---
title: Sioux Falls Transportation Benchmark
url: https://www.emergentmind.com/topics/sioux-falls-scenario
type: topic
---

# Sioux Falls Transportation Benchmark

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 [2508.06234]. 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 [2508.06234]. 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 [2508.06234]. 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 [2508.06234]. 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 $= 1.00$ [2508.06234]. 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 [2110.11943]. 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 $E\approx 228$ arcs [2504.00716].

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 [2508.06234]. In this framework, a $k$-th order network is built from observed contiguous subpaths of length $k$, with nodes
$$
v^{(k)}=\langle v_{i-k+1},\ldots,v_i\rangle
$$
and directed edges linking overlapping subpaths. The corresponding transition probability matrix $P^{(k)}$ 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 [2508.06234].

The reported higher-order structural metrics show rapid state-space growth and declining connectivity. The number of nodes increases from 24 at $k=1$ to 76 at $k=2$, 252 at $k=3$, 641 at $k=4$, and 1,081 at $k=5$; density falls from $0.1377$ at $k=1$ to $0.0026$ at $k=4$ and $0.0009$ at $k=5$; and the largest connected component ratio drops from $1.000$ at $k=1$–$3$ to $0.931$ at $k=4$ and $0.725$ at $k=5$ [2508.06234]. Average out-degree likewise declines from $3.17$ at $k=1$ to $1.00$ at $k=5$ [2508.06234].

The optimal memory length selected by a likelihood ratio test is reported as $k^*=4$, with the $p$-value dropping below $0.05$ when going from $k=4$ to $k=5$ [2508.06234]. Link-prediction accuracy for the classical network rises from approximately $0.63$ at $k=1$ to a peak of approximately $0.77$ at $k=4$, then drops at $k=5$ [2508.06234]. Centrality alignment is also irregular: $\rho(1)=0.645$, $\rho(2)=0.268$, recovery to $\rho(4)=0.630$, then slight decline [2508.06234].

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 [2508.06234]. 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 [2109.01578]. In that formulation, the network remains the 24-node, 76-directed-link Sioux Falls benchmark, but node $2$ is designated as a single super-shelter $s$, and all evacuee flows are directed to this safety node [2109.01578]. Evacuee origins are all nodes $i\neq 2$, with demands $q_i$ summing to 360,600 vehicles, and candidate alternative-fuel stations are placed at nodes $ST=\{5,11,12,15,16\}$ [2109.01578].

The model introduces tree-design and flow variables
$x_{ij}^k\in\{0,1\}$,
$f_{ij}^k\ge 0$,
$V_{ij}=\sum_k f_{ij}^k$,
$y_i^{k,l}\in\{0,1\}$,
and
$w_i^k\in\{0,1\}$,
with link travel time $t_{ij}(V_{ij})$ following the standard Bureau of Public Roads function [2109.01578]. The objective minimizes total evacuation time:
$$
\min
\sum_{(i,j)\in A}\sum_{k\in K} t_{ij}(V_{ij})\,f_{ij}^k
+\sum_{i\in N}\sum_{k\in K} r_k\Bigl(\sum_{l=T_k}^{|N|-1}y_i^{k,l}\Bigr)\,q_i^k.
$$
Here $T_k$ is an integer hop limit used as a driving-range proxy, and refueling time is modeled as $r_k\times(\text{number of hops in last leg})$, with $r_k=15$ minutes per hop in the Sioux Falls experiments [2109.01578].

The reported numerical results show that range constraints materially alter the evacuation plan. For a conventional case with no range constraint, travel time is $8.5157\times 10^6$ h, refuel time is $0$, and total evacuation time is $8.5157\times 10^6$ h [2109.01578]. For the range-constrained case with $T=4$ hops and stations at $5,11,12,15,16$, travel time is $8.7586\times 10^6$ h, refuel time is $3.8043\times 10^5$ h, and total evacuation time is $9.1390\times 10^6$ h, an increase of approximately $7.32\%$ in overall evacuation time [2109.01578]. Sensitivity analysis yields total evacuation times of $9.1396\times 10^6$ h for $T=3$, $8.9180\times 10^6$ h for $T=5$, and convergence to the conventional case at $T=7$, with $T\ge 8$ identical to conventional [2109.01578].

Station density and siting also matter. For $T=4$, one-station cases average $13.5\%$ above conventional, two-station cases average $25.1\%$, and the five-station case converges to the reported $7.32\%$ increase; stations closer to node $2$ yield larger benefits [2109.01578]. In heterogeneous-fleet settings, a two-type mix with $T_1=8$ hops on 5 stations and $T_2=4$ hops on 3 stations gives total evacuation time $=2.0651\times 10^7$ h, while a three-type mix gives $1.7188\times 10^7$ h with routing variations by type to avoid conflicts [2109.01578]. 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 [2109.01578].

## 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 $N=24$ nodes and the classical set of 76 directed links, with aggregate travel demand $d_{ij}>0$ between each ordered O–D pair $(i,j)$, $i\neq j$, taken from the TNTP morning-peak 3-hour matrix [2308.04820]. Each O–D demand is split into $K=3$ populations—students, business travelers, and leisure travelers—so that $d_{ijk}=w_k d_{ij}$ with $\sum_k w_k=1$ [2308.04820]. The considered modes are walking, public bus, autonomous Mobility-on-Demand (AMoD), and shared bikes [2308.04820].

Mode-specific costs combine travel time and monetary fare through
$$
c_{ijk}^m(x)=t_{ij}^m(x)+\frac{p_{ij}^m}{V_{T,k}},
$$
with values of time $V_{T,\text{student}}=15$ USD/h, $V_{T,\text{business}}=35$ USD/h, and $V_{T,\text{leisure}}=7$ USD/h [2308.04820]. Walking, bus, and bike are modeled without congestion, whereas AMoD travel time follows a BPR formula with $\alpha=0.15$, $\beta=4$, edge capacity $\kappa=250$ veh, and nominal speed derived from $40$ km/h [2308.04820]. Capacity constraints are imposed on vehicle availability at each node, with
$C^{bus}_{i,\mathrm{avail}}=6000$,
$C^{AMoD}_{i,\mathrm{avail}}=50$,
and
$C^{bike}_{i,\mathrm{avail}}=50$
[2308.04820].

The equilibrium is characterized as a Nash equilibrium of non-atomic travelers and can be computed via a convex optimization problem with KKT conditions [2308.04820]. Solving the convex program in CVXPY/ECOS yields aggregate mode shares of $49.9\%$ bus, $17.3\%$ AMoD, $30.6\%$ bike, and $2.2\%$ walk [2308.04820]. Business travelers use AMoD at $46.8\%$, leisure travelers use bike at $62.8\%$, and the average cost per traveler is $6.88$ USD, with business $=11.20$ USD, students $=6.14$ USD, and leisure $=3.48$ USD [2308.04820]. Sensitivity analyses show that relocating AMoD and bike fleets to densely populated nodes increases AMoD revenue by $5\%$ and bike revenue by $9\%$ while leaving the population-average cost essentially unchanged, but increasing the upper tail of cost for certain O–D pairs [2308.04820]. Varying the public-transit fare $p^{bus}\in[0,4]$ USD causes average travel cost to rise monotonically, while total CO$_2$ emissions are non-monotonic [2308.04820].

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 [2504.00716]. Here, switching arcs are bidirectional zero-length arcs between each node in $G_W$ and its copy in $G_R$ or $G_M$ whenever within $50$ m, with fixed boarding/alighting time of $1$ min and switching-arc capacity $h_{S,ij}=500$ users/h [2504.00716]. Demand consists of all $M=24\cdot 23=552$ O–D pairs, with rates $\alpha_m$ extracted from TLC trip-record data, scaled to Sioux Falls population, and assigned to the corresponding origin/destination in $V_W$ [2504.00716]. 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 [2504.00716].

The reported numerical findings indicate complementarity between AMoD and micromobility rather than pure substitution. As $n_R$ increases from $0$ to approximately $4{,}000$, the AMoD time-share grows from $0\%$ to approximately $40\%$, micromobility from $0\%$ to approximately $30\%$, and walking falls from $100\%$ to approximately $30\%$; average passenger time decreases from approximately $28$ min at $n_R=500$ to approximately $16$ min at $n_R=7{,}000$, then plateaus [2504.00716]. Increasing micromobility fleet size $n_M$ from $0$ to approximately $6{,}000$ raises micromobility share from $0\%$ to approximately $35\%$ and AMoD share from $10\%$ to approximately $45\%$, while average passenger time decreases linearly from approximately $26$ min to approximately $17$ min and then levels off [2504.00716]. Increasing per-node micromobility rebalancing capacity $\beta_M$ from $0$ to $100$ veh/h reduces total AMoD rebalancing flow by approximately $65\%$, from approximately $1{,}200$ veh/h to approximately $400$ veh/h [2504.00716].

## 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—$7{,}000$ vehicles from node $1\to 19$ and $7{,}000$ from node $19\to 1$—and a horizon $T=50$ with $\Delta t=0.5$, giving $100$ discrete steps [2110.11943]. Link travel times are given by
$$
c_\ell(\mu_\ell)=t_\ell^0\Bigl[1+\alpha\Bigl(\frac{\mu_\ell}{\mu_{\ell,c}}\Bigr)^\beta\Bigr],
$$
with empirical parameters such as $\alpha=0.15$ and $\beta=4$ [2110.11943]. The finite-$N$ dynamic routing game is intractable for large $N$, and the mean field game replaces the $N$-player interaction by a symmetric policy and deterministic flow $m_t$ coupled through backward HJB and forward continuity equations [2110.11943].

The computational result reported for Sioux Falls is that one OMD iteration costs $O(|A|^2\cdot T)\approx O(76^2\cdot 100)$ 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 [2110.11943]. The average deviation incentive falls below $1.55$ time-units after 100 iterations for a baseline mean travel-time of approximately $27.5$ [2110.11943]. At equilibrium, the two O–D streams distribute over a handful of disjoint paths so that no used path has strictly larger travel-time [2110.11943].

A separate day-to-day model studies route-guidance misinformation with endogenous trust in a CAV environment [2605.14204]. 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 [2605.14204]. 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 [2605.14204]. Trust is encoded as a Beta evidence model with expected trust
$$
T_k^{(d)}=\frac{\alpha_k^{(d)}}{\alpha_k^{(d)}+\beta_k^{(d)}},
$$
and reliance is given by
$$
\lambda_k^{(d)}=\bar\lambda_k T_k^{(d)}.
$$
A trust-activation threshold is defined through the first-day guidance error, and the weighted compliance index
$$
\chi(\pi)=\sum_k \pi_k\theta_k u_k
$$
governs the leading $\ll O(\gamma^2)\gg$ impact of a small fixed-trust attack [2605.14204].

The numerical experiments use a 200-day simulation with an attack schedule on days 51–100 [2605.14204]. In the stealthy regime at $\gamma=0.3$, fixed-trust attack-window PoAtt is $1.062$ and dynamic-trust PoAtt is $1.060$, with TIA approximately $2\%$ and no trust erosion because $e_k<\epsilon$ [2605.14204]. In the detectable regime at $\gamma=0.7$, fixed-trust PoAtt is $1.316$, dynamic-trust PoAtt is $1.028$, and trust-induced attenuation is approximately $91\%$; the transient peak $\mathrm{PoAtt}_{dyn}$ is approximately $1.07$ before trust collapse [2605.14204]. At $\gamma=1.0$, system performance returns to baseline on day 101, but aggregate trust takes 77 days to recover to $95\%$ of its pre-attack value, creating a 77-day hidden vulnerability window [2605.14204]. The paper summarizes the mechanism as threshold-activated behavioral resilience, with an empirical activation threshold of approximately $\hat\gamma\approx 0.5$ on Sioux Falls [2605.14204].

## 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 [2511.16547]. This network modification is explicitly intended to inflate energy consumption per link and stress the charging and energy constraints [2511.16547]. To mimic sparse infrastructure, three charging stations are placed at nodes $\{3,6,20\}$, and across all 15 instances these are the only stationary charging facilities [2511.16547].

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 $200$ kWh [2511.16547]. Shared scenario parameters are vehicle speed $v=60$ mph, EV energy-use rate $=0.4$ kWh/mile, stationary charger power $=180$ kW, V2V power transfer $=50$ kW with $90\%$ efficiency, platoon energy-saving $\eta_1=10\%$, ER battery capacity $=100$ kWh, ES battery capacity $=200$ kWh, ER minimum safety SoC $=2$ kWh, and cost weights $a=B=1$ [2511.16547]. The static PV2VC problem is formulated as a MILP on $G(N,A)$ with decision variables
$X_{ij}^k$,
$F_{ij}^k$,
$Q_{ij}^{rs}$,
$T_i^k$,
$E_i^k$,
and
$U_i^k$,
and objective
$$
\min_{X,F,T}\;\sum_{r\in R}\Biggl[\sum_{(i,j)\in A}a\,C_{ij}\,d_{ij}\,\bigl(X_{ij}^{r}-\eta_{1}F_{ij}^{r}\bigr)+B\,\bigl(T_{s_r}^{r}-t_r\bigr)\Biggr].
$$
Time-synchronization constraints ensure joined platoon members depart and arrive on link $(i,j)$ at the same times if $P_{ij}^{rs}=1$ [2511.16547].

Relative to the MILP-obtained EVRP benchmark, the reported GA solutions produce the following percentage savings. In Scenario S1, total-cost saving is $3.12\%$, energy saving is $4.05\%$, and travel-time saving is $2.20\%$; in S2, $3.81\%$, $5.22\%$, and $2.51\%$; in S3, $5.96\%$, $7.37\%$, and $4.27\%$; in S4, $6.38\%$, $7.01\%$, and $5.74\%$; and in S5, $11.26\%$, $9.44\%$, and $11.65\%$ [2511.16547]. The abstract separately states that PV2VC technology can save up to $11.07\%$ in energy consumption, $11.65\%$ in travel time, and $11.26\%$ in total cost [2511.16547]. The source further reports that simply allowing stationary-CS platooning yielded at most $3.65\%$ total-cost savings and often negative travel-time impacts due to synchronization waits [2511.16547].

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 [2109.01578]. 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.

Source: https://www.emergentmind.com/topics/sioux-falls-scenario