Congestion Mitigation Path Planning

• Congestion Mitigation Path Planning (CMPP) is defined as an approach that embeds congestion as a design variable across robotics, traffic, and networking fields.
• It employs techniques such as homotopic route diversification, decentralized advisory control, and graph optimization to efficiently distribute flow and reduce bottlenecks.
• Evaluations using metrics like tube length, throughput, and collision avoidance validate CMPP's performance and highlight promising avenues for multi-layer, congestion-aware systems.

Congestion Mitigation Path Planning (CMPP) denotes a class of planning and control problems in which congestion is treated as an explicit design variable rather than a downstream side effect of shortest-path choice. In swarm robotics, CMPP is defined as the problem of finding safe, efficient, and flow-aware pathways for large numbers of robots moving through obstacle-dense environments (Mao et al., 2024). Closely related formulations appear in mixed-autonomy traffic, where the “path” is a sequence of speed advisories; in software-defined networking, where flows are proactively re-routed away from bottlenecks; in mixed expressway–arterial traffic control, where route guidance is coupled with perimeter control and ramp metering; and in dense multi-agent navigation, where coarse time-independent routes are selected to reduce local congestion before local collision avoidance is applied (Hasan et al., 2024, N. et al., 2018, Di et al., 2024, Kato et al., 7 Aug 2025). The literature therefore treats CMPP as a cross-domain problem spanning geometric motion planning, flow optimization, robust routing, and learned control.

1. Scope, semantics, and problem classes

In geometric robotics, congestion arises when many agents attempt to pass through narrow gaps or bottlenecks in close temporal or spatial proximity, causing slow-downs, mutual collision risk, and queueing behavior (Mao et al., 2024). The corresponding CMPP strategy is to plan multiple homotopically distinct routes that negotiate large-volume openings rather than the singular shortest tunnel, thereby distributing robot flow across several corridors.

In traffic systems, the same underlying problem is reformulated in control space. In the mixed-autonomy ring-road setting of “Cooperative Advisory Residual Policies for Congestion Mitigation,” the planner does not compute a geometric route; instead, the “path” is a sequence of speed advisories $a_t^{advice}$ intended to increase the network’s average speed and suppress shock-waves (Hasan et al., 2024). Zhou et al. similarly position longitudinal motion planning as a congestion-relevant layer beneath high-level route and lane planning, with the role of smoothing traffic flow, suppressing stop-and-go waves, and avoiding the creation of shockwaves (Zhou et al., 2019).

In communication networks, CMPP appears as traffic engineering. In SDN, the controller periodically monitors utilization, detects bottleneck links, and re-routes the largest flow through a lightly loaded alternate path, while a Bayesian admission test is used to reduce congestion propagation (N. et al., 2018). In segment-routing backbones, alternative SR paths are precomputed so that traffic can be quickly steered away from congested links while retaining resilience under any single-link failure (Martin et al., 2024).

In dense multirobot systems, CMPP may be posed directly on a sparse graph. “Congestion Mitigation Path Planning for Large-Scale Multi-Agent Navigation in Dense Environments” defines CMPP as a path-planning problem in which congestion is embedded directly into the cost function, with agents following time-independent, coarse-level routes and relying on an online local collision-avoidance layer such as ORCA or PIBT (Kato et al., 7 Aug 2025). A related large-scale formulation uses a hierarchical planner in which a multi-commodity-flow high level reduces cell congestion and a low-level planner computes collision-free paths inside each cell (Pan et al., 2024).

A common misconception is that CMPP is synonymous with shortest-path computation under dynamic weights. The literature is broader. Some formulations operate in Euclidean free space and reason about homotopy classes and corridor width (Mao et al., 2024); some operate in spatio-temporal topological graphs without any inter-robot communication (Wang et al., 2022); some combine route choice with ramp metering and perimeter control (Di et al., 2024); and some replace routing altogether with personalized advisory control (Hasan et al., 2024).

2. Formalizations of congestion and path quality

A central distinction across CMPP formulations is how congestion is quantified. In Tube RRT*, the free space is

$$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$

and two feasible paths are homotopic if they can be continuously deformed into one another inside $\mathcal{F}$ while preserving endpoints (Mao et al., 2024). A corridor is represented as a chain of overlapping maximal inscribed spheres

$\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$

with overlap constraint $r_{i-1}+r_i>\|q_i-q_{i-1}\|$. The edge score combines normalized path length and inverse overlap volume,

$$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$

so narrow gaps incur a heavy penalty (Mao et al., 2024). Congestion is therefore represented through gap volume.

In the sparse-graph CMPP formulation of 2025, congestion is attached to vertices via incoming-edge flow. For each directed edge $e=(u,v)$,

$$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$

and the congestion at vertex $v$ is

$$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$

This “product minus one” cost grows steeply when many agents enter the same area from different directions: $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$0 agents on one edge yield $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$1, whereas four incoming edges with $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$2 agents each yield $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$3 (Kato et al., 7 Aug 2025). Congestion is therefore modeled as multidirectional merging rather than raw occupancy.

In SDN, congestion is represented by link utilization and residual bandwidth:

$$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$4

A link is declared a bottleneck if $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$5, with $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$6 (N. et al., 2018). The path-planning problem then becomes one of rerouting elephant flows while ensuring that the alternate path has enough headroom to avoid congestion propagation.

In mixed-autonomy traffic, the congestion objective is encoded in rewards rather than route cost. The congestion-mitigation term is

$$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$7

augmented by an action-smoothness penalty

$$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$8

Evaluation collapses mean speed and temporal speed variance into a “Congestion Factor,”

$$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$9

(Hasan et al., 2024). Congestion is thus expressed through shock-wave suppression and speed regularity.

In mixed road networks, Di et al. formulate a route-guidance model over a multi-class CTM and MFD-coupled network, with an MPC objective that minimizes total system travel time over a horizon by combining CTM occupancy, MFD accumulation, and OD travel time (Di et al., 2024). In UAS traffic, congestion is identified by local density, occupancy, headway, queue length, and look-ahead conflict-risk probability, and detours are activated when predicted zone occupancy exceeds a threshold (Abdul et al., 2024).

These formalizations are not interchangeable. Minimum sphere volume, multidirectional merge penalties, speed variance, link utilization, and MFD accumulation all capture different operational meanings of congestion. This suggests that CMPP is best understood as a family of congestion-aware objectives rather than a single canonical metric.

3. Algorithmic families

One major family consists of geometry-aware planners that diversify homotopy or topology. Tube RRT* grows an RRT* tree in the space of spheres rather than point nodes, rewires according to minimal cumulative cost, and inherits asymptotic optimality from RRT*. As the number of samples $\mathcal{F}$0, the tree approaches the corridor of minimum cost, with overall time complexity $\mathcal{F}$1 for central planning and $\mathcal{F}$2 for homotopic path interpolation (Mao et al., 2024). The 2022 coordination-free multirobot planner similarly exploits topological diversity, using $\mathcal{F}$3-homology classes and an $\mathcal{F}$4-signature on a spatio-temporal graph. A* on the augmented graph returns shortest paths in distinct topological classes, after which robots independently sample path classes from a locally computed probability distribution (Wang et al., 2022).

A second family shapes independent paths to reduce later conflicts. Space Utilization Optimization and its heuristic realization SU-I construct occupancy tables over vertices and edges and impose the additive penalty

$\mathcal{F}$5

with $\mathcal{F}$6 (Han et al., 2021). Because the added penalty is bounded by $\mathcal{F}$7, SU-I acts as a strict tie-breaker among distance-optimal paths and preserves single-path optimality while reducing projected congestion.

A third family formulates congestion mitigation directly as graph optimization. The 2025 CMPP paper gives an exact MINLP with binary edge-use variables $\mathcal{F}$8 and congestion variables $\mathcal{F}$9, solved exactly with SCIP for small instances and approximately with A-CMTS for large instances (Kato et al., 7 Aug 2025). A-CMTS is a two-layer search: the high level branches on the most congested vertex and forces or forbids a chosen incoming edge for a chosen agent, while the low level computes a path minimizing incremental congestion. Hierarchical Large Scale Multirobot Path (Re)Planning adopts a related but distinct strategy: a high-level ILP routes commodities over a cell graph with objective

$\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$0

where $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$1 tracks per-commodity path load and $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$2 tracks peak cell influx, and a low-level MAPF/C planner computes collision-free trajectories inside each cell (Pan et al., 2024).

A fourth family couples congestion-aware search with learned components. NAHACO retains the classical ACO transition probability

$\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$3

but replaces static heuristics with neural, attention-based, dynamically calibrated heuristic scores and introduces the congestion-aware reinforcement loss CARL to update the neural module using ant tour costs (Zhang et al., 30 Mar 2025). In stochastic transportation networks, GPG-HT models reliable shortest path under stochastic dependencies using a history-aware Decision Transformer and Generalized Policy Gradient, optimizing on-time arrival probability while conditioning on the full past trajectory (Wei et al., 24 Aug 2025). This extends CMPP toward uncertainty-aware routing rather than purely deterministic congestion avoidance.

A fifth family treats congestion mitigation as routing under operational constraints. In SDN, the controller constructs a virtual topology by assigning infinite weight to bottleneck links, computes alternate paths with Dijkstra, and vets candidate paths with a three-node Bayesian Network whose hidden variable is Link Availability (N. et al., 2018). In segment-routing networks, the precomputation problem is cast either as a robust flow maximization under all single-link failures, solved via Benders decomposition, or as a relaxed combinatorial survivability problem solved in polynomial time by RAPCP (Martin et al., 2024).

4. Coordination architectures and execution layers

CMPP does not imply a single coordination model. Tube RRT* assumes centralized planning, and its authors explicitly list centralized planning as an assumption, while noting that decentralized replanning in large swarms may be possible by sharing corridor seeds (Mao et al., 2024). By contrast, the 2022 topological multirobot planner is explicitly coordination-free: robots know only the static map and their own poses, do not broadcast or share intents, probabilities, or live locations, and independently compute path-class probabilities and sample routes (Wang et al., 2022). SU-I is similarly decentralized at the heuristic level, even when embedded inside larger planners (Han et al., 2021).

Many CMPP systems are hierarchical. In dense multi-agent navigation on sparse graphs, the output is a set of coarse-level, time-independent routes, while collision avoidance is delegated to ORCA in continuous space or PIBT in discrete space (Kato et al., 7 Aug 2025). The hierarchical large-scale multirobot planner makes this split explicit: global routing occurs on a static cell graph; local goal assignment inside cells is solved by an ILP; and low-level collision avoidance is handled by ECBS, LNS-MAPF, and SIPP/C, with a buffer protocol at cell faces to support continuous replanning and non-stop execution (Pan et al., 2024). Tube RRT* likewise separates corridor planning from execution by a distributed virtual tube controller (Mao et al., 2024).

In traffic systems, the coordination structure can be minimal. The advisory residual-policy framework requires only a single vehicle with a human driver and local onboard observations such as ego speed, leader speed, and headway, without roadside sensors or centralized sensor infrastructure (Hasan et al., 2024). The driver model explicitly captures uncertainty in compliance through Gaussian noise, uniform random reaction delay, and intentional speed offset. In mixed road networks, the opposite design choice appears: route guidance, perimeter control, and ramp metering are jointly optimized in a centralized MPC loop over CTM and MFD states (Di et al., 2024).

Dense urban airspace introduces yet another execution model. UAS follow preapproved nominal paths from UTM, monitor positional broadcasts in their local zone and look-ahead horizon, and activate deterministic local rerouting rules into adjacent unoccupied airspace when congestion is predicted (Abdul et al., 2024). The approach is decentralized at execution time but depends on nominal path information and reserved surrounding airspace.

These contrasts show that CMPP spans centralized, decentralized, and mixed architectures. What remains consistent is the division between a congestion-aware planning or advisory layer and an execution layer that enforces kinematic, safety, or communication constraints.

5. Evaluation methodologies and reported results

Evaluation protocols vary sharply by domain, but most studies compare congestion-aware planning against shortest-path-following, disabled congestion terms, or simpler baselines. In Tube RRT*, the reported metrics are Average Tube Length (ATL), Minimum Sphere Volume (MSV), and Computation Time (CT). On maps of size $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$4 with $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$5–$\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$6 randomly placed cubic obstacles and a swarm of $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$7 drones, the comparison at $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$8 obstacles gives Disabled: $\Sigma_c=\{(q_0,r_0),(q_1,r_1),\dots,(q_m,r_m)\},$9, $r_{i-1}+r_i>\|q_i-q_{i-1}\|$0, $r_{i-1}+r_i>\|q_i-q_{i-1}\|$1; and Tube-RRT*: $r_{i-1}+r_i>\|q_i-q_{i-1}\|$2, $r_{i-1}+r_i>\|q_i-q_{i-1}\|$3, $r_{i-1}+r_i>\|q_i-q_{i-1}\|$4. Flight-level validation reports $r_{i-1}+r_i>\|q_i-q_{i-1}\|$5–$r_{i-1}+r_i>\|q_i-q_{i-1}\|$6 faster overall traversal time, lower peak-to-peak speed variations, and no inter-drone safety breaches at narrow gaps (Mao et al., 2024).

The coordination-free topological planner evaluates average and maximum travel time, collision time, and sensitivity to traffic-density information. On “cage_1” with $r_{i-1}+r_i>\|q_i-q_{i-1}\|$7 robots and $r_{i-1}+r_i>\|q_i-q_{i-1}\|$8 pedestrians, the ensemble model with max-time cost reaches average travel time $r_{i-1}+r_i>\|q_i-q_{i-1}\|$9 of baseline and maximum travel time $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$0; without the density map, the ratios worsen to $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$1 and $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$2; and in real-robot experiments on “cage_2” with $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$3, the average travel time is $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$4 of shortest-path baseline and the maximum travel time is $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$5 (Wang et al., 2022). SU-I evaluates peak vertex usage, total path collisions, solver time, and throughput. On a $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$6 grid with $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$7 obstacles and $$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$8–$$\mathrm{Score}(x_a,x_b)=\rho_d\cdot \frac{\|q_b-q_a\|}{\|q_{goal}-q_{init}\|}+\rho_v\cdot\left(\frac{V_{int}(x_a,x_b)}{\sigma_v}+\epsilon\right)^{-1},$$9 robots, SU-I cuts peak single-vertex usage by $e=(u,v)$0–$e=(u,v)$1 immediately, converges by $e=(u,v)$2 iterations, and, when integrated into DDM, reduces mean runtime by more than $e=(u,v)$3 and sum-of-cost by approximately $e=(u,v)$4 (Han et al., 2021).

In dense-graph CMPP, evaluation emphasizes throughput and downstream local-planner effectiveness. With ORCA in continuous space, at $e=(u,v)$5 agents, success at $e=(u,v)$6 improves from $e=(u,v)$7 to $e=(u,v)$8 under CMPP guidance. With PIBT in discrete lifelong MAPF, throughput increases by up to $e=(u,v)$9 on warehouse-10-20-10-2-1 at $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$0 and by $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$1 on random-64-64-10 at $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$2 (Kato et al., 7 Aug 2025). The hierarchical cell-based multirobot replanner reports empirical results of a $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$3-times speedup in computation time relative to the baseline multi-agent pathfinding approach, real-time performance with up to $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$4 robots in simulation, and a representative experiment with $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$5 physical Crazyflie nano-quadrotors (Pan et al., 2024).

Traffic-oriented CMPP uses different performance measures. Residual advisory policies on a single-lane ring road in SUMO and CARLA are evaluated by Congestion Factor, with RP and PeRP improving CF by $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$6–$$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$7 over PCP in $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$8-run simulations and by up to $$f_e:=\left|\left\{i\in A\mid \exists k,\;(\pi_i[k],\pi_i[k+1])=(u,v)\right\}\right|,$$9 in a user study with $v$0 licensed drivers; ANOVA shows significant effects of policy type and hold length on CF with $v$1 (Hasan et al., 2024). In the mixed expressway–arterial MPC framework, the cooperative guidance and control strategy reduces average total accumulation from $v$2 to $v$3 vehicles relative to NGNC, raises average total throughput from $v$4 to $v$5, and reduces TSTT by approximately $v$6 (Di et al., 2024). In stochastic transportation networks, GPG-HT reports up to $v$7 on-time-arrival probability gain over Dijkstra on mean travel times at tight budgets and approaches the theoretical upper bound of $v$8 by achieving $v$9 on the synthetic task (Wei et al., 24 Aug 2025).

Communication-network CMPP uses packet loss, throughput, delay, reroutable flow, or survivability. The proactive SDN scheme improves throughput from approximately $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$0 to $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$1 and reduces loss from $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$2 to $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$3 in a single-flow scenario; for $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$4 concurrent flows, average packet loss improves from $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$5 to $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$6, average throughput from approximately $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$7 to approximately $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$8, and average end-to-end delay from $$C(v):=\left(\prod_{e\in\delta^-(v)}(f_e+1)\right)-1.$$9 to $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$00 (N. et al., 2018). In segment-routing networks, RAPCP answers in less than $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$01 on all instances, while the Benders-based robust method provides better worst-case reroutable flow at the cost of tens of seconds (Martin et al., 2024).

6. Limitations, misconceptions, and open directions

The literature repeatedly emphasizes that congestion mitigation is geometry- and domain-limited. Tube RRT* assumes static obstacles only, requires centralized planning, and notes that in extremely narrow environments with few homotopy options, congestion mitigation is limited by geometry (Mao et al., 2024). The coordination-free topological planner has no formal guarantee on overall collision-free operation, only local collision avoidance through repulsion and cancellation (Wang et al., 2022). SU-I may lose advantage in extremely dense narrow passages where robots must funnel through nearly identical alternates, although it still preserves distance optimality (Han et al., 2021).

Traffic-control formulations have their own restrictions. The advisory residual-policy framework assumes a single-lane ring road, one advisory vehicle, fixed hold length $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$02, and offline VAE training, with proposed extensions to multi-lane networks, multiple advisors, adaptive hold lengths, and online adaptation of trait inference (Hasan et al., 2024). Zhou et al. identify a broader data problem: public self-driving datasets contain few sustained congested segments and often lack throttle/brake telemetry, annotated headways, and system-level labels such as speed variance or string-stability amplification factors, limiting the training of congestion-aware longitudinal motion planning (Zhou et al., 2019). Di et al. assume MFD stationarity and homogeneity within each arterial subregion, CTM parameter fidelity, and a constant compliance fraction, and note limitations from off-ramp spillbacks, driver-response prediction, and calibration errors (Di et al., 2024).

Large-scale routing formulations also face structural trade-offs. The 2025 dense-environment CMPP paper assumes time-independent routes and delegates timing and synchronization to the local layer; unpredictable behavior or strong adversarial delays may violate congestion estimates (Kato et al., 7 Aug 2025). Segment-routing precomputation is presently framed for single-link failures; the authors list multi-link-failure resiliency, partial traffic splitting among $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$03 paths, distributed heuristics, and dynamic policy adaptation under live load feedback as future extensions (Martin et al., 2024). In SDN, periodic polling every $$\mathcal{F}=X\setminus\left(\bigcup_{i=1}^N O_i\right),$$04 adds controller overhead and detection delay, and no topology abstractions are provided for very large networks (N. et al., 2018).

A further misconception is that congestion is always best addressed by centralized, globally optimal planning. Several papers instead emphasize lightweight, distributed, or rule-based mechanisms: coordination-free stochastic route diversification in topology space (Wang et al., 2022), local advisory control using one human-driven vehicle (Hasan et al., 2024), and UAS rerouting using only local positional broadcasts and nominal path information (Abdul et al., 2024). Conversely, some settings explicitly require heavy global coordination, as in MPC over CTM–MFD mixed-road models (Di et al., 2024) or exact MINLP over sparse graphs (Kato et al., 7 Aug 2025). The controversy is therefore not over whether congestion should be modeled, but over where in the stack it should be modeled: in global route choice, local motion control, execution-time rerouting, or robust precomputation.

Open directions named in the literature include dynamic-obstacle extensions for homotopic tube planning (Mao et al., 2024), richer congestion forecasts and occasional broadcast in coordination-free multirobot systems (Wang et al., 2022), integration of string-stability theory into learned longitudinal controllers (Zhou et al., 2019), dynamic graph updates and integration with placement or task allocation (Kato et al., 7 Aug 2025), and hierarchical or graph-sparsification methods for city-scale stochastic routing (Wei et al., 24 Aug 2025). Taken together, these directions indicate that CMPP is evolving from isolated path-planning heuristics toward multi-layer congestion-aware systems that jointly address geometry, uncertainty, scalability, and execution.