- Free-flow time t0
- Flow share
- Current cost
- Conductance vs maxg/max
Click or tap a road or ferry to close it (red ×), and again to reopen it. Drag to pan; pinch, Ctrl / ⌘ + scroll or the + / − buttons zoom. From the keyboard: focus the map, arrow keys pan, + / − zoom, 0 resets; the lists further down can close and reopen links too.
Controls
0 < μ < 1: the dynamics settles on the traffic (Wardrop) equilibrium for these link costs, and converges from any positive start — our own (unpublished, not citable) derivation. Flow spreads over several routes. It is an ODE result: no rate, and the discrete step is a numerical approximation.
μ = 1: converges to the shortest route when it is unique (Bonifaci, Mehlhorn & Varma 2012).
μ > 1: several stable outcomes: which corridor survives depends on the starting state (two-edge ring: Tero et al. 2007); we found no general theorem.
Closures
Presets replace the current set of closures. You can also click links on the map.
No links closed.
Live indicators
- OD cost P
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- Relative Wardrop gap
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- max |Δg| per unit time
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- Cheapest route now (πmin)
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- Model time (steps)
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- Linear solve (CG iterations · residual)
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- State
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What these mean
- OD cost P
- The potential difference between Athlone and Nottingham at the current state, in stylised minutes: porigin − pdestination.
- Relative Wardrop gap
- 1 − d·πmin / Σe xe·te(xe), with d = 1 and πmin the cheapest route under the current link costs (Dijkstra). It is 0 exactly when every route that carries flow is a cheapest route. Links held at the numerical floor are left out of the sum, so their leakage cannot mask a settled state.
- max |Δg| per unit time
- The largest change of any conductance in the last step divided by Δt, relative to the largest conductance.
- State: settling / settled
- “Settled” needs both: max |Δg| per unit time below 10−7 (relative) and the Wardrop gap below 10−6. Until then the state reads “settling”; the flows are still changing, and on the full network model (F) the last stretch is slow.
- Linear solve
- Each step solves Kirchhoff's equations for the current conductances by conjugate gradients (Jacobi-preconditioned, float64, warm-started from the previous potentials). The residual is relative to the unit demand; it is loosened while the network is changing fast and tightened as it settles, and capped so a frame never takes too long.
- Numerical floor
- No conductance is allowed below 10−9 × the largest one. This keeps the linear solve well-posed; it is a numerical device, not part of the model. Closed links are removed outright (conductance 0).
Irish Sea corridors
Share of the travellers that cross by each ferry corridor.
Pinch points
Closure impact precomputed at μ = 0.5
No precomputed closure impacts are available for this data.
Top-flow links now
What these mean
- Flow concentration
- How much of the traffic one link carries. “Top-flow links now” lists the links with the largest share at this moment; several links in a row on the same road carry the same share and are listed once.
- Irish Sea cut
- The set of all car-ferry links between Ireland and Great Britain. Every Athlone–Nottingham journey has to cross it, so the corridor shares add up to 100%.
- Closure impact
- The percentage by which the equilibrium OD cost rises when one link is closed, precomputed at μ = 0.5 for the current cost model by an independent solver; “disconnects” marks a link whose closure cuts Athlone off from Nottingham.
What this is / what this isn't
What this is
- A live illustration, in your browser, of the mathematics of our research record: Tero-type conductance dynamics, the model behind Physarum-style routing.
- Run on a stylised network built from OpenStreetMap motorways, trunk roads and car ferries, with one unit of demand from Athlone to Nottingham.
- Each step solves Kirchhoff’s equations for the current conductances, then moves every link towards the conductance its flow asks for.
- Link costs are stylised: free-flow times from speed limits and class defaults (for ferries, sailing time plus a boarding overhead), shaped by the cost model and congestion scale you choose.
What this isn’t
- Not an experiment: no traffic data is used, and nothing is calibrated or benchmarked.
- Not a claim that Physarum routing beats satnavs or standard solvers.
- Not a navigation tool: do not plan a journey with it. Timetables, capacities, prices, tolls and real congestion are not modelled.
- Not evidence about the real roads: closure impacts are outputs of the model on stylised costs.