.pdf
27. Mingardo, G., Van Wee, B., & Rye, T. (2015) Urban parking policy in Europe: A conceptualization of past and possible future trends. Transportation Research Part A: Policy and Practice, 74, p. 268-281, from https://doi.org/10.1016/j.tra.2015.02.005
28. Brueckner, J. K., & Franco, S. F. (2017) Parking and urban form. Journal of Economic Geography, 17(1), p. 95-127, from https://doi.org/10.1093/jeg/lbv048
29. Zong, F., He, Y., & Yuan, Y. (2015) Dependence of parking pricing on land use and time of day. Sustainability, 7(7), p. 9587-9607, from https://doi.org/10.3390/su7079587
30. Takayama, Y., & Kuwahara, M. (2016) Scheduling preferences, parking competition, and bottleneck congestion: A model of trip timing and parking location choices by heterogeneous commuters. MPRA Paper 68938, University Library of Munich, Germany, from https://core.ac.uk/download/pdf/213980139.pdf
31. He, F., Yin, Y., Chen, Z., & Zhou, J. (2015) Pricing of parking games with atomic players. Transportation Research Part B: Methodological, 73, p. 1-12, from https://doi.org/10.1016/j.trb.2014.12.003
32. Kokolaki, E., Karaliopoulos, M., & Stavrakakis, I. (2012) Leveraging information in vehicular parking games, from https://arxiv.org/pdf/1207.5747.pdf
33. Mackowski, D., Bai, Y., & Ouyang, Y. (2015) Parking space management via dynamic performance-based pricing. Transportation Research Part C: Emerging Technologies, 59, p. 66-91, from https://doi.org/10.1016/j.trc.2015.05.021
34. Wenbo, F., & Khan, M. B. (2012) Modeling the parking pricing of multiple parking facilities under different operation regimes. Journal of Transportation Technologies, 2(03), p. 260, from http://dx.doi.org/10.4236/jtts.2012.23028
35. Inci, E., & Lindsey, R. (2015) Garage and curbside parking competition with search congestion. Regional Science and Urban Economics, 54, p. 49-59, from https://doi.org/10.1016/j.regsciurbeco.2015.07.003
36. Arnott, R. On the optimal target curbside parking occupancy rate. Economics of Transportation, 2014, 3(2), p. 133-144, from https://doi.org/10.1016/j.ecotra.2014.07.001
37. Benenson, I., Martens, K., & Birfir, S. (2008) PARKAGENT: An agent-based model of parking in the city. Computers, Environment and Urban Systems, 32(6), p. 431-439, from https://doi.org/10.1016/j.compenvurbsys.2008.09.011
38. Tsai, M. T., & Chu, C. P. (2012)Evaluating parking reservation policy in urban areas: An environmental perspective. Transportation Research Part D: Transport and Environment 17(2), p. 272-272, from https://doi.org/10.1016/j.trd.2011.10.006
39. Dowling, C., Fiez, T., Ratliff, L., & Zhang, B. (2018) How Much Traffic is Searching for Parking? Simulating Curbside Parking as a Network of Finite Capacity Queues., from https://www.thetalkingmachines.com/sites/default/files/feeds/2018/02/22/12/1702.06156.pdf
40. Balijepalli, N. C., Shepherd, S. P., & Kant, P. (2015) Calibration and validation of parking search-time function. In Proceedings of the Institution of Civil Engineers-Transport, Thomas Telford Ltd, 168(1), p. 3-14, from http://eprints.whiterose.ac.uk/82751/
41. Arnott, R., Inci, E., & Rowse, J. (2015) Downtown curbside parking capacity. Journal of Urban Economics, 86, p. 83-97, from https://doi.org/10.1016/j.jue.2014.12.005
42. Koryagin, M. E. (2008) Competition of public transport flows. Automation and Remote Control, 69(8), p.1380-1389, from https://doi.org/10.1134/S0005117908080109
