ASET-RSET maps after Schröder et al. (2020)

Schröder, Arnold and Seyfried (2020) turned the ASET-RSET comparison from one number at one point into maps: a time for every map element of a room (0.6 m in their demonstration). This page re-runs their demonstration case under the conditions of the authors’ release, with our own FDS fire and pyFDS-Evac crowds, and shows three things:

• ASET per fire quantity. When each cell first exceeds a limit for smoke, temperature, CO, CO₂, radiation and dose, and which of them matter for this fire.
• RSET per cell. When the last person leaves each cell (paper §2.3). In the paper’s method this map is the evacuation side, compared with ASET cell by cell.
• DIFF = ASET − RSET. Where in the room the smoke arrives before the last person has left, and how the door-flow model, pre-movement and a second door move that.

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The result in brief

One door, the exit flow capped at 1.00 persons/s, everyone moving at t = 0, smoke criterion K ≥ 0.23 1/m at 2.0 m, maximum over n = 10 seeds:

• Smoke sets ASET here. Every cell reaches K ≥ 0.23 1/m at 2.0 m, the last one at 83 s (84 s on the 0.1 m grid, 83 s with two doors). The temperature, radiation and dose limits are reached only next to the burner, if at all. The release fire produces no CO, so the CO criteria do not apply.
• The queue at the door fails. The negative cells are the corner in front of the door, where people wait at the capped exit. Smoke reaches those cells at 72–74 s; the last person leaves them at about 100 s.
• The door-flow model decides the one-door sign. Without the cap, the room empties in 42–45 s and no cell has DIFF < 0. With two doors even the uncapped crowd fails, by 11 s, beside the west door near the fire.
• The grids agree. The 0.1 m FDS grid moves min DIFF by less than 1 s and the negative area by 0.3 m².
• The negative area is about a third of the paper’s. The release’s own RSET map has a queue about twice as large as ours (Against the paper).

The room

A 30 × 10 × 3 m room with one door, a fire in the opposite corner and 100 people who all start moving at once (paper §2.1). The paper’s text gives no fire details (“as the fire properties are of no importance for this work, we deliberately leave out details”). We take them from the authors’ release:

• a constant 60 kW fire, HRRPUA 60 kW/m² on a 1 × 1 m floor vent at x, y = 1–2 m, burning polyurethane (NFPA Babrauskas, soot yield 0.129), with the FDS defaults for everything the release leaves unset;
• one door, 1.0 m wide at y = 8–9 m in the east wall, 2.0 m high, open;
• 100 people placed at random over the floor, free speed N(1.3, 0.1) m/s, the exit capped at 1.00 persons/s, the flow we measured from the release’s ten JuPedSim runs.

We run FDS 6.10.1 on 0.2 m cells (0.1 m as a grid check) to 600 s, and the collision-free speed model with radius 0.15 m, 10 seeds per version. Every input, with its source, is under Setup, deviations and caveats.

ASET: which fire quantity matters

ASET of a cell is the first time a criterion holds anywhere in that cell at 2.0 m, counted from ignition. We screened every criterion of three published sets, plus the pyFDS-Evac doses, and counted the cells that exceed each one by 600 s. The headline set is vfdb Table 8.3, < 30 min: the only column that contains both of the paper’s values. The paper cites vfdb for 0.23 1/m only and names no column (our inference); the vfdb < 5 min column and EA Fig. 8 are sensitivity rows. Smoke sets ASET under all three.

Map cells (0.6 m) exceeded by 600 s at z = 2.0 m, any FDS node of the cell. Open markers: no cell. One marker shape per FDS run.

“0” means not reached by 600 s at 2.0 m for this fire. Where a criterion reads “not applicable”, the fire model does not produce the quantity, so the map says nothing about it.

The largest values anywhere on the 2.0 m slice, 0–600 s (0.2 m / 0.1 m grid, one door): K 6.4 / 10.4 1/m, T 80 / 118 °C, CO₂ 0.65 / 1.16 %, O₂ never below 19.9 / 19.2 %, gas FED 2.4·10⁻⁵ / 8.5·10⁻⁴ (CO₂ and O₂ terms only), convective heat FED 0.070 / 0.097.

Tenability criteria in the literature

A tenability criterion turns a fire field into a time. Published criteria differ in four ways: the effect they mark, whether they are a limit or a dose, the exposure time and height they assume, and the share of the population they cover. The physiology behind each hazard is on the Fundamentals pages (incapacitation thresholds, visibility, heat, irritants, ASET and RSET).

Where this page’s criteria sit. The vfdb < 30 min values are fixed, location-based guide values: the most conservative of the three stay classes, at the lower end of the smoke limits in the literature and well below any incapacitation endpoint. A map that crosses them shows where conditions stop meeting the protection goal. Incapacitation needs a dose along each person’s path.

The ASET maps

One door, 0.2 m FDS grid. Dotted beige: not by 600 s, censored and not filled with a value.

Smoke fills the room from the burner corner eastward. The plume rises along the west wall, which exceeds within 10 s. The door cells follow at 72–74 s, and the south-east corner is last, at about 83 s.

Our ASET against the release

The release contains the authors’ ASET map (0_ASET/aset_map.txt: FDS 6.5.3, K ≥ 0.23 1/m at 2.0 m, 10 s steps, cells unexceeded by 120 s set to 120 s). Built with the same 10 s steps and 120 s fill, our map has the same median, 60 s, and puts 71 % of the cells in the same 10 s step and 87 % within one step. Where they differ, ours is mostly earlier (21 % of cells against 9 % later; mean −4.7 s). The release leaves 19 cells in the western third unexceeded by 120 s; ours has none.

Release: doi:10.5281/zenodo.3875550, aset_map.txt, PIL resize of the 0.2 m slice to 0.6 m cells. Ours: any FDS node of the cell. Burner red, exit green.

The fields behind the maps agree up to 40 s and then part. Compared node by node on the 2.0 m slice at 10, 20, …, 120 s, our K and the release’s lie on the same side of 0.23 1/m at 90–100 % of nodes up to 40 s. From 50 s on our K is higher by 0.03–0.05 1/m on average and the share falls to 68–85 %. The cause is not established (Caveats). The headline map uses about 1 s steps, which makes it about 6 s earlier on average than our 10 s map and 11 s earlier than the release’s.

RSET: when the last person leaves each cell

RSET of a cell is the last time any agent is in it (paper §2.3, Eqs. 4–5), counted from ignition. The agents here walk at free speed, keep their first exit and ignore the smoke (“arm U”), so their RSET does not depend on the fire.

The door flow

The collision-free speed model on its own empties the room through the 1.0 m door in 42–45 s. The release’s JuPedSim runs need 96–103 s. We therefore run two versions on the same FDS output:

• capped: the exit removes at most one agent per second (enable_throughput_throttling, max_throughput: 1.0; see Scenario JSON), the flow we measured over 10–90 % of the agents in the release’s ten runs (0.96–1.05 persons/s);
• uncapped: the model’s own flow, reported as a model difference.

n = 10 seeds per version: line median, band minimum to maximum. Dotted grey: the release’s ten JuPedSim runs (doi:10.5281/zenodo.3875550, 1 frame/s). Black squares: the paper’s Fig. 3, read off (100 at 0 s is N).

The RSET maps

RSET, maximum over n = 10 seeds, 0.6 m cells. The plan is the same in every figure: 30 m × 10 m, burner red in the south-west corner, exits green, grey cells never visited by any agent.

With the cap, RSET is highest in the corner in front of the door, where the queue forms (101 s). Without it, no cell is occupied after 44 s. With two doors, N = 100 capped, the room is empty by 63 s; with N = 200, by 117 s.

Pre-movement is a constant delay for everyone. “The default” is the pyFDS-Evac default when a scenario sets no pre-movement key: a constant 10 s, the FDS+Evac PRE_MEAN (the gamma preset applies only on request).

DIFF: where smoke arrives before the last person leaves

DIFF = ASET − RSET per cell (paper Eq. 7). A cell fails when DIFF < 0; DIFF = 0 counts as a pass. DIFF is the time window between the first exceedance in a cell and the last presence of any agent there. The paper notes that “the exposure time of individuals cannot be concluded from this value” (p. 6); for per-agent exposure, see A crowd in a fire. Because DIFF is a margin in seconds, the maps compare versions by how much time each leaves, which is how Babrauskas et al. (2010, pp. 350–351) propose to use ASET − RSET. RSET here is the maximum over seeds, high-end with respect to the seed spread. Pre-movement is constant, so the behavioural spread that Babrauskas et al. (2010, p. 348) ask to be covered is not sampled.

One door, animated

One door, exit capped at 1.00 persons/s, pre-movement 0, seed 1 (the seed closest to the median of 99.9 s; its room empties at 99.8 s), 8 times real time. Background: K at 2.0 m from the FDS slice. Red cross: an agent in a cell whose ASET (K ≥ 0.23 1/m) has passed. Dashed outline: the DIFF < 0 cells of map (a) below. Regenerated by scripts/docs/study_animations.py.

Before 69 s no agent stands in a cell whose ASET has passed. From 75 s every agent still inside does, all of them in the queue at the capped door, up to 25 at 74 s. The agents ignore the smoke (arm U), so a cross marks where the map fails; nobody walks differently.

One door. ASET: K ≥ 0.23 1/m, any node of the cell, z = 2.0 m, about 1 s steps. RSET: maximum over n = 10 seeds. No visited cell is censored.

0.2 m FDS grid; in brackets the 0.1 m grid. Of the 847 cells with floor, 739 are visited in the capped versions; the others are shown as “not visited” and are outside the five DIFF states.

• Pre-movement shifts min DIFF one for one. It delays everyone by the same constant, so −27, −37, −57, −87 s carry no new information. Only the area and C change shape across the pre-movement versions. A constant delay is a simplification: pre-movement is a distribution whose shape depends on occupancy, warning and management, and in a dense room the first movers set the queue (Purser 2003, pp. 92, 94–97).
• C is Σ DIFF · A over the failing cells, in m²s (paper Eq. 8, without the 20 s bins of Fig. 7 and the release code). The paper’s authors “do not yet have a direct physical interpretation” of it (p. 7). Use it to rank versions.
• The door jambs. The walkable area has 0.8 m deep jambs either side of the door (Setup). They take about 1.4 m² out of the corner where RSET is highest, so the areas here are up to that much smaller than without them.

Maximum over n = 10 seeds. Filled: 0.2 m FDS grid; open diamonds: 0.1 m grid; grey bar: the grid band. Two doors: no 0.1 m run, so no grid band.

Two doors

Two doors, capped, pre-movement 0, seed 7 (the seed closest to the median of 53.7 s; its room empties at 54.2 s), 8 times real time. Same encoding as the one-door animation; the outline is the DIFF < 0 area of map (a) below.

From 15 s agents at the west door D2 stand in cells whose ASET has passed, up to 25 of them at 30 s, and from 47 s every agent still inside does. No agent at the east door D1 does. D2, about 7 m from the burner, sets the two-door result.

Two doors, 0.2 m FDS grid only: there is no 0.1 m two-door run, so no grid band.

• The second door is our assumption. The paper names no position for it. We mirrored D1 onto the west wall, about 7 m from the burner. Smoke reaches the cells at D2 at 19–29 s, against 69–70 s at D1, so D2 sets every two-door min DIFF.
• Here the uncapped crowd fails too. Its worst cell, at (0.9, 6.9) m on the way to D2, exceeds at 14 s; agents pass it until about 25 s.
• N = 200 tests the paper’s thought experiment. In §3.1 the paper doubles the occupants and adds a second exit, and states that the margin “remains more or less unchanged”. Here N = 200 with two doors gives −97 s against −27 s for one door with N = 100, and the last agent leaves at 102–118 s against 100–101 s. We attribute the difference to our D2 position; we did not run another position. The paper does not report a simulation of this case (“experiment in mind”), so the result neither confirms nor refutes it.
• The split follows shortest paths. The paper assumes shortest-path route choice. We implement it by splitting the spawn area at x = 15 m, so each agent starts with its nearer door. Every agent leaves through the door of its half.
• Seeds split the crowd. Each seed draws the west count from a binomial distribution with the west share of the floor, 0.49335. Over the ten seeds 50.4 % of the agents go west (N = 100) and 51.4 % (N = 200). Seed 10 of N = 200 puts 118 agents west and sets the maximum; the per-seed mean of min DIFF is −82.3 s.

How far to trust the numbers

Six sources of spread, on min DIFF for one door, capped, pre-movement 0:

The seed spread is small because the cap sets the exit times. With pre-movement 0 the grids agree within one cell on the area; with a 30 s wait they do not (82.9 against 68.8 m²).

Against the paper

• The min DIFF agreement is structural. The worst cell is the last cell before the door, at (29.7, 8.1) m. Its RSET is about N/1.00 ≈ 100 s (measured 101 s), set by the cap; its ASET is 73 s. So −27 s tests when smoke reaches the door, a single cell of the map.
• The −29 s is the paper’s number. It is read off Fig. 5. The release’s DIFF_map.txt has a minimum of −29 s, but its shape (18 × 51) differs from that of aset_map.txt (17 × 50), so it cannot come from the released ASET map.
• The area is about three times smaller. Ours fails in a compact block of 21 cells in front of the door; the paper’s Fig. 7 has about 55 failing elements. The released RSET map (JuPedSim Gompertz model, 1.0 m door, 95th-percentile pooling) has 61, 44 and 24 map elements occupied at or after 60, 75 and 90 s; ours has 27, 18 and 10 cells (maximum pooling). The authors’ queue covers about twice the floor area at the same flow, so it is less dense. That alone would account for most of the gap (our reading of the release, 1_RSET/RSET_map_all_seeds.txt).
• The fire is the authors’. The paper’s text does not state it; the release uses a constant 60 kW on 1 × 1 m. Its Fig. 7 (about 20 m² failing, C about −300 m²s, read off; ours, with 20 s bins: −124 m²s, context only) matches the 60 kW, N = 100 point of Figs. 5 and 8.

Sensitivity: the room rebuilt from the paper alone

Before we used the release, we rebuilt the room from the paper’s text and figures only (the hrr060 family): a 1.2 m door at y = 8.2–9.4 m, read off Fig. 2; a 0.6 × 0.6 m burner at x, y = 0.6–1.2 m with the same 60 kW; flexible polyurethane foam GM21 (soot yield 0.131, CO yield 0.010, χr 0.52; SFPE Handbook, 6th ed., App. C, Table C.12, p. 3427); v0 = 1.2 m/s, the paper’s Eq. 6 example; and the exit capped at 0.96 persons/s, read off Fig. 3. The same evacuation versions run on the current engine:

The capped crowd leaves 62.5 agents at 40 s and 24.3 at 80 s, and the last agent leaves at 105–106 s. The door cells exceed at 74–76 s, 2–3 s later than under the release conditions, and the slower cap empties the room about 5 s later; together they make min DIFF about 3.4 s lower (−30.9 against −27.5 s). The hrr060 fire grid-converges less well: on the 0.1 m grid a late pocket beside the plume first exceeds at up to 203 s, against 88 s on the 0.2 m grid, and 6.2 % of cells differ by more than 30 s.

How the maps are computed

1. ASET. FDS writes slices at z = 2.0 m every second. For each criterion, each FDS node gets the first time it holds. A 0.6 m map cell takes the earliest of its nodes (the ∃ rule, the block maximum). The clock starts at ignition; a cell that never exceeds by the FDS end, 600 s, stays open (“not by 600 s”).
2. RSET. PedPy compute_rset_map with RsetMethod.MAX: the last frame at which any agent is in the cell, at 10 frames/s, frame 0 at ignition. ASET and RSET share PedPy’s cell edges (asserted). The room is 10 m deep, so the top row is 0.4 m, and every area uses the true cell area.
3. Pooling. The maximum per cell over n = 10 seeds.
4. DIFF on every visited cell, in five states: pass, fail, ≥ bound (ASET not reached), ≤ bound and undetermined (RSET open; empty here, because every run empties the room).

RSET of a cell is travel time plus the modelled pre-movement, counted from ignition, with no detection or alarm time, and it is the last time anyone is in that cell. ISO/TR 16738, Eq. 2, defines RSET for a whole building as the sum of detection, alarm, pre-movement and travel times.

The agents ignore the fire, as in the paper’s method: “there is no inherent need to couple the fire and evacuation models … the coupling is solely conducted when analysing the model output” (§1). All runs use arm U: --smoke-blind --disable-tenability --smoke-slice-height 2.0 (see Usage). The trajectories are identical on the 0.2 m and the 0.1 m FDS output for all 50 one-door runs (asserted), so one RSET set per door layout serves both grids. Smoke feedback on speed and route choice lies outside this study.

Reproduce

The FDS decks, the scenarios and their generators are in assets/schroeder2020_room/. The FDS output and the authors’ release are not in the repository. Copy each rel_* folder into a folder DATA outside the repository and run FDS 6.10.1 in it, for example (cd DATA/rel_1door && mpiexec -n 6 fds rel_1door.fds). Then, with an empty folder RUNS outside the repository and, for the comparison with the release, the unpacked release in RELEASE:

uv run --with "pedpy>=1.5.1" python scripts/docs/schroeder_room_maps.py \
    --data DATA --runs RUNS --family rel --release RELEASE

Without --release it skips the comparison with the release. It runs the 160 evacuations (existing ones are reused), checks that every agent leaves, prints every number on this page as Markdown tables, and writes the figures to site/static/images/studies/schroeder2020/. It needs PedPy ≥ 1.5.1 for compute_rset_map. --family hrr060 with its own RUNS folder gives the paper-only rebuild; it prints all its tables and writes only the figure this page uses, hrr060/diff_1door.png.

The animations and the grid figures come from two further scripts, run after it on the same folders:

uv run --with "pedpy>=1.5.1" python scripts/docs/study_animations.py \
    schroeder --data DATA --runs RUNS --family rel
uv run python scripts/docs/schroeder_grid_figures.py --data DATA \
    --cache RUNS/cache --family rel

grid_perturbation.png comes from the same grid script with --family hrr060.

Provenance. The evacuation runs on this page were made at 4a7142f, a branch commit that is not on main; its pyfds_evac/ equals main at 100e91d. Each run’s manifest records that commit with git_dirty: false and agent_seeding: spawn-key-blake2b-v2. A re-run of all 160 evacuations on main at 449a755d, and again at 9c820e0f (Python 3.12.13, through the release check, release_check.sh --full --only study-schroeder2020), prints the same values for the headline, so cite 9c820e0f. When the code changes, re-run the command into a new RUNS folder and compare the printed tables with this page.

Setup, deviations and caveats

Caveats on the comparison with the release

• Soot and heat of combustion in FDS 6.10.1. From the same reaction line, FDS 6.10.1 computes a heat of combustion of 18,075 kJ/kg, the release’s FDS 6.5.3 17,993 kJ/kg (+0.46 %). The default hydrogen fraction of soot changed from 0.1 (6.5.3) to 0 (6.10.1, pure carbon), which changes the stoichiometry. At the same HRR our fire therefore burns 0.46 % less fuel and makes 0.46 % less soot. We keep the 6.10.1 default, as the release keeps the 6.5.3 default.
• K at 2.0 m is higher than the release’s from 50 s on, by 0.03–0.05 1/m on average, so our ASET map is earlier there. The cause is not established. The FDS version (with extinction model 1 against 2, ambient water vapour mass fraction 0.00594 against 0.00515) and the mesh decomposition both differ; the soot change acts the other way.
• HRR. The release’s FDS .out file shows 68.9 kW at its last time step. That is an instantaneous value (time step 0.9 ms at 120 s): the release’s ASET_animation_hrr.csv averages 60.0 kW over 10–120 s and over 110–120 s, as does ours (60.00 kW over 10–120 s and over 120–600 s).
• Agents also spawn in the door passage. The spawn area includes the passage between the jambs, so our first agent leaves within 2 s (last recorded at 0.4–1.9 s), the release’s at 1–3 s. In a clear-air check, excluding the passage from the spawn area moves the first exit to 0.7–1.9 s and the count left at 40 s from 60.5 to 60.6.
• No CO. The release sets no CO yield, so the FDS default of zero applies. The CO criteria and the CO term of the FED do not apply; the gas FED holds only CO₂ and O₂.
• Radiative fraction 0.35, the FDS default; the release does not print it, and we assume the 6.5.3 default is the same.

Grid

The characteristic fire diameter at 60 kW is D* ≈ 0.31 m, so D*/δx = 1.56 at 0.2 m and 3.1 at 0.1 m, and H/D* = 9.6. The FDS User’s Guide (§6.3.6) warns against taking any tabulated D*/δx as an acceptable minimum. Under the release conditions the two grids agree closely: min DIFF within 1 s, the door-region ASET within 3 s, and the area within 0.3 m² without pre-movement. With a 30 s wait the areas differ (82.9 against 68.8 m²), so both grids are given.

The FDS device trees stand at cell centres on both grids: at (5.1, 5.1), (15.1, 5.1) and (25.1, 8.5) m with points at z = 0.1–2.9 m on the 0.2 m grid, and at (5.05, 5.05), (15.05, 5.05) and (25.05, 8.55) m with points at z = 0.05–2.95 m on the 0.1 m grid. None lies on a mesh interface. The maps use only the slices; the trees give the layer profiles below.

Limits and open issues

• Not modelled here: smoke slowing agents or changing their route, and signs losing visibility. Both are open questions for the built-in maps (#210). Sign visibility is a wayfinding map and never enters DIFF (#140).
• Pre-movement is a constant here, as in the paper. A distributed pre-movement per person is the next scenario for this room.
• Engine issues that touch this study: exit throttling has no test (#355). Fixed since the earlier version: an agent leaves when its centre is within 0.03 m of the exit polygon (#349, #401); the initial exit is ranked from each agent (#350), although the room keeps two spawn areas split at x = 15 m; the smoke-blind arm (#341) and the guard against sampling past the FDS end time (#340) are in place.
• One room, one fire. The paper’s other combinations of HRR and N were not run.

Sources

What next

• ASET, RSET and the egress timeline: the classic single-point comparison this page maps.
• A crowd in a fire: per-agent exposure and a location ASET map on an FDS fire.
• RSET from an ensemble of seeds.
• Visibility through smoke, Fractional effective dose, Heat.

pyFDS-Evac is research software, provided without warranty.