Distribution of Deviation Distance to Alternative Fuel Stations

Author(s)
Masashi Miyagawa

ABSTRACT

This paper derives the distribution of the deviation distance to visit an alternative fuel station. Distance is measured as the Euclidean distance on a continuous plane. The distribution explicitly considers the vehicle range and whether the round trip between origin and destination can be made. Three cases are examined: fuel is available at both origin and destination, fuel is available at either origin or destination, and fuel is available at neither origin nor destination. The analytical expressions for the distribution demonstrate how the vehicle range, the shortest distance, and the refueling availability at origin and destination affect the deviation distance. The distribution will thus be useful to estimate the number of vehicles refueled at a station.

This paper derives the distribution of the deviation distance to visit an alternative fuel station. Distance is measured as the Euclidean distance on a continuous plane. The distribution explicitly considers the vehicle range and whether the round trip between origin and destination can be made. Three cases are examined: fuel is available at both origin and destination, fuel is available at either origin or destination, and fuel is available at neither origin nor destination. The analytical expressions for the distribution demonstrate how the vehicle range, the shortest distance, and the refueling availability at origin and destination affect the deviation distance. The distribution will thus be useful to estimate the number of vehicles refueled at a station.

Cite this paper

M. Miyagawa, "Distribution of Deviation Distance to Alternative Fuel Stations,"*American Journal of Operations Research*, Vol. 3 No. 3, 2013, pp. 363-368. doi: 10.4236/ajor.2013.33033.

M. Miyagawa, "Distribution of Deviation Distance to Alternative Fuel Stations,"

References

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[2] M. Melaina and J. Bremson, “Refueling Availability for Alternative Fuel Vehicle Markets: Sufficient Urban Station Coverage,” Energy Policy, Vol. 36, No. 8, 2008, pp. 3233-3241. doi:10.1016/j.enpol.2008.04.025

[3] M. A. Nicholas, S. L. Handy and D. Sperling, “Using Geographic Information Systems to Evaluate Siting and Networks of Hydrogen Stations,” Transportation Research Record, Vol. 1880, 2004, pp. 126-134. doi:10.3141/1880-15

[4] M. A. Nicholas and J. Ogden, “Detailed Analysis of Urban Station Siting for California Hydrogen Highway Network,” Transportation Research Record, Vol. 1983, 2006, pp. 121-128. doi:10.3141/1983-17

[5] Y. Honma and O. Kurita, “A Mathematical Model on the Optimal Number of Hydrogen Stations with Respect to the Diffusion of Fuel Cell Vehicles,” Journal of the Operations Research Society of Japan, Vol. 51, No. 2, 2008, pp. 166-190.

[6] M. Kuby and S. Lim, “The Flow-Refueling Location Problem for Alternative-Fuel Vehicles,” Socio-Economic Planning Sciences, Vol. 39, No. 2, 2005, pp. 125-145. doi:10.1016/j.seps.2004.03.001

[7] M. Kuby, L. Lines, R. Schultz, Z. Xie, J. G. Kim and S. Lim, “Optimization of Hydrogen Stations in Florida Using the Flow-Refueling Location Model,” International Journal of Hydrogen Energy, Vol. 34, No. 15, 2009, pp. 6045-6064. doi:10.1016/j.ijhydene.2009.05.050

[8] S. Lim and M. Kuby, “Heuristic Algorithms for Siting Alternative-Fuel Stations Using the Flow-Refueling Location Model,” European Journal of Operational Research, Vol. 204, No. 1, 2010, pp. 51-61. doi:10.1016/j.ejor.2009.09.032

[9] I. Capar and M. Kuby, “An Efficient Formulation of the Flow Refueling Location Model for Alternative-Fuel Stations,” IIE Transactions, Vol. 44, No. 8, 2012, pp. 622636. doi:10.1080/0740817X.2011.635175

[10] M. Kuby and S. Lim, “Location of Alternative-Fuel Stations Using the Flow-Refueling Location Model and Dispersion of Candidate Sites on Arcs,” Networks and Spatial Economics, Vol. 7, No. 2, 2007, pp. 129-152. doi:10.1007/s11067-006-9003-6

[11] C. Upchurch, M. Kuby and S. Lim, “A Model for Location of Capacitated Alternative-Fuel Stations,” Geographical Analysis, Vol. 41, No. 1, 2009, pp. 85-106. doi:10.1111/j.1538-4632.2009.00744.x

[12] J. G. Kim and M. Kuby, “The Deviation-Flow Refueling Location Model for Optimizing a Network of Refueling Stations,” International Journal of Hydrogen Energy, Vol. 37, No. , 2012, pp. 5406-5420. doi:10.1016/j.ijhydene.2011.08.108

[13] M. J. Hodgson, “The Location of Public Facilities Intermediate to the Journey to Work,” European Journal of Operational Research, Vol. 6, No. 2, 1981, pp. 199-204. doi:10.1016/0377-2217(81)90208-3

[14] M. J. Hodgson, “A Flow-Capturing Location-Allocation Model,” Geographical Analysis, Vol. 22, No. 3, 1990, pp. 270-279. doi:10.1111/j.1538-4632.1990.tb00210.x

[15] O. Berman, R. C. Larson and N. Fouska, “Optimal Location of Discretionary Service Facilities,” Transportation Science, Vol. 26, No. 3, 1992, pp. 201-211. doi:10.1287/trsc.26.3.201

[16] M. J. Hodgson, K. E. Rosing and A. L. G. Storrier, “Applying the Flow-Capturing Location-Allocation Model to an Authentic Network: Edmonton, Canada,” European Journal of Operational Research, Vol. 90, No. 3, 1996, pp. 427-443. doi:10.1016/0377-2217(95)00034-8

[17] O. Berman, D. Bertsimas and R.C. Larson, “Locating Discretionary Service Facilities, II: Maximizing Market Size, Minimizing Inconvenience,” Operations Research, Vol. 43, No. 4, 1995, pp. 623-632. doi:10.1287/opre.43.4.623

[18] I. Averbakh and O. Berman, “Locating Flow-Capturing Units on a Network with Multi-Counting and Diminishing Returns to Scale,” European Journal of Operational Research, Vol. 91, No. 3, 1996, pp. 495-506. doi:10.1016/0377-2217(94)00369-6

[19] W. Zeng, M. J. Hodgson and I. Castillo, “The Pickup Problem: Consumers’ Locational Preferences in Flow Interception,” Geographical Analysis, Vol. 41, No. 1, 2009, pp. 107-126. doi:10.1111/j.1538-4632.2009.00741.x

[20] K. Tanaka and T. Furuta, “A Hierarchical Flow Capturing Location Problem with Demand Attraction Based on Facility Size, and Its Lagrangian Relaxation Solution Method,” Geographical Analysis, Vol. 44, No. 1, 2012, pp. 15-28. doi:10.1111/j.1538-4632.2011.00837.x

[21] O. Berman, “Deterministic Flow-Demand Location Problems,” Journal of the Operational Research Society, Vol. 48, No. 1, 1997, pp. 75-81.

[22] W. Zeng, I. Castillo and M. J. Hodgson, “A Generalized Model for Locating Facilities on a Network with FlowBased Demand,” Networks and Spatial Economics, Vol. 10, No. 4, 2010, pp. 579-611. doi:10.1007/s11067-008-9073-8

[23] M. Miyagawa, “Distributions of Rectilinear Deviation Distance to Visit a Facility,” European Journal of Operational Research, Vol. 205, No. 1, 2010, pp. 106-112. doi:10.1016/j.ejor.2009.12.002

[24] S. Chien and P. Schonfeld, “Optimization of Grid Transit System in Heterogeneous Urban Environment,” Journal of Transportation Engineering, Vol. 123, No. 1, 1997, pp. 28-35. doi:10.1061/(ASCE)0733-947X(1997)123:1(28)

[25] M. M. Aldaihani, L. Quadrifoglio, M. M. Dessouky and R. Hall, “Network Design for a Grid Hybrid Transit Service,” Transportation Research Part A, Vol. 38, No. 7, 2004, pp. 511-530. doi:10.1016/j.tra.2004.05.001

[26] C. F. Daganzo, “Structure of Competitive Transit Networks,” Transportation Research Part B, Vol. 44, No. 4, 2010, pp. 434-446. doi:10.1016/j.trb.2009.11.001

[27] J. R. Roy, “Spatial Interaction Modelling,” Springer-Verlag, Berlin, 2010.

[1] M. W. Melaina, “Initiating Hydrogen Infrastructures: Preliminary Analysis of a Sufficient Number of Initial Hydrogen Stations in the US,” International Journal of Hydrogen Energy, Vol. 28, No. 7, 2003, pp. 743-755. doi:10.1016/S0360-3199(02)00240-9

[2] M. Melaina and J. Bremson, “Refueling Availability for Alternative Fuel Vehicle Markets: Sufficient Urban Station Coverage,” Energy Policy, Vol. 36, No. 8, 2008, pp. 3233-3241. doi:10.1016/j.enpol.2008.04.025

[3] M. A. Nicholas, S. L. Handy and D. Sperling, “Using Geographic Information Systems to Evaluate Siting and Networks of Hydrogen Stations,” Transportation Research Record, Vol. 1880, 2004, pp. 126-134. doi:10.3141/1880-15

[4] M. A. Nicholas and J. Ogden, “Detailed Analysis of Urban Station Siting for California Hydrogen Highway Network,” Transportation Research Record, Vol. 1983, 2006, pp. 121-128. doi:10.3141/1983-17

[5] Y. Honma and O. Kurita, “A Mathematical Model on the Optimal Number of Hydrogen Stations with Respect to the Diffusion of Fuel Cell Vehicles,” Journal of the Operations Research Society of Japan, Vol. 51, No. 2, 2008, pp. 166-190.

[6] M. Kuby and S. Lim, “The Flow-Refueling Location Problem for Alternative-Fuel Vehicles,” Socio-Economic Planning Sciences, Vol. 39, No. 2, 2005, pp. 125-145. doi:10.1016/j.seps.2004.03.001

[7] M. Kuby, L. Lines, R. Schultz, Z. Xie, J. G. Kim and S. Lim, “Optimization of Hydrogen Stations in Florida Using the Flow-Refueling Location Model,” International Journal of Hydrogen Energy, Vol. 34, No. 15, 2009, pp. 6045-6064. doi:10.1016/j.ijhydene.2009.05.050

[8] S. Lim and M. Kuby, “Heuristic Algorithms for Siting Alternative-Fuel Stations Using the Flow-Refueling Location Model,” European Journal of Operational Research, Vol. 204, No. 1, 2010, pp. 51-61. doi:10.1016/j.ejor.2009.09.032

[9] I. Capar and M. Kuby, “An Efficient Formulation of the Flow Refueling Location Model for Alternative-Fuel Stations,” IIE Transactions, Vol. 44, No. 8, 2012, pp. 622636. doi:10.1080/0740817X.2011.635175

[10] M. Kuby and S. Lim, “Location of Alternative-Fuel Stations Using the Flow-Refueling Location Model and Dispersion of Candidate Sites on Arcs,” Networks and Spatial Economics, Vol. 7, No. 2, 2007, pp. 129-152. doi:10.1007/s11067-006-9003-6

[11] C. Upchurch, M. Kuby and S. Lim, “A Model for Location of Capacitated Alternative-Fuel Stations,” Geographical Analysis, Vol. 41, No. 1, 2009, pp. 85-106. doi:10.1111/j.1538-4632.2009.00744.x

[12] J. G. Kim and M. Kuby, “The Deviation-Flow Refueling Location Model for Optimizing a Network of Refueling Stations,” International Journal of Hydrogen Energy, Vol. 37, No. , 2012, pp. 5406-5420. doi:10.1016/j.ijhydene.2011.08.108

[13] M. J. Hodgson, “The Location of Public Facilities Intermediate to the Journey to Work,” European Journal of Operational Research, Vol. 6, No. 2, 1981, pp. 199-204. doi:10.1016/0377-2217(81)90208-3

[14] M. J. Hodgson, “A Flow-Capturing Location-Allocation Model,” Geographical Analysis, Vol. 22, No. 3, 1990, pp. 270-279. doi:10.1111/j.1538-4632.1990.tb00210.x

[15] O. Berman, R. C. Larson and N. Fouska, “Optimal Location of Discretionary Service Facilities,” Transportation Science, Vol. 26, No. 3, 1992, pp. 201-211. doi:10.1287/trsc.26.3.201

[16] M. J. Hodgson, K. E. Rosing and A. L. G. Storrier, “Applying the Flow-Capturing Location-Allocation Model to an Authentic Network: Edmonton, Canada,” European Journal of Operational Research, Vol. 90, No. 3, 1996, pp. 427-443. doi:10.1016/0377-2217(95)00034-8

[17] O. Berman, D. Bertsimas and R.C. Larson, “Locating Discretionary Service Facilities, II: Maximizing Market Size, Minimizing Inconvenience,” Operations Research, Vol. 43, No. 4, 1995, pp. 623-632. doi:10.1287/opre.43.4.623

[18] I. Averbakh and O. Berman, “Locating Flow-Capturing Units on a Network with Multi-Counting and Diminishing Returns to Scale,” European Journal of Operational Research, Vol. 91, No. 3, 1996, pp. 495-506. doi:10.1016/0377-2217(94)00369-6

[19] W. Zeng, M. J. Hodgson and I. Castillo, “The Pickup Problem: Consumers’ Locational Preferences in Flow Interception,” Geographical Analysis, Vol. 41, No. 1, 2009, pp. 107-126. doi:10.1111/j.1538-4632.2009.00741.x

[20] K. Tanaka and T. Furuta, “A Hierarchical Flow Capturing Location Problem with Demand Attraction Based on Facility Size, and Its Lagrangian Relaxation Solution Method,” Geographical Analysis, Vol. 44, No. 1, 2012, pp. 15-28. doi:10.1111/j.1538-4632.2011.00837.x

[21] O. Berman, “Deterministic Flow-Demand Location Problems,” Journal of the Operational Research Society, Vol. 48, No. 1, 1997, pp. 75-81.

[22] W. Zeng, I. Castillo and M. J. Hodgson, “A Generalized Model for Locating Facilities on a Network with FlowBased Demand,” Networks and Spatial Economics, Vol. 10, No. 4, 2010, pp. 579-611. doi:10.1007/s11067-008-9073-8

[23] M. Miyagawa, “Distributions of Rectilinear Deviation Distance to Visit a Facility,” European Journal of Operational Research, Vol. 205, No. 1, 2010, pp. 106-112. doi:10.1016/j.ejor.2009.12.002

[24] S. Chien and P. Schonfeld, “Optimization of Grid Transit System in Heterogeneous Urban Environment,” Journal of Transportation Engineering, Vol. 123, No. 1, 1997, pp. 28-35. doi:10.1061/(ASCE)0733-947X(1997)123:1(28)

[25] M. M. Aldaihani, L. Quadrifoglio, M. M. Dessouky and R. Hall, “Network Design for a Grid Hybrid Transit Service,” Transportation Research Part A, Vol. 38, No. 7, 2004, pp. 511-530. doi:10.1016/j.tra.2004.05.001

[26] C. F. Daganzo, “Structure of Competitive Transit Networks,” Transportation Research Part B, Vol. 44, No. 4, 2010, pp. 434-446. doi:10.1016/j.trb.2009.11.001

[27] J. R. Roy, “Spatial Interaction Modelling,” Springer-Verlag, Berlin, 2010.