Congestion and extreme events in urban street networks

Ajay Agarwal; M. S. Santhanam

REVIEW 3 major objections 4 minor 43 references

Congestion and extreme events in urban street networks

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Real city street networks, like a square grid, tip from free-flow to congested traffic at a critical vehicle birth rate, and low-degree junctions host extreme events more often than hubs.

desk verdict A solid simulation study with a plausible new regime that is not yet statistically established; worth sending to a referee who will demand error bars and finite-size checks. read the letter →

arxiv 2505.15613 v1 pith:3N5Z7MWM submitted 2025-05-21 physics.soc-ph cond-mat.dis-nnphysics.data-an

Ajay Agarwal , M. S. Santhanam This is my paper · ORCID

classification physics.soc-phcond-mat.dis-nnphysics.data-an PACS 89.40.Bb05.40.Fb

keywords congestionextremeeventsurbanstreetnetworksplanarphasetransitionrandomwalktransportmodelfree-flowandcongestedregimes

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses a random-walk model of vehicles—each node can create, serve, queue, and reject traffic—to ask whether real city street networks show the same congestion and extreme-event physics as simpler network models. Across the street networks of Ahmedabad, Delhi, Mumbai, and New York, and on a regular square grid, the authors find a free-flow-to-congested phase transition as the vehicle birth rate rises. Traffic-aware routing shifts the transition but cannot eliminate congestion. In the free-flow regime, low-degree junctions are more likely to see extreme traffic spikes than hub junctions, the same ordering previously reported for non-planar scale-free networks. The authors conclude that, for congestion and extreme events, real street networks and a square grid behave nearly alike, with a semi-congested regime appearing only in organically grown cities.

What carries the argument

The load-bearing object is a transport model built from FIFO queues: at each time step a node creates a vehicle with probability $p$, serves up to $r_i$ queued vehicles into a randomly chosen neighbour, and rejects incoming traffic with probability $\eta(n_i)$ that switches on when the queue exceeds capacity $n^*_i$. The order parameter $\rho$ in Eq. (2) classifies the resulting state as free flow ($\rho=0$), weakly congested ($0<\rho<1$), or congested ($\rho=1$). Three parameterisations of the same machinery—constant ($M_c$), degree-dependent ($M_d$), and capacity-scaled with total rejection at overload ($M_{dr}$)—probe how node degree changes the transition. Extreme events are defined within the free-flow state as crossings of the node-dependent threshold $q_i=\langle n_i\rangle + m\,\sigma_i$, and the probability $P^{\,i}_{EE}$ is averaged over nodes of equal degree to produce the degree-ordering result.

What would settle it

Run the same three model variants on, say, 50 real street networks of widely varying size, measuring $\rho$ with error bars from many independent runs. If the semi-congested band ($0<\rho<1$) disappears or shrinks as network size grows, or if any network in free flow shows hub nodes with extreme-event probability as high as low-degree nodes, the paper's universality claims fail.

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Extended reading notes

Core claim

The central claim is that planar urban street networks exhibit the same congestion phase transition as a regular square grid: for all four cities and the grid, there exists a critical vehicle birth rate $p_c$ such that the total vehicle count $A(t)$ fluctuates around a mean in the free-flow phase and grows without bound in the congested phase, as measured by the order parameter $\rho = \lim_{t\to\infty}[A(t+\tau)-A(t)]/(N p \tau)$. This holds under three model variants—constant parameters ($M_c$), degree-dependent capacity and outflux ($M_d$), and degree-scaled outflux with total rejection at overload ($M_{dr}$). In the free-flow state, the extreme-event probability $P^{\,i}_{EE}$, defined as the fraction of time the node's queue exceeds $q_i = \langle n_i\rangle + m\,\sigma_i$, is larger on small-degree nodes than on hubs. In the $M_{dr}$ variant, organically grown cities (Ahmedabad, Delhi, Mumbai) show a semi-congested regime with $0<\rho<1$, where congested and free-flow behaviour coexist, while grid-like New York and the square lattice do not. The paper concludes that street networks and the square grid display similar congestion and extreme-event properties, and that the hub/low-degree extreme-event ordering does not require scale-free or non-planar topology.

Load-bearing premise

The claim that a distinct semi-congested regime exists rests on eyeballing the time evolution of total vehicle count for a few parameter combinations on only four cities, with no statistical test or scaling analysis to show the regime would survive with a larger network or longer simulation, and the authors themselves say more networks are needed.

Editorial extensions

If this is right

All four city networks and the square grid show the same free-flow-to-congested transition, so a regular grid is a serviceable first model for city-wide congestion phase behaviour.
Because traffic-aware routing moves the critical birth rate but cannot remove congestion, routing alone is not a cure for network saturation.
The semi-congested regime in organically grown cities means such networks can run with some parts jammed and others free-flowing, a mixed state that grid-like New York and the square lattice do not show.
The extreme-event ordering—low-degree nodes more prone to spikes than hubs—carries over from non-planar scale-free networks to planar street networks and the square grid.
Extreme-event probabilities stay at the same order of magnitude across different $(a_0,b_0)$ pairs inside the free-flow regime, so the phenomenon does not depend on the exact parameter values.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the semi-congested regime is genuine phase coexistence rather than a finite-time artifact, it should show hysteresis: ramping $p$ up and then down should trace different paths through the phase diagram. This is a testable extension the paper does not perform.
A natural next step is to ask whether the degree ordering of extreme events survives under shortest-path or congestion-aware routing, which the paper's random-walk dynamics do not include; if it fails, the ordering is tied to the dynamics rather than the planar topology.
Because low-degree junctions are the extreme-event hot spots, traffic-management schemes aimed at protecting small intersections might suppress the worst spikes more effectively than hub-focused interventions—an engineering corollary the authors do not draw.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read this one before you think about the abstract. The paper does something simple and useful: it runs a known traffic model (De Martino et al. with FIFO queues) on real street networks from four cities and compares to a grid. The main finding, that the free-flow to congested transition looks the same on all of these and that extreme events are more likely at small-degree nodes, is shown consistently across three model variants. That last result is a genuine extension of the scale-free network result to planar street networks, and it is not trivial.

The interesting new claim is the semi-congested regime in organically grown cities (Delhi, Mumbai, Ahmedabad) and its absence in New York and the grid. That is a plausible structural difference, and if it holds, it matters for urban traffic modeling. The problem is the evidence. The regime is defined by eyeballing A(t) shapes (linear, piecewise-linear, coexisting, free-flow) for selected (a0,b0) pairs, with no error bars, no finite-size scaling, no stated simulation time, and no threshold on what counts as rho=0. A slowly congesting transient can look exactly like piecewise-linear growth and produce rho in (0,1). The paper also never gives the value of m in the extreme event threshold, and the statements about pc

Also minor: there is a typo in Sec. III C where the congested phase is said to have rho=0 (should be rho=1), and no code or data are provided, which makes the missing details harder to fill in. The authors do admit the four-city sample is small, which is honest.

This paper deserves a serious referee. The questions it asks are good, the simulations are cheap to reproduce in principle, and the main qualitative claims are likely to survive closer scrutiny. The revision should add error bars, a finite-size check, the actual value of m, and ideally the code. I would send it to peer review, and I would not be surprised if it comes back stronger after those fixes.

Referee Report

3 major / 4 minor

Summary. The manuscript studies a stochastic transport model in which particles are created at nodes with probability p, move via random hops with rejection and absorption, and are stored in FIFO queues; three parameterizations are studied: constant parameters (Model Mc), degree-dependent capacity and outflux (Model Md), and a rejection rule with scaled parameters (Model Mdr). Simulations are run on street networks of Ahmedabad, Delhi, Mumbai, and Manhattan from OpenStreetMap and on a 1000-node square lattice. The paper reports a free-flow-to-congested transition as p increases in all networks and models, a weakly congested or semi-congested regime in the organically evolved networks in Model Mdr that is absent in Manhattan and the grid, and a higher extreme-event probability at low-degree nodes than at hubs. The paper also claims that congestion cannot be fully mitigated by traffic-aware routing and that the street networks and grid behave similarly overall.

Significance. If the claims are correct, the paper extends previously known phase-transition and extreme-event results from synthetic scale-free networks to realistic planar street networks, and the proposed semi-congested regime in organically grown cities would be an interesting, potentially actionable phenomenon. The strengths are the use of three related transport models on real urban networks, the systematic comparison with a square lattice, and the clear demonstration that a simple random-walk-based model captures qualitatively plausible congestion behavior. The main novel claim, however, rests on a visual classification of time series without statistical error bars or finite-size scaling, and the extreme-event section omits a key threshold parameter; these need to be supplied before the results can be evaluated.

major comments (3)

[Sec. III C, Figs. 6-8] The existence and distinctness of the semi-congested/weakly congested regime is the central novel claim, but it is established by visually classifying A(t) into "linear, piece-wise linear, coexisting and free-flow" for selected (a0,b0) pairs and by the rho heat map in Fig. 8; no quantitative criterion, no error bars, no finite-size scaling, and no simulation length T are reported. Because a slowly congesting finite-time transient can display piecewise-linear A(t) and produce 0<rho<1, the current evidence cannot distinguish a genuine regime from a long transient. Please provide a statistical definition of the regimes, show rho as a function of observation time to demonstrate stationarity, and vary the network size (or at least state T and show error bars) for the heat-map boundaries.
[Sec. III D, Eq. (4), Fig. 9] The threshold m in qi = <ni> + m*sigma_i is never specified, and the simulation duration T in Eq. (5) is not given. Since P_EE depends on m and on the length of the stationary time series, the claim that low-degree nodes have higher extreme-event probability in Fig. 9 cannot be reproduced or quantitatively assessed. State the value of m used, report T, and show that the degree dependence is robust over a range of m.
[Sec. III A, Fig. 4 (and Sec. III B, Fig. 5)] The statements "pc < mu" and "pc decreases mildly with eta" are read off from rho(p) data without defining how pc is estimated and without confidence intervals. As these statements are part of the phase-transition comparison across networks, the pc extraction rule and its uncertainty should be reported, or the claims should be formulated more cautiously.

minor comments (4)

[Sec. III C, text near Fig. 6] The text states that a congested regime has "rho = 0" immediately before describing Fig. 6(a), while the same paragraph and the Fig. 6(a) caption define the congested state by rho = 1; correct this inconsistency.
[Sec. III D, Eqs. (5) and (6)] Equations (5) and (6) are identical definitions of P_EE and should be merged into a single equation.
[Sec. III B] The side claim that Model Md completely eradicates congestion on scale-free networks (rho(p)=0 for any eta) is unsupported by any displayed data and is referenced to an unpublished Master's thesis [43]; this should either be shown with data or removed, since it is not needed for the paper's main argument.
[Table I and ref. [39]] There are minor typographical errors: "cirlce" should be "circle" in the Table I caption, and "Openstreemap" in ref. [39] should be "OpenStreetMap".

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the paper reports simulation measurements with standard order-parameter and threshold definitions; statistical robustness concerns are separate from circularity.

full rationale

All central quantities are measured from simulation rather than derived from the model inputs by construction. The order parameter rho (Eq. 2) and the extreme-event threshold q_i = mean + m sigma (Eq. 4) are operational definitions applied to the simulated time series; the threshold is not fitted to make small-degree nodes have more extreme events, and P_EE is computed after the fact from the same stationary series in a standard way. The phase classification in Sec. III C uses A(t) shapes and rho values as descriptive labels; it is not a fit of a parameter that is then re-reported as a prediction. The comparison with the 2D lattice and with scale-free networks uses prior work (refs [30,31]) as external benchmarks, and the one self-citation (ref [43]) accompanies simulations the authors state they performed, so it is not load-bearing. The absence of error bars, finite-size scaling, and statistical criteria for the semi-congested regime is a rigor/correctness limitation, not circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central results depend on a small set of chosen simulation parameters and on a subjective classification of dynamical regimes; no new entities are postulated. The model parameters mu, n*, r, a0, b0 are inherited from prior work or hand-selected, and the extreme event threshold multiplier m is never stated, which is a reproducibility gap.

free parameters (5)

mu (particle absorption probability) = 0.2
Chosen constant, not fitted to data; used across all models and affects the location of pc but not the qualitative conclusions.
n* (buffer capacity) in Model Mc = 10
Chosen constant in constant-parameter model; influences onset of congestion.
r (outflux) in Model Mc = 1
Chosen constant; combined with mu sets the critical birth probability scale.
m (extreme event threshold multiplier) = not specified in paper
Defines q_i = <n_i> + m sigma_i in Eq. 4, but the value used for Fig. 9 is never stated, making the PEE result not fully reproducible.
a0, b0 (capacity/outflux scaling in Model Mdr) = scanned; free-flow at (6,6) for organic cities and (4,4) for grid-like
Chosen by hand to identify free-flow states for extreme event analysis; the selection criterion is qualitative.

assumptions (4)

domain assumption The random walk birth-death-queue model with independent particles is a valid abstraction of urban vehicular traffic for congestion and extreme event questions.
The paper assumes this model captures the essential physics; it is a variant of De Martino et al. [30,31].
domain assumption The order parameter rho computed over finite simulation time reliably separates free-flow, weakly congested, and congested phases, and the observed regimes are steady-state phases rather than finite-time transients.
No finite-size scaling or statistical test is provided; the classification is based on the temporal shape of A(t).
domain assumption Street networks of the four selected cities, each truncated to ~1000 nodes, are representative of organically evolved versus planned urban networks.
The paper draws general conclusions about organic versus planned cities from three Indian cities and Manhattan.
domain assumption OpenStreetMap data retrieved via OSMnx in October 2024, converted to simple undirected graphs, adequately represent the road networks.
The conversion to a simple undirected graph discards directionality and turn restrictions, which may affect traffic dynamics.

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Cite this review

Pith. "Pith review of Congestion and extreme events in urban street networks." pith.science (2026). https://pith.science/paper/3N5Z7MWM

@misc{pith2026250515613,
  author       = {Pith},
  title        = {Pith review of: Congestion and extreme events in urban street networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3N5Z7MWM}},
  note         = {Machine review of arXiv:2505.15613}
}

read the original abstract

Congestion and extreme events in transportation networks are emergent phenomena with significant socio-economic implications. In this work, we study congestion and extreme event properties on real urban street (planar) networks drawn from four cities and compare it with that on a regular square grid. For dynamics, we employ three variants of random walk with additional realistic transport features. In all the four urban street networks and 2D square grid and with all dynamical models, phase transitions are observed from a free flow to congested phase as a function of birth rate of vehicles. These transitions can be modified by traffic-aware routing protocols, but congestion cannot be entirely mitigated. In organically evolved street networks, we observe a semi-congested regime which has both congested and free-flow components. In the free-flow regime, the extreme event occurrence probability is larger for small degree nodes than for hubs, a feature originally observed in non-planar scale-free networks. In general, with respect to congestion and extreme events, the urban street networks and regular square grid display similar properties.

Figures

Figures reproduced from arXiv: 2505.15613 by the authors.

**Figure 3.** FIG. 3. Spatial network of urban streets of selected region (see Table [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** FIG. 4. Simulation results for Model- [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: FIG. 5. Simulation results for Model- [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 7.** Figure 7: FIG. 7. Dynamics on New York street network. (a) Congested [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: FIG. 8. Heat map showing the phases of congestion for dif [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

**Figure 9.** Figure 9: FIG. 9. Probability for the occurrence of extreme events [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

S.Albeverio, V.Jentsch,andH.Kantz, Extreme events in nature and society (Springer Science & Business Media, 2006)

work page 2006

[2] [2]

M. S. Santhanam and H. Kantz, Return interval distribu- tion of extreme events and long-term memory, Physical Review E78, 051113 (2008)

work page 2008

[3] [3]

Kishore, M

V. Kishore, M. S. Santhanam, and R. E. Amritkar, Ex- treme events on complex networks, Physical review let- ters 106, 188701 (2011)

work page 2011

[4] [4]

Kishore, M

V. Kishore, M. S. Santhanam, and R. E. Amritkar, Ex- treme events and event size fluctuations in biased random walks on networks, Physical Review E85, 056120 (2012)

work page 2012

[5] [5]

M. S. Santhanam, Extreme event recurrence time distri- butions and long memory, Extreme Events and Natural Hazards: The Complexity Perspective196, 335 (2012)

work page 2012

[6] [6]

Kishore, A

V. Kishore, A. R. Sonawane, and M. S. Santhanam, Manipulation of extreme events on scale-free networks, Physical Review E88, 014801 (2013). 8

work page 2013

[7] [7]

Kumar, S

A. Kumar, S. Kulkarni, and M. Santhanam, Extreme events in stochastic transport on networks, Chaos: An Interdisciplinary Journal of Nonlinear Science30 (2020)

work page 2020

[8] [8]

Gupta and M

K. Gupta and M. S. Santhanam, Extreme events in nagel–schreckenberg model of traffic flow on complex net- works, The European Physical Journal Special Topics 230, 3201 (2021)

work page 2021