Sioux Falls Transportation Benchmark

• The Sioux Falls Scenario is a canonical transportation network benchmark defined by a 24-node, 76-link directed graph with fixed origin–destination demand, enabling controlled experiments in traffic and routing models.
• It incorporates detailed structural analyses and higher-order network representations to assess metrics like average out-degree, density, and connectivity, aiding comparative evaluations of diverse routing and evacuation studies.
• Adapted variants addressing multi-modal mobility, dynamic congestion, and electric vehicle routing illustrate its versatility in testing models for evacuation planning, energy constraints, and infrastructure adaptations.

The Sioux Falls Scenario is a canonical transportation-network benchmark centered on a directed road network with 24 nodes and 76 links, commonly instantiated with fixed origin–destination demand and used to evaluate traffic assignment, routing, evacuation, mobility-system design, and charging models (Zhang et al., 8 Aug 2025). In the literature considered here, it appears both as the classical Sioux Falls network and as several adapted variants: a first-order benchmark with 552 nonzero O–D pairs and fixed trip rates as in LeBlanc et al. (1975), a benchmark instance with 528 O–D pairs and 6,180 enumerated paths, and modified forms that embed shelters, refueling stations, mode-transfer layers, dummy terminal links, or sparse charging infrastructure (Zhang et al., 8 Aug 2025). The scenario is therefore less a single immutable dataset than a family of closely related benchmark constructions built on the same 24-node, 76-link core.

1. Canonical network and benchmark role

The classical Sioux Falls network is described as a system of 24 numbered intersections connected by 76 directed road segments (Zhang et al., 8 Aug 2025). In most implementations it is paired with a 24×24 demand matrix $Q$ in which $Q_{ij}>0$ only for the 552 nonzero O–D pairs, while other studies use fixed O–D demands from the standard Sioux Falls data set, morning-peak 3-hour demands from TNTP, or specialized two-pair demand specifications for dynamic routing games (Zhang et al., 8 Aug 2025). This repeated reuse is what makes the scenario a benchmark: different methods can be compared on a shared topology while altering demands, state variables, or behavioral assumptions.

For the first-order network, the reported structural metrics are average out-degree $= 3.17$, diameter $= 6$, average shortest-path length $= 3.01$, density $= 76/[24\cdot 23] \approx 0.1377$, and largest connected component ratio $= 1.00$ (Zhang et al., 8 Aug 2025). Other papers retain the same 24-node, 76-link base graph while augmenting it in model-specific ways. In the mean-field dynamic routing formulation, one “dummy” origin and destination link is added for each node that appears as an OD terminal (Cabannes et al., 2021). In the intermodal AMoD–micromobility model, the road layer is combined with walking and micromobility layers into a supergraph $G=(V,A)$ with $V=V_W\cup V_M\cup V_R$ and total $N\approx 72$ nodes and $Q_{ij}>0$0 arcs (Koumleh et al., 1 Apr 2025).

A plausible implication is that Sioux Falls functions as a controlled experimental substrate rather than a single behavioral model. The network is fixed enough to support reproducibility, yet sufficiently compact to permit substantial variation in flow models, equilibrium concepts, and infrastructure assumptions.

2. Structural analysis and higher-order network representations

Higher-order network analysis has been used to examine the representativeness of the classical Sioux Falls benchmark beyond first-order topology (Zhang et al., 8 Aug 2025). In this framework, a $Q_{ij}>0$1-th order network is built from observed contiguous subpaths of length $Q_{ij}>0$2, with nodes

$Q_{ij}>0$3

and directed edges linking overlapping subpaths. The corresponding transition probability matrix $Q_{ij}>0$4 normalizes observed transition counts, and path-dependent structure is characterized through entropy, fragmentation, likelihood-ratio model selection, link-prediction accuracy, and higher-order PageRank alignment (Zhang et al., 8 Aug 2025).

The reported higher-order structural metrics show rapid state-space growth and declining connectivity. The number of nodes increases from 24 at $Q_{ij}>0$5 to 76 at $Q_{ij}>0$6, 252 at $Q_{ij}>0$7, 641 at $Q_{ij}>0$8, and 1,081 at $Q_{ij}>0$9; density falls from $= 3.17$0 at $= 3.17$1 to $= 3.17$2 at $= 3.17$3 and $= 3.17$4 at $= 3.17$5; and the largest connected component ratio drops from $= 3.17$6 at $= 3.17$7–$= 3.17$8 to $= 3.17$9 at $= 6$0 and $= 6$1 at $= 6$2 (Zhang et al., 8 Aug 2025). Average out-degree likewise declines from $= 6$3 at $= 6$4 to $= 6$5 at $= 6$6 (Zhang et al., 8 Aug 2025).

The optimal memory length selected by a likelihood ratio test is reported as $= 6$7, with the $= 6$8-value dropping below $= 6$9 when going from $= 3.01$0 to $= 3.01$1 (Zhang et al., 8 Aug 2025). Link-prediction accuracy for the classical network rises from approximately $= 3.01$2 at $= 3.01$3 to a peak of approximately $= 3.01$4 at $= 3.01$5, then drops at $= 3.01$6 (Zhang et al., 8 Aug 2025). Centrality alignment is also irregular: $= 3.01$7, $= 3.01$8, recovery to $= 3.01$9, then slight decline (Zhang et al., 8 Aug 2025).

These findings are interpreted in the source as evidence that the classical Sioux Falls network exhibits limited path diversity, rapid structural fragmentation at higher orders, and weak alignment with empirical routing behavior (Zhang et al., 8 Aug 2025). This suggests that the scenario is well suited to first-order traffic-assignment tests, but may be less reliable for tasks that depend strongly on path memory or trajectory realism.

3. Evacuation planning and alternative-fuel constraints

In evacuation planning, the Sioux Falls scenario has been adapted to study seamless evacuation route plans for alternative-fuel vehicles under hop-constrained refueling requirements (Purba et al., 2021). In that formulation, the network remains the 24-node, 76-directed-link Sioux Falls benchmark, but node $= 76/[24\cdot 23] \approx 0.1377$0 is designated as a single super-shelter $= 76/[24\cdot 23] \approx 0.1377$1, and all evacuee flows are directed to this safety node (Purba et al., 2021). Evacuee origins are all nodes $= 76/[24\cdot 23] \approx 0.1377$2, with demands $= 76/[24\cdot 23] \approx 0.1377$3 summing to 360,600 vehicles, and candidate alternative-fuel stations are placed at nodes $= 76/[24\cdot 23] \approx 0.1377$4 (Purba et al., 2021).

The model introduces tree-design and flow variables $= 76/[24\cdot 23] \approx 0.1377$5, $= 76/[24\cdot 23] \approx 0.1377$6, $= 76/[24\cdot 23] \approx 0.1377$7, $= 76/[24\cdot 23] \approx 0.1377$8, and $= 76/[24\cdot 23] \approx 0.1377$9, with link travel time $= 1.00$0 following the standard Bureau of Public Roads function (Purba et al., 2021). The objective minimizes total evacuation time:

$= 1.00$1

Here $= 1.00$2 is an integer hop limit used as a driving-range proxy, and refueling time is modeled as $= 1.00$3, with $= 1.00$4 minutes per hop in the Sioux Falls experiments (Purba et al., 2021).

The reported numerical results show that range constraints materially alter the evacuation plan. For a conventional case with no range constraint, travel time is $= 1.00$5 h, refuel time is $= 1.00$6, and total evacuation time is $= 1.00$7 h (Purba et al., 2021). For the range-constrained case with $= 1.00$8 hops and stations at $= 1.00$9, travel time is $G=(V,A)$0 h, refuel time is $G=(V,A)$1 h, and total evacuation time is $G=(V,A)$2 h, an increase of approximately $G=(V,A)$3 in overall evacuation time (Purba et al., 2021). Sensitivity analysis yields total evacuation times of $G=(V,A)$4 h for $G=(V,A)$5, $G=(V,A)$6 h for $G=(V,A)$7, and convergence to the conventional case at $G=(V,A)$8, with $G=(V,A)$9 identical to conventional (Purba et al., 2021).

Station density and siting also matter. For $V=V_W\cup V_M\cup V_R$0, one-station cases average $V=V_W\cup V_M\cup V_R$1 above conventional, two-station cases average $V=V_W\cup V_M\cup V_R$2, and the five-station case converges to the reported $V=V_W\cup V_M\cup V_R$3 increase; stations closer to node $V=V_W\cup V_M\cup V_R$4 yield larger benefits (Purba et al., 2021). In heterogeneous-fleet settings, a two-type mix with $V=V_W\cup V_M\cup V_R$5 hops on 5 stations and $V=V_W\cup V_M\cup V_R$6 hops on 3 stations gives total evacuation time $V=V_W\cup V_M\cup V_R$7 h, while a three-type mix gives $V=V_W\cup V_M\cup V_R$8 h with routing variations by type to avoid conflicts (Purba et al., 2021). The paper’s stated conclusion is that an evacuation route could prove unique to a single vehicle fuel type, while being infeasible to the others (Purba et al., 2021).

4. Multi-modal mobility, intermodality, and equilibrium

The Sioux Falls scenario is also used to study mode choice and system design in multi-modal settings. In a game-theoretic formulation of multi-modal mobility systems, the network has $V=V_W\cup V_M\cup V_R$9 nodes and the classical set of 76 directed links, with aggregate travel demand $N\approx 72$0 between each ordered O–D pair $N\approx 72$1, $N\approx 72$2, taken from the TNTP morning-peak 3-hour matrix (Zardini et al., 2023). Each O–D demand is split into $N\approx 72$3 populations—students, business travelers, and leisure travelers—so that $N\approx 72$4 with $N\approx 72$5 (Zardini et al., 2023). The considered modes are walking, public bus, autonomous Mobility-on-Demand (AMoD), and shared bikes (Zardini et al., 2023).

Mode-specific costs combine travel time and monetary fare through

$N\approx 72$6

with values of time $N\approx 72$7 USD/h, $N\approx 72$8 USD/h, and $N\approx 72$9 USD/h (Zardini et al., 2023). Walking, bus, and bike are modeled without congestion, whereas AMoD travel time follows a BPR formula with $Q_{ij}>0$00, $Q_{ij}>0$01, edge capacity $Q_{ij}>0$02 veh, and nominal speed derived from $Q_{ij}>0$03 km/h (Zardini et al., 2023). Capacity constraints are imposed on vehicle availability at each node, with $Q_{ij}>0$04, $Q_{ij}>0$05, and

$Q_{ij}>0$06

(Zardini et al., 2023).

The equilibrium is characterized as a Nash equilibrium of non-atomic travelers and can be computed via a convex optimization problem with KKT conditions (Zardini et al., 2023). Solving the convex program in CVXPY/ECOS yields aggregate mode shares of $Q_{ij}>0$07 bus, $Q_{ij}>0$08 AMoD, $Q_{ij}>0$09 bike, and $Q_{ij}>0$10 walk (Zardini et al., 2023). Business travelers use AMoD at $Q_{ij}>0$11, leisure travelers use bike at $Q_{ij}>0$12, and the average cost per traveler is $Q_{ij}>0$13 USD, with business $Q_{ij}>0$14 USD, students $Q_{ij}>0$15 USD, and leisure $Q_{ij}>0$16 USD (Zardini et al., 2023). Sensitivity analyses show that relocating AMoD and bike fleets to densely populated nodes increases AMoD revenue by $Q_{ij}>0$17 and bike revenue by $Q_{ij}>0$18 while leaving the population-average cost essentially unchanged, but increasing the upper tail of cost for certain O–D pairs (Zardini et al., 2023). Varying the public-transit fare $Q_{ij}>0$19 USD causes average travel cost to rise monotonically, while total CO$Q_{ij}>0$20 emissions are non-monotonic (Zardini et al., 2023).

A distinct intermodal AMoD–micromobility model embeds the same 24-node, 76-link road network into a three-layer supergraph with walking, micromobility, and road arcs (Koumleh et al., 1 Apr 2025). Here, switching arcs are bidirectional zero-length arcs between each node in $Q_{ij}>0$21 and its copy in $Q_{ij}>0$22 or $Q_{ij}>0$23 whenever within $Q_{ij}>0$24 m, with fixed boarding/alighting time of $Q_{ij}>0$25 min and switching-arc capacity $Q_{ij}>0$26 users/h (Koumleh et al., 1 Apr 2025). Demand consists of all $Q_{ij}>0$27 O–D pairs, with rates $Q_{ij}>0$28 extracted from TLC trip-record data, scaled to Sioux Falls population, and assigned to the corresponding origin/destination in $Q_{ij}>0$29 (Koumleh et al., 1 Apr 2025). The optimization minimizes total passenger time and, after piecewise-linearization of the road BPR delay, becomes a convex–piecewise-linear program solvable as an LP (Koumleh et al., 1 Apr 2025).

The reported numerical findings indicate complementarity between AMoD and micromobility rather than pure substitution. As $Q_{ij}>0$30 increases from $Q_{ij}>0$31 to approximately $Q_{ij}>0$32, the AMoD time-share grows from $Q_{ij}>0$33 to approximately $Q_{ij}>0$34, micromobility from $Q_{ij}>0$35 to approximately $Q_{ij}>0$36, and walking falls from $Q_{ij}>0$37 to approximately $Q_{ij}>0$38; average passenger time decreases from approximately $Q_{ij}>0$39 min at $Q_{ij}>0$40 to approximately $Q_{ij}>0$41 min at $Q_{ij}>0$42, then plateaus (Koumleh et al., 1 Apr 2025). Increasing micromobility fleet size $Q_{ij}>0$43 from $Q_{ij}>0$44 to approximately $Q_{ij}>0$45 raises micromobility share from $Q_{ij}>0$46 to approximately $Q_{ij}>0$47 and AMoD share from $Q_{ij}>0$48 to approximately $Q_{ij}>0$49, while average passenger time decreases linearly from approximately $Q_{ij}>0$50 min to approximately $Q_{ij}>0$51 min and then levels off (Koumleh et al., 1 Apr 2025). Increasing per-node micromobility rebalancing capacity $Q_{ij}>0$52 from $Q_{ij}>0$53 to $Q_{ij}>0$54 veh/h reduces total AMoD rebalancing flow by approximately $Q_{ij}>0$55, from approximately $Q_{ij}>0$56 veh/h to approximately $Q_{ij}>0$57 veh/h (Koumleh et al., 1 Apr 2025).

5. Dynamic routing, congestion, and trust-aware resilience

The Sioux Falls scenario has been used for both dynamic routing games with congestion and day-to-day resilience analysis under route-guidance misinformation. In the mean field approach to dynamic routing games, the Sioux Falls instance is defined by the 76-link network, two O–D pairs—$Q_{ij}>0$58 vehicles from node $Q_{ij}>0$59 and $Q_{ij}>0$60 from node $Q_{ij}>0$61—and a horizon $Q_{ij}>0$62 with $Q_{ij}>0$63, giving $Q_{ij}>0$64 discrete steps (Cabannes et al., 2021). Link travel times are given by

$Q_{ij}>0$65

with empirical parameters such as $Q_{ij}>0$66 and $Q_{ij}>0$67 (Cabannes et al., 2021). The finite-$Q_{ij}>0$68 dynamic routing game is intractable for large $Q_{ij}>0$69, and the mean field game replaces the $Q_{ij}>0$70-player interaction by a symmetric policy and deterministic flow $Q_{ij}>0$71 coupled through backward HJB and forward continuity equations (Cabannes et al., 2021).

The computational result reported for Sioux Falls is that one OMD iteration costs $Q_{ij}>0$72 elementary updates and is independent of total vehicle count; on a standard 8-core CPU, 100 OMD iterations on the Sioux Falls MFG complete in under 5 minutes (Cabannes et al., 2021). The average deviation incentive falls below $Q_{ij}>0$73 time-units after 100 iterations for a baseline mean travel-time of approximately $Q_{ij}>0$74 (Cabannes et al., 2021). At equilibrium, the two O–D streams distribute over a handful of disjoint paths so that no used path has strictly larger travel-time (Cabannes et al., 2021).

A separate day-to-day model studies route-guidance misinformation with endogenous trust in a CAV environment (Ka et al., 13 May 2026). In that setting, the Sioux Falls network is represented by 24 nodes, 76 directed links, 528 O–D pairs, and 6,180 enumerated paths from the benchmark instance in Han et al. 2020 (Ka et al., 13 May 2026). Within-day congestion is modeled by Newell’s simplified cumulative-curve LWR with triangular fundamental diagrams, while day-to-day route choice follows bounded-rationality logit learning with trust-dependent reliance on external guidance (Ka et al., 13 May 2026). Trust is encoded as a Beta evidence model with expected trust

$Q_{ij}>0$75

and reliance is given by

$Q_{ij}>0$76

A trust-activation threshold is defined through the first-day guidance error, and the weighted compliance index

$Q_{ij}>0$77

governs the leading $Q_{ij}>0$78 impact of a small fixed-trust attack (Ka et al., 13 May 2026).

The numerical experiments use a 200-day simulation with an attack schedule on days 51–100 (Ka et al., 13 May 2026). In the stealthy regime at $Q_{ij}>0$79, fixed-trust attack-window PoAtt is $Q_{ij}>0$80 and dynamic-trust PoAtt is $Q_{ij}>0$81, with TIA approximately $Q_{ij}>0$82 and no trust erosion because $Q_{ij}>0$83 (Ka et al., 13 May 2026). In the detectable regime at $Q_{ij}>0$84, fixed-trust PoAtt is $Q_{ij}>0$85, dynamic-trust PoAtt is $Q_{ij}>0$86, and trust-induced attenuation is approximately $Q_{ij}>0$87; the transient peak $Q_{ij}>0$88 is approximately $Q_{ij}>0$89 before trust collapse (Ka et al., 13 May 2026). At $Q_{ij}>0$90, system performance returns to baseline on day 101, but aggregate trust takes 77 days to recover to $Q_{ij}>0$91 of its pre-attack value, creating a 77-day hidden vulnerability window (Ka et al., 13 May 2026). The paper summarizes the mechanism as threshold-activated behavioral resilience, with an empirical activation threshold of approximately $Q_{ij}>0$92 on Sioux Falls (Ka et al., 13 May 2026).

6. Electric-vehicle routing and charging adaptations

The Sioux Falls scenario has also been modified to study electric-vehicle routing and charging technologies. In the modular platoon-based vehicle-to-vehicle electric charging problem, the base topology is the 24-node, 76-link directed Sioux Falls network, but every original travel-time value in minutes is multiplied by a factor so that the resulting “cost” becomes a distance in miles (Fu et al., 20 Nov 2025). This network modification is explicitly intended to inflate energy consumption per link and stress the charging and energy constraints (Fu et al., 20 Nov 2025). To mimic sparse infrastructure, three charging stations are placed at nodes $Q_{ij}>0$93, and across all 15 instances these are the only stationary charging facilities (Fu et al., 20 Nov 2025).

The experiments replace a full O–D matrix with a small set of electricity requests, each having a fixed sequence of customer-visit nodes, while electricity suppliers initially sit at charging-station nodes with full charge of $Q_{ij}>0$94 kWh (Fu et al., 20 Nov 2025). Shared scenario parameters are vehicle speed $Q_{ij}>0$95 mph, EV energy-use rate $Q_{ij}>0$96 kWh/mile, stationary charger power $Q_{ij}>0$97 kW, V2V power transfer $Q_{ij}>0$98 kW with $Q_{ij}>0$99 efficiency, platoon energy-saving $= 3.17$00, ER battery capacity $= 3.17$01 kWh, ES battery capacity $= 3.17$02 kWh, ER minimum safety SoC $= 3.17$03 kWh, and cost weights $= 3.17$04 (Fu et al., 20 Nov 2025). The static PV2VC problem is formulated as a MILP on $= 3.17$05 with decision variables $= 3.17$06, $= 3.17$07, $= 3.17$08, $= 3.17$09, $= 3.17$10, and $= 3.17$11, and objective

$= 3.17$12

Time-synchronization constraints ensure joined platoon members depart and arrive on link $= 3.17$13 at the same times if $= 3.17$14 (Fu et al., 20 Nov 2025).

Relative to the MILP-obtained EVRP benchmark, the reported GA solutions produce the following percentage savings. In Scenario S1, total-cost saving is $= 3.17$15, energy saving is $= 3.17$16, and travel-time saving is $= 3.17$17; in S2, $= 3.17$18, $= 3.17$19, and $= 3.17$20; in S3, $= 3.17$21, $= 3.17$22, and $= 3.17$23; in S4, $= 3.17$24, $= 3.17$25, and $= 3.17$26; and in S5, $= 3.17$27, $= 3.17$28, and $= 3.17$29 (Fu et al., 20 Nov 2025). The abstract separately states that PV2VC technology can save up to $= 3.17$30 in energy consumption, $= 3.17$31 in travel time, and $= 3.17$32 in total cost (Fu et al., 20 Nov 2025). The source further reports that simply allowing stationary-CS platooning yielded at most $= 3.17$33 total-cost savings and often negative travel-time impacts due to synchronization waits (Fu et al., 20 Nov 2025).

Taken together with the alternative-fuel evacuation study, these results show how the Sioux Falls core graph is repeatedly used to test energy-constrained routing under sparse infrastructure, refueling detours, state-of-charge safety thresholds, and moving-charge coordination (Purba et al., 2021). A plausible implication is that the scenario remains attractive because its scale is small enough for exact or hybrid optimization, yet rich enough to expose nontrivial interactions among path choice, infrastructure siting, charging, and temporal synchronization.