01
Connectivity as an expected value
The paper reports an expected connectivity of 207.79 after the collapse and 208.22 after reconstruction. The difference is small in absolute terms but indicates the bridge’s structural role in the network.
CompetitionCV award2025
MCM 2025 — Better Traffic, Better City
2025美赛D题论文
A transport-network resilience study of the Baltimore bridge collapse using directed graphs, random walks, Monte Carlo simulation and reconstruction scenarios.
25p
MCM paper
10k
random-walk simulations
2.1%
post-collapse disturbance impact
01 / Overview
What this package actually contains.
The 2025 MCM paper studies how the Francis Scott Key Bridge collapse changes Baltimore’s transport-network connectivity and stability. It models the city as a directed graph and compares the collapsed, reconstructed and random-disturbance scenarios.
Objectives
- 01Represent Baltimore’s transport network as a directed graph.
- 02Quantify connectivity before and after the bridge collapse.
- 03Test network stability under random disturbances and reconstruction scenarios.
Competition narrative
Problem, model, result, paper.
The page foregrounds the modelling decision and result before implementation details.
Stage 01
City graph
Nodes and directed routes with bridge-dependent links.
Stage 02
Random walk
Repeated movement simulation over the graph.
Stage 03
Connectivity metric
Expected reachable connectivity across simulations.
Stage 04
Disturbance tests
Random edge failures and response comparison.
Stage 05
Policy scenarios
Post-collapse versus post-reconstruction comparison.
02 / Package highlights
What this work demonstrates.
- Measures network connectivity before and after disruption with 10,000 simulations.
- Compares post-collapse and post-reconstruction stability under random disturbances.
- Turns a public-infrastructure event into a quantitative resilience model.
03 / Model
The modelling choices behind the result.
02
Stability under disturbance
Random disturbances reduce expected connectivity by about 2.1% in the collapsed state and only about 0.99% after reconstruction. This separates the immediate connectivity level from the network’s resilience to further shocks.
04 / Key code
Selected modelling code.
Only verified source excerpts and pseudocode taken from the project papers are shown.
Paper pseudocodePseudocode
Random-walk connectivity pseudo-code
Algorithm outline stated in the MCM paper; this is not claimed as original executable source.
MCM 2025 §4.1.2
PROCEDURE RANDOM_WALK_CONNECTIVITY(G, start, steps)
visited <- {start}
node <- start
REPEAT steps TIMES
neighbours <- OUTGOING_NEIGHBOURS(G, node)
IF neighbours IS EMPTY THEN BREAK
node <- RANDOM_CHOICE(neighbours)
visited <- visited UNION {node}
RETURN |visited| / |V(G)|
END PROCEDURE
PROCEDURE EXPECTED_CONNECTIVITY(G, runs)
total <- 0
REPEAT runs TIMES
start <- RANDOM_CHOICE(V(G))
total <- total + RANDOM_WALK_CONNECTIVITY(G, start, 500)
RETURN total / runs
END PROCEDUREPaper pseudocodePseudocode
Scenario comparison pseudo-code
Paper-level Monte Carlo outline for collapsed and reconstructed network states.
MCM 2025 §4.1.3–4.1.4
FOR EACH scenario IN {post_collapse, post_reconstruction}
baseline <- EXPECTED_CONNECTIVITY(scenario.graph, 10000)
disturbances <- EMPTY LIST
REPEAT 100 TIMES
G' <- COPY(scenario.graph)
REMOVE_RANDOM_EDGES(G', fraction = 5%)
disturbances.APPEND(EXPECTED_CONNECTIVITY(G', 10000))
disturbed_mean <- MEAN(disturbances)
change_pct <- (disturbed_mean - baseline) / baseline * 100
END FORReproducibility notes
- The model separates network topology from traffic volume.
- Monte Carlo simulation expresses uncertainty as a distribution rather than one path.
- Reconstruction and disturbance scenarios are evaluated with the same metric.
Limitations / next steps
- The graph abstraction omits capacity, congestion and travel-time constraints.
- Policy conclusions should be validated with real traffic counts and route-choice behaviour.
05 / Downloads
Files in this folder.
Open the original report, presentation or source archive. PDF cover pages with private details were removed.
PDFOpen file
MCM 2025 paper
EN · 25 pages · 4.0 MB25-page competition paper on traffic-network resilience.