Macroscopic traffic flow network modeling for wildfire evacuation: A game-theoretic junction optimization approach with application to the Lahaina fire

Annie Lu; Hong Kiat Tan; Alexander Xue; Alice Koniges; Andrea L. Bertozzi

doi:10.3934/dcds.2026162

Article Contents

2027, Volume 59: 123-184. Doi: 10.3934/dcds.2026162

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Macroscopic traffic flow network modeling for wildfire evacuation: A game-theoretic junction optimization approach with application to the Lahaina fire

1.
Department of Mathematics, University of California, Los Angeles, USA
2.
Department of Information and Computer Sciences, University of Hawai‘i at Mānoa, USA
3.
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA

^*Corresponding author: Hong Kiat Tan
^*Corresponding author: Hong Kiat Tan

^†These authors contributed equally to this work.

Received: March 30, 2026

Revised: July 29, 2026

Published online: August 31, 2026

This work was supported by NSF grants CCF-2345255 and CCF-2345256. The authors used AI tools (Claude and ChatGPT) to help with code development and suggestions for some of the English exposition.

Abstract / Introduction Full Text(HTML) Figure(34) / Table(15) Related Papers Cited by

Abstract

The 2023 Lahaina wildfire killed 102 people on a peninsula served by a single two-lane highway, making exit lane capacity the binding constraint on evacuation time. We model the evacuation as a system of hyperbolic scalar conservation laws on a directed graph with game-theoretic junction conditions that maximize total network flux, an evacuation-calibrated piecewise linear-quadratic flux function, and a loss-driven optimization framework that tunes traffic distribution toward priority corridors. Analytical results on a toy network and numerical simulations of the Lahaina road network reveal a phase transition in exit lane capacity. Additional lanes improve throughput linearly until a computable critical threshold, beyond which no route optimization yields further benefit. For Lahaina, reversing one southbound lane captures nearly all achievable improvement, and a fourth lane can be reserved for emergency vehicles with negligible impact on civilian clearance time. These results provide a rigorous mathematical basis for contraflow recommendations in wildland-urban interface evacuations.

Keywords:

System of scalar conservation laws on networks,
game-theoretic junction optimization,
macroscopic traffic flow,
wildfire evacuation,
phase transitions.

Mathematics Subject Classification: Primary: 90B20, 35L65; Secondary: 90C26, 90C35, 65M08, 91A80.

Citation:

Full Text(HTML)

Figure 1. Overview of the paper's pipeline, from network modeling and traffic evolution to optimization and simulation of the Lahaina network

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Figure 2. An example of a traffic network of interest. Here, the scalar conservation law on each road is solved away from the junction, indicated by the . On the other hand, junctions are labelled with . Determining the density of cars at the junction would require resolving the junction conditions

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Figure 3. Locating the solution of Theorem 2.1 for the one-in-two-out junction in (a), with preferences skewed towards road 2. In (b)–(d), corresponding to cases (ⅰ)–(ⅲ) of the theorem, the shaded box $ [0, c_2] \times [0, c_3] $ is the set of admissible outgoing fluxes, the thick line $ \hat\gamma_2 + \hat\gamma_3 = c_1 $ is the maximum flux road 1 can supply, the dashed ray is the preference direction $ (\alpha, 1-\alpha) $, the dash-dotted ray is the right-of-way direction $ (c_2, c_3) $, and the solid dot is the solution. In (c), the open circle marks the infeasible preference target and the cross marks the preference-respecting fallback with lower throughput. See the discussion following Theorem 2.1

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Figure 4. An example illustrating how distances along each road (indicated by a number close to each road) and junction (indicated by a number inside each circle representing a junction) are being assigned in a subgraph of the original network containing the exiting road (Hwy30[7]) and junction (h5). In (A), the illustrated network diagram is presented, representing the segment of the real-world network in (B) (reproduced from [31])

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Figure 5. Color legend for LOS classification

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Figure 6. A simple toy model. Road 1 is the entrance to the network, and Road 5 is the exit. Roads 2 and 3 represent a path through a residential area with multiple stops, while Road 4 represents a continuous path via a highway

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Figure 7. Cars exited as a function of the number of exit road lanes $ n_5 $ (treated as a continuous variable), for the congested toy network with $ \rho_{\text{init}} = 0.9 $ and $ T = 1000 $ seconds. The phase transition at $ n_5^\star = 1.8 $ is clearly visible

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Figure 8. Snapshots of the congested toy network (all interior roads initialized at $ \rho_{\text{init}} = 0.9 $) at $ t = 0 $ (left) and $ t = 1000 $ seconds (right), for $ n_5 = 1 $ (top) and $ n_5 = 2 $ (bottom). See Appendix C for a detailed rarefaction analysis

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Figure 9. Traffic congestion points during the Lahaina fire. Reproduced from [31]

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Figure 10. AM Base Network and Road Color Legend. Simulated from 11:00–13:25

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Figure 11. PM Base Network and Road Color Legend. Note that Road 8, a nondescript dirt road, is not in PM Base, but is found in other PM Networks

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Figure 12. Snapshots of the AM Base Network at $ t = 0,900, 1800 $ seconds for $ \gamma = 0.075 $ with $ nt_{opt} = 0 $. The network quickly floods, with all roads fully congested by $ t = 2550 $

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Figure 13. Cumulative absolute difference between $ nt_{opt} = 0 $ and $ nt_{opt} = 1, 60 $. (A) Difference in cars exited ($ \gamma = 0.01 $). (B) Difference in weighted integrated cars ($ \gamma = 0.0375 $). Time is given in thousands of seconds

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Figure 14. Cumulative time integrated cars for various $ \gamma_2 $ values with $ \gamma_1 = 0.01 $

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Figure 15. The final network state (end of PM 5) for $ \gamma_1 = 0.01 $, with $ \gamma_2 = 0.01, 0.10, $ and $ 1.00 $

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Figure 16. Cumulative time integrated cars for various $ \gamma_2 $ values with $ \gamma_1 = 0.0375 $

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Figure 17. The final network state (end of PM 5) for $ \gamma_1 = 0.0375 $, with $ \gamma_2 = 0.0375, 0.10, $ and $ 1.00 $

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Figure 18. The cumulative difference in cars exited between 3 and 4 exit lanes and 2 lanes across PM networks 2, 3, and 4 for $ \gamma_1 = 0.0375 $, $ \gamma_2 = 0.0375 $

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Figure 19. Final snapshots of PM 4 for 2, 3, and 4 exit lanes with $ \gamma_1 = 0.0375 $, $ \gamma_2 = 0.0375 $

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Figure 20. Snapshots of PM 2 for 3 exit lanes with $ \gamma_1 = 0.0375 $, $ \gamma_2 = 0.0375 $

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Figure 21. Snapshots of PM 4 for 2 exit lanes with $ \gamma_1 = 0.0375 $, $ \gamma_2 = 0.0375 $

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Figure 22. The cumulative difference in cars exited between 3 and 4 exit lanes and 2 lanes across PM networks 2, 3, and 4 for $ \gamma_1 = 0.0375 $, $ \gamma_2 = 0.1000 $

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Figure 23. Final snapshots of PM 4 for 2, 3, and 4 exit lanes with $ \gamma_1 = 0.0375 $, $ \gamma_2 = 0.1000 $

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Figure 24. AM Network 2. To be simulated from 13:25-14:21. Figure (A) shows the roads to be removed from the AM base network in gray: (gray-purple) Eastbound Papalaua Street Segment from Front Street to Hwy-30. Figure (B) shows the final network to be simulated for AM network 2

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Figure 25. AM Network 3. To be simulated from 14:21-15:00. Figure (A) shows the roads to be removed from the PM base network in gray: (gray-orange) Eastbound Lahainaluna Road Segment from Front Street to Hwy-30, and Westbound Lahainaluna Road Segment from Waine'e Street to Hwy-30. Figure (B) shows the final network to be simulated for AM network 3

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Figure 26. PM Network 2. To be simulated from 15:25-16:29. Figure (A) shows the roads to be removed from the PM base network in gray: (gray-red) Lahaina Bypass Segment from Lahainaluna Road to Keawe Street Extension. Figure (B) shows the final network to be simulated for PM network 2

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Figure 27. PM Network 3. To be simulated from 16:29-16:35. Figure (A) shows the additional roads added to PM network 2 in gray: (gray-red) Eastbound Keawe Street Extension, (gray-brown) Oil Road. Figure (B) shows the final network to be simulated for PM network 3

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Figure 28. PM Network 4. To be simulated from 16:35-16:47. Figure (A) shows the roads removed from PM network 3 in gray: (gray-purple) Dickenson Street segment connecting Waine'e Street and Hwy-30. Figure (B) shows the final network to be simulated for PM network 4

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Figure 29. PM Network 5. To be simulated from 16:47-17:10. Figure (A) shows the additional roads added to PM network 4 in gray: (gray-green) Southbound Front Street, (gray-yellow) Southbound Waine'e Street, (gray-blue) Southbound Hwy-30, (gray-maroon) Exit via Lahaina Bypass, (gray-light pink) Source via nondescript dirt road. Figure (B) shows the final network to be simulated for PM network 5. Due to the large number of added roads, only the light colored roads (yellow, pink) are circled for visibility

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Figure 30. Snapshots of the AM Base Network at $ t = 0,600, 1200 $ seconds for $ \gamma = 0.01 $ with $ nt_{opt} = 0 $ seconds

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Figure 31. Snapshots of the AM Base Network at $ t = 600 $ for $ \gamma = 0.01 $ with $ nt_{opt} = 0, 1 $ and $ 60 $ seconds

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Figure 32. Snapshots of the AM Base Network at $ t = 0, 3000, 6000 $ seconds for $ \gamma = 0.0375 $ with $ nt_{opt} = 0 $ seconds

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Figure 33. Snapshots of the AM Base Network at $ t = 900 $ for $ \gamma = 0.0375 $ with $ nt_{opt} = 0, 1 $ and $ 60 $ seconds

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Figure 34. Snapshots for the congested toy network with only road 1 initialized ($ \rho_{\text{init}} = 0.9 $) at $ t = 0 $ seconds (left) and $ t = 1000 $ seconds (right), for $ n_5 = 1 $ (top) and $ n_5 = 2 $ (bottom)

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Table 1. Symbolic parameters for the toy network. Roads 2 and 3 share parameters. Each lane on the exit road has the same characteristics as road 1, so $ f_{c, 5} = n_5 f_{c, 1} $, $ \sigma_5 = n_5\sigma_1 $, and $ A_5 = A_1/n_5 $

Road	Length	Lanes ($ n_i $)	Free-flow speed ($ v_i $)	Flux capacity ($ f_{c, i} $)
Entry (road 1)	$ L_1 $	$ 1 $	$ v_1 $	$ f_{c, 1} $
Road 2	$ L_2 $	$ 1 $	$ v_2 $	$ f_{c, 2} $
Road 3	$ L_3 $	$ 1 $	$ v_2 $	$ f_{c, 2} $
Road 4	$ L_4 $	$ 1 $	$ v_4 $	$ f_{c, 4} $
Exit (road 5)	$ L_5 $	$ n_5 $	$ v_1 $	$ n_5 f_{c, 1} $

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Table 2. Congested toy network ($ \rho_{\text{init}} = 0.9 $ on all interior roads) with $ T = 1000 $ seconds and $ nt_{\text{opt}} = 1 $ second. The transition from 1 to 2 lanes improves cars exited by 80%, while 3 lanes provides no further benefit, consistent with $ n_5^\star = 1.8 $

$ n_5 $	Weighted Time-Int Cars	Cars Exited	Optimal $ \alpha $
1	851.56	126.37	0.50
2	762.25	227.48	0.50
3	762.25	227.48	0.50

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Table 3. Weighted time-integrated cars by $ nt_{opt} $ and $ \gamma $ for Phase 1 (AM Base Network). For $ \gamma = 0.01 $, the loss function is not monotone in $ nt_{opt} $ due to the network being nearly empty; see Appendix A for discussion

$ nt_{opt} $	$ \gamma = 0.01 $	$ \gamma = 0.0375 $	$ \gamma = 0.075 $	$ \gamma = 0.125 $	$ \gamma = 1.00 $
0	747.73	6,365.52	7,754.90	7,857.96	7,874.50
1	728.50	6,485.01	7,755.87	7,858.34	7,874.90
10	729.01	6,495.34	7,755.91	7,858.39	7,874.91
60	735.51	6,591.61	7,756.04	7,858.42	7,874.99
600	701.94	6,828.82	7,776.05	7,858.61	7,875.26

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Table 4. Cumulative Optimization Metrics ($ \gamma = 0.01, 0.0375 $)

$ nt_{opt} $	$ \gamma = 0.01 $			$ \gamma = 0.0375 $
$ nt_{opt} $	Weighted Time-Int Cars	Cars Entered	Cars Exited	Weighted Time -Int Cars	Cars Entered	Cars Exited
0	1,221.03	3,530.33	3,781.12	12,391.88	9,730.70	8,834.23
1	1,197.97	3,530.33	3,792.66	12,577.69	9,742.63	8,834.23
60	1,197.97	3,530.33	3,795.40	12,627.03	9,741.70	8,834.23

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Table 5. Optimization Metrics for Various $ nt_{opt} $ Times (seconds) with $ \gamma = 0.01 $

$ nt_{opt} $	Weighted Time-Integrated Cars	Cars Entered	Cars Exited
0	747.73	1,885.00	2,151.70
1	728.50	1,885.00	2,164.13
10	729.01	1,885.00	2,165.74
60	735.51	1,885.00	2,166.35
600	701.94	1,885.00	2,180.22

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Table 6. Optimization Metrics for Various $ nt_{opt} $ Times (seconds) with $ \gamma = 0.0375 $

$ nt_{opt} $	Weighted Time-Integrated Cars	Cars Entered	Cars Exited
0	6,365.52	5,528.19	4,815.65
1	6,485.01	5,546.28	4,815.65
10	6,495.34	5,548.56	4,815.65
60	6,591.61	5,547.20	4,815.65
600	6,828.82	5,566.66	4,815.65

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Table 7. Weighted Time-Integrated Cars by $ nt_{opt} $ (seconds) and $ \gamma $ for large $ \gamma = 0.075, 0.125, 1.000 $

$ nt_{opt} $	$ \gamma = 0.075 $	$ \gamma = 0.125 $	$ \gamma = 1.00 $
0	7,754.90	7,857.96	7,874.50
1	7,755.87	7,858.34	7,874.90
10	7,755.91	7,858.39	7,874.91
60	7,756.04	7,858.42	7,874.99
600	7,776.05	7,858.61	7,875.26

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Table 8. Honopiilani Highway (Hwy30) road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
Hwy30[0]	Hwy-30:	0.01	2	35	Parkway	875	$ f(\rho) = \begin{cases} 35 \rho, & 0< \rho \leq 0.125\\-5.714\rho^2+1.429\rho+4.286, & 0.125< \rho \leq 1 \end{cases} $
	(source) $ \rightarrow $ Prison St	(default)
Hwy30[1]	Hwy-30:	0.28	2	35	Parkway	875	$ f(\rho) = \begin{cases} 35 \rho, & 0< \rho \leq 0.125\\-5.714\rho^2+1.429\rho+4.286, & 0.125< \rho \leq 1 \end{cases} $
	Prison St $ \rightarrow $ Dickenson St
Hwy30[2]	Hwy-30:	0.16	2	35	Parkway	875	$ f(\rho) = \begin{cases} 35 \rho, & 0< \rho \leq 0.125\\-5.714\rho^2+1.429\rho+4.286, & 0.125< \rho \leq 1 \end{cases} $
	Dickenson St $ \rightarrow $ Lahainaluna Rd
Hwy30[3]	Hwy-30:	0.12	2	40	Parkway	1000	$ f(\rho) = \begin{cases} 40 \rho, & 0< \rho \leq 0.125\\-6.531\rho^2+1.633\rho+4.898, & 0.125< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $ Papalaua St
Hwy30[4]	Hwy-30:	0.32	2	40	Parkway	1000	$ f(\rho) = \begin{cases} 40 \rho, & 0< \rho \leq 0.125\\-6.531\rho^2+1.633\rho+4.898, & 0.125< \rho \leq 1 \end{cases} $
	Papalaua St $ \rightarrow $ Kenui St
Hwy30[5]	Hwy-30:	0.17	2	40	Parkway	1000	$ f(\rho) = \begin{cases} 40 \rho, & 0< \rho \leq 0.125\\-6.531\rho^2+1.633\rho+4.898, & 0.125< \rho \leq 1 \end{cases} $
	Kenui St $ \rightarrow $ Keawe St
Hwy30[6]	Hwy-30:	0.66	2	40	Parkway	1000	$ f(\rho) = \begin{cases} 40 \rho, & 0< \rho \leq 0.125\\-6.531\rho^2+1.633\rho+4.898, & 0.125< \rho \leq 1 \end{cases} $
	Keawe St $ \rightarrow $ Front St
Hwy30[7]	Hwy-30:	0.01	2	40	Parkway	1000	$ f(\rho) = \begin{cases} 40 \rho, & 0< \rho \leq 0.125\\-6.531\rho^2+1.633\rho+4.898, & 0.125< \rho \leq 1 \end{cases} $
	Front St $ \rightarrow $ (exit)	(default)

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Table 9. Front Street (Front) road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
Front[0]	Front:	0.01	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad &0.125< \rho \leq 1 \end{cases} $
	(source) $ \rightarrow $ Prison St	(default)			Collector
Front[1]	Front:	0.06	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Prison St $ \rightarrow $ Canal St				Collector
Front[2]	Front:	0.14	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Canal St $ \rightarrow $ Dickenson St				Collector
Front[3]	Front:	0.16	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Dickenson St $ \rightarrow $ Lahainaluna Rd				Collector
Front[4]	Front:	0.05	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $ Wahie Ln				Collector
Front[5]	Front:	0.10	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Wahie Ln $ \rightarrow $ Papalaua St				Collector
Front[6]	Front:	0.17	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Papalaua St $ \rightarrow $ Baker St				Collector
Front[7]	Front:	0.17	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Baker St $ \rightarrow $ Kenui St				Collector
Front[8]	Front:	0.10	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Kenui St $ \rightarrow $ Puunoa Pl				Collector
Front[9]	Front:	0.78	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Puunoa Pl $ \rightarrow $ Hwy-30				Collector

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Table 10. Waine'e Street (Wainee) road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
Wainee[0]	Waine'e:	0.01	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	(source) $ \rightarrow $ Prison St	(default)			Street
Wainee[1]	Waine'e:	0.14	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Prison St $ \rightarrow $ Hale St				Street
Wainee[2]	Waine'e:	0.10	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Hale St $ \rightarrow $ Dickenson St				Street
Wainee[3]	Waine'e:	0.11	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Dickenson St $ \rightarrow $ Panaewa St				Street
Wainee[4]	Waine'e:	0.05	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Panaewa St $ \rightarrow $ Lahainaluna Rd				Street
Wainee[5]	Waine'e:	0.14	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $ Papalaua St				Collector
Wainee[6]	Waine'e:	0.16	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Papalaua St $ \rightarrow $ Baker St				Collector
Wainee[7]	Waine'e:	0.16	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Baker St $ \rightarrow $ Kenui St				Collector

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Table 11. Residential Roads West of Hwy-30 road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
Prison[0]	Prison:	0.16	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Front St$ \rightarrow $ Wainee St				Street
Prison[1]	Prison:	0.08	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Wainee St$ \rightarrow $ Hwy-30				Street
Dicken[0]	Dickenson:	0.05	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Front St $ \rightarrow $Luakini St				Collector
Dicken[1]	Dickenson:	0.09	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Luakini St$ \rightarrow $ Wainee St				Collector
Dicken[2]	Dickenson:	0.11	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Wainee St$ \rightarrow $ Hwy-30				Collector
Papal[0]	Papalaua:	0.15	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Front St$ \rightarrow $ Wainee St				Collector
Papal[1]	Papalaua:	0.07	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Wainee St$ \rightarrow $ Hwy-30				Collector
Kenui[0]	Kenui:	0.10	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Front St $ \rightarrow $ Kahoma Vlg				Collector
Kenui[1]	Kenui:	0.08	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Kahoma Vlg$ \rightarrow $ Wainee St				Collector
Kenui[2]	Kenui:	0.02	1	20	Minor	400	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.1\\-2.469\rho^2+0.494\rho +1.975, \quad & 0.1< \rho \leq 1 \end{cases} $
	Wainee St$ \rightarrow $ Hwy-30				Collector

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Table 12. Keawe Street Extension (Keawe) and Lahaina Bypass (LB) road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
Keawe[0]	Keawe:	0.10	2	25	Major	550	$ f(\rho) = \begin{cases} 25 \rho, \quad & 0< \rho \leq 0.11\\-3.472\rho^2+0.764\rho+2.708, \quad & 0.11< \rho \leq 1 \end{cases} $
	Hwy-30 $ \rightarrow $ Gateway Shopping Ctr				Collector
Keawe[1]	Keawe:	0.09	2	25	Major	550	$ f(\rho) = \begin{cases} 25 \rho, \quad & 0< \rho \leq 0.11\\-3.472\rho^2+0.764\rho+2.708, \quad & 0.11< \rho \leq 1 \end{cases} $
	Gateway Shopping Ctr $ \rightarrow $ Oil Rd				Collector
LB[0]	Lahaina Bypass:	0.01	1	30	Arterial/	650	$ f(\rho) = \begin{cases} 30 \rho, \quad & 0< \rho \leq 0.108\\-4.085\rho^2+0.885\rho + 3.202, \quad & 0.108< \rho \leq 1 \end{cases} $
	(source)$ \rightarrow $ Lahainaluna Rd	(default)			Parkway
LB[1]	Lahaina Bypass:	1.06	1	30	Arterial/	650	$ f(\rho) = \begin{cases} 30 \rho, \quad & 0< \rho \leq 0.108\\-4.085\rho^2+0.885\rho + 3.202, \quad & 0.108< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $ Oil Rd				Parkway

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Table 13. LahainaLuna Road (LL) road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
LL[0]	Lahainaluna:	0.14	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Front St $ \rightarrow $ Wainee St				Collector
LL[1]	Lahainaluna:	0.09	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Wainee St $ \rightarrow $ Hwy-30				Collector
LL[2]	Lahainaluna:	0.14	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Hwy-30 $ \rightarrow $ Kuhua St				Collector
LL[3]	Lahainaluna:	0.05	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Kuhua St $ \rightarrow $ Pauoa St				Collector
LL[4]	Lahainaluna:	0.09	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Pauoa St $ \rightarrow $ Kale St				Collector
LL[5]	Lahainaluna:	0.08	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Kale St $ \rightarrow $ Paunau St				Collector
LL[6]	Lahainaluna:	0.06	1	20	Major	500	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.125\\-3.265\rho^2+0.816\rho+2.449, \quad & 0.125< \rho \leq 1 \end{cases} $
	Paunau St $ \rightarrow $ Kelawea St				Collector
LL[7]	Lahainaluna:	0.12	1	30	Major	600	$ f(\rho) = \begin{cases} 30 \rho, \quad & 0< \rho \leq 0.1\\-3.701\rho^2+0.741\rho+2.963, \quad & 0.1< \rho \leq 1 \end{cases} $
	Kelawea St $ \rightarrow $ Kalena St				Collector
LL[8]	Lahainaluna:	0.13	1	30	Major	600	$ f(\rho) = \begin{cases} 30 \rho, \quad & 0< \rho \leq 0.1\\-3.701\rho^2+0.741\rho+2.963, \quad & 0.1< \rho \leq 1 \end{cases} $
	Kalena St $ \rightarrow $ Dirt Road				Collector
LL[9]	Lahainaluna:	0.03	1	30	Major	600	$ f(\rho) = \begin{cases} 30 \rho, \quad & 0< \rho \leq 0.1\\-3.701\rho^2+0.741\rho+2.963, \quad & 0.1< \rho \leq 1 \end{cases} $
	Dirt Road $ \rightarrow $ Lahaina Bypass				Collector
LL[10]	Lahainaluna:	0.01	1	30	Major	600	$ f(\rho) = \begin{cases} 30 \rho, \quad & 0< \rho \leq 0.1\\-3.701\rho^2+0.741\rho+2.963, \quad & 0.1< \rho \leq 1 \end{cases} $
	Lahaina Bypass $ \rightarrow $ (source)	(default)			Collector

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Table 14. Source Roads with non-default lengths East of Hwy-30 road data used for Lahaina

#	Name	(mi) Length	Lanes	(mi/hr) Speed Limit	Road Class	(veh/hr/lane) $ f_{max} $	(per 1 lane) Normalized Flux
1	Kuhua:	0.28	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street
2	Komo Mai:	0.18	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	(source)$ \rightarrow $ Keawe St Ext				Street
3	Pauoa:	0.18	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street
4	Kale:	0.18	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street
5	Paunau:	0.18	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street
6	Kelawea:	0.15	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street
7	Kalena:	0.18	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street
8	Nondescript Dirt Road:	0.25	1	20	Local	300	$ f(\rho) = \begin{cases} 20 \rho, \quad & 0< \rho \leq 0.075\\-1.753\rho^2+0.263\rho +1.490, \quad & 0.075< \rho \leq 1 \end{cases} $
	Lahainaluna Rd $ \rightarrow $(source)				Street

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Table 15. Hwy-30/Honopiilani Highway (Hwy30) initial road data used for AM Base Network

Name	Segment	AADT (veh)	Google Data Available? (Y/N)	LOS	$ v_0 $ (mi/hr)	Normalized Initial Density (per 1 lane)
Highway 30	(source) $ \rightarrow $ Lahainaluna Rd	19,796	Y	B	24.5	$ \rho_0 =0.178 $
	Lahainaluna Rd $ \rightarrow $ Kenui St	19,796	Y	B	28	$ \rho_0 =0.178 $
	Kenui St $ \rightarrow $ Keawe St	19,796	Y	C	20	$ \rho_0 = 0.245 $
	Keawe St $ \rightarrow $ (exit)	37,300	Y	B	28	$ \rho_0 = 0.178 $
Front Street	(source) $ \rightarrow $ Hwy-30	6,060	N	D	8	$ \rho_0 = 0.300 $
Waine'e Street	(source) $ \rightarrow $ Lahainaluna Rd	0	N	A	20	$ \rho_0 = 0 $
	Lahainaluna Rd $ \rightarrow $ Kenui St	3,939	N	A	20	$ \rho_0 = 0.056 $
Prison Street	Front St $ \rightarrow $ Hwy-30	0	N	A	20	$ \rho_0 = 0 $
Dicckenson Street	Front St $ \rightarrow $ Hwy-30	3,333	N	A	20	$ \rho_0 = 0.047 $
Papalaua Street	Front St $ \rightarrow $ Hwy-30	3,434	N	A	20	$ \rho_0 = 0.049 $
Kenui Street	Front St $ \rightarrow $ Hwy-30	2,652	N	A	20	$ \rho_0 = 0.038 $
Keawe Street	Hwy-30 $ \rightarrow $ Gateway Shopping Ctr	20,196	Y	C	12.5	$ \rho_0 = 0.217 $
	Gateway Shopping Ctr $ \rightarrow $ Oil Rd	20,196	Y	B	17.5	$ \rho_0 = 0.157 $
	Oil Rd $ \rightarrow $ Lahaina Bypass	20,196	Y	C	12.5	$ \rho_0 = 0.217 $
Lahaina Bypass	(source) $ \rightarrow $ Keawe St Ext	16,218	Y	B	21	$ \rho_0 = 0.154 $
Lahaina Luna Road	Front St $ \rightarrow $ Wainee St	8,585	N	C	10	$ \rho_0 = 0.245 $
	Wainee St $ \rightarrow $ Kelawea St	8,585	Y	B	14	$ \rho_0 = 0.178 $
	Kelawea St $ \rightarrow $ (source)	8,585	Y	B	21	$ \rho_0 = 0.143 $

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Macroscopic traffic flow network modeling for wildfire evacuation: A game-theoretic junction optimization approach with application to the Lahaina fire

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Macroscopic traffic flow network modeling for wildfire evacuation: A game-theoretic junction optimization approach with application to the Lahaina fire

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