Joint Dynamic Lane Reversal and Variable Speed Limit Control: A Graphormer-Based Approach

I. INTRODUCTION

• Network-wide reconfiguration must account for how traffic redistributes and preserve junction reachability at every step, including while lanes clear for reversal.The paper also identifies a gap in learned policies that jointly control lanes and speed limits on general networks while permitting one-way roads.Source: §I · pp. 1–2
• Action resolution accepts direction-closing proposals only while strong connectivity holds, relaxing or reverting others and preserving reachability during lane clearing.The formulation combines dynamic lane allocation, directional speed limits, one-way roads, explicit lane clearing, and a strongly connected navigable graph.Source: §I · p. 2
• A shared transformer attends across road-time tokens, uses endpoint relations between roads, and is pretrained on action-conditioned forecasting before per-road PPO fine-tuning.The mixed reward includes neighboring roads and the network, reflecting traffic costs imposed on roads that absorb diverted traffic.Source: §I · p. 2

II. PRIOR WORK

• The paper reviews prior work spanning lane reversal, variable speed limits, integrated controls, learning-based coordination, and spatio-temporal and graph attention.Its stated positioning is a learned policy combining network-wide lane and speed control with one-way roads and guaranteed strong connectivity.Source: §I · pp. 1–2, §II · p. 2

A. Lane Reversal and Contraflow

• Prior lane-reversal methods largely optimize against given or forecast demand, while an RL approach keeps at least one lane open in each direction; this work permits one-way roads when connectivity holds.Lane clearing is modeled explicitly, so a reversal takes effect only once traffic allows.Source: A. Lane Reversal and Contraflow · pp. 2–3

B. Variable Speed Limits

• Prior variable speed-limit work includes freeway and network settings, whereas this paper sets limits on every road and direction of an urban network jointly with lane allocations.The cited work includes advisory signs, model-predictive control, and reinforcement learning approaches to speed control.Source: B. Variable Speed Limits · p. 3

C. Integrated Control

• Integrated lane or width reallocation with flow and speed control has used model-based optimization on freeways and motorways; this work targets general networks with integer lane counts and directed-reachability constraints.The prior settings described include continuous-width or bidirectional roads.Source: C. Integrated Control · p. 3

D. Learning-Based Network Traffic Control

• Prior network traffic RL shares information or parameters across intersection agents; this work shares one model across roads, uses per-road PPO, and combines invalid-action masking with connectivity shielding.Its self-supervised pretraining forecasts traffic conditioned on intervening actions.Source: D. Learning-Based Network Traffic… · p. 3

E. Spatio-Temporal and Graph Attention

• Unlike attention models that separate spatial and temporal steps, this model attends jointly over road-time pairs and biases attention by relations between adjacent roads, including flow directions at their shared junction.Its directional spatial embedding distinguishes how neighboring roads are split between a road’s two head junctions; the controller graph is kept separate from the navigable graph.Source: E. Spatio-Temporal and Graph Attention · pp. 3–4

F. Positioning

• The paper positions its approach as combining learned network-wide lane and speed control, one-way roads, and guaranteed strong connectivity through graph-theory-based action resolution and a shared transformer.Source: F. Positioning · p. 4

A. Road Graphs

• A road graph admits strongly connected one-way orientations when it has no bridges; bridge roads therefore retain both directions, and action resolution preserves connectivity as lanes change.Strong connectivity means every junction can reach every other, and the navigable arc set must satisfy that condition at each time step.Source: A. Road Graphs · pp. 4–5

B. Controller Graph

• The controller graph is the line graph of the infrastructure: roads are vertices, and roads sharing a junction are adjacent.It captures direct traffic coupling, whereas information sharing is not restricted to this graph’s neighborhoods.Source: B. Controller Graph · p. 5

C. Lane Allocations and Speed Limits

• Lanes changing direction are closed to both directions until vehicles leave in their old direction, then reopen together in the new direction.During clearing, the open lanes in the two directions need not sum to the road’s total lanes.Source: C. Lane Allocations and Speed Limits · p. 5, Figure 2 · p. 5
• Active speed limits range from a positive crawl speed to the engineer-set nominal limit, with normalized values interpolating between those bounds.Lowering a limit slows traffic but cannot stop it; closing all lanes in a direction is required to stop that direction’s traffic.Source: C. Lane Allocations and Speed Limits · p. 6

D. Joint Action

• At each decision step, the joint action proposes one forward lane count per road and normalized speed limits for each road and direction.Clearing roads must keep their target lanes; non-clearing bridge roads must retain at least one lane in each direction.Source: D. Joint Action · p. 6

E. Action Resolution

• A proposed lane change sets a target, but lanes being reassigned remain closed until their old-direction traffic clears; speed limits take effect immediately.The prospective navigable arc set is assessed before clearing completes, when the road has the fewest open lanes.Source: E. Action Resolution · pp. 6–7, Figure 3 · p. 7
• Strong connectivity is enforced during resolution: non-closing proposals are accepted, while closing proposals are tested individually in random order.Rejected proposals are relaxed to preserve one lane in the would-be-closed direction on multi-lane roads, or reverted on single-lane roads.Source: D. Joint Action · p. 6, E. Action Resolution · p. 7
• When individually safe closing proposals conflict collectively, the random order determines which is accepted and which is relaxed.The procedure avoids systematically favoring a particular road when such proposals conflict.Source: E. Action Resolution · p. 7
• If the initial navigable arc set is strongly connected, action resolution preserves strong connectivity at every step and between steps, regardless of clearing completion times.The proposition covers any admissible actions and any order for considering closing roads.Source: E. Action Resolution · pp. 7–8

IV. PROPOSED ARCHITECTURE

• All road controllers share one transformer, with each controller read out from the shared model’s outputs for its road.The architecture uses spatial embeddings for roads and temporal embeddings for positions within the input window.Source: §IV · p. 8
• GERASTSA jointly attends across space and time, allowing every token to attend to every road at its own and earlier time steps.Attention is biased by learned relations between road endpoints, including how adjacent roads meet at a junction.Source: §IV · p. 8
• The model processes roads in a fixed indexing and has configured limits for window length, relation distance, and maximum junction degree.Its hyperparameters also specify widths, head and layer counts, and a layer-normalization stabilizer.Source: §IV · p. 8

A. GERASTSA Block

• Within a sample, attention spans all road–time tokens, and the mask allows or forbids attention between tokens.The token map flattens window positions and road indices into one sequence.Source: A. GERASTSA Block · p. 8
• Road-pair relations distinguish self, adjacency by the directions of flow into a shared junction, and hop distance capped at a maximum.Each relation selects a learned bias for every attention head; that bias is shared across time lags.Source: A. GERASTSA Block · p. 9, Figure 4 · p. 9
• Temporal order enters through the attention mask and temporal embeddings, while the relational bias depends on the roads rather than the time lag.The block’s output passes through a learnable output projection.Source: A. GERASTSA Block · p. 9
• Attention scores combine scaled query–key products with relational bias and a mask, and the resulting weights are zero where attention is forbidden.The block projects tokens into queries, keys, and values before splitting them into heads.Source: A. GERASTSA Block · p. 9

• The same model maps each network history to an output vector for every sample, road, and window position, without parameters tied to a particular road.Re-indexing roads permutes outputs accordingly, and parameter shapes do not depend on the road count or graph.Source: B. GERASTSA Transformer · pp. 9–10
• Left-padding aligns samples’ last time steps, and valid tokens cannot attend to padding, so valid-position outputs match those from processing each sample alone.Outputs at padding positions are ignored.Source: B. GERASTSA Transformer · pp. 9–10, Figure 6 · p. 11
• A GERASTSA block attends over flattened road–time tokens, adding learned endpoint-relation bias and a mask that restricts attention to valid causal positions.The transformer stacks these blocks with feedforward networks in residual layers, then applies layer normalization and a linear map to produce outputs.Source: Figure 5 · p. 10, B. GERASTSA Transformer · p. 10, Figure 6 · p. 11
• The spatial embedding sums learned rows selected by each road’s junction degrees, while the temporal embedding marks each position relative to the window’s last time step.The embeddings are added to the linearly lifted input at every road and position.Source: B. GERASTSA Transformer · p. 10

• A vectorized mesoscopic simulator runs parallel environments, applies joint road-controller actions through action resolution, and completes clearing after vehicles leave clearing lanes.All simulated vehicles are homogeneous CAVs communicating with road infrastructure.Source: A. Environment · p. 11
• The simulated network has 60 roads and 200 lanes on a 6 × 6 junction grid, with 2, 4, or 6 lanes per road and nominal speed limits of 40, 60, or 70 km/h.Roads are oriented eastward or southward; 30 have two lanes, 20 have four, and 10 have six.Source: A. Environment · p. 11
• Each episode simulates a day with decisions every 600 seconds, morning and evening commuter peaks, and roads initially split evenly between directions at nominal speed limits.The morning rush peaks at 08:00 toward the commercial zone, and the evening return peaks at 17:30.Source: A. Environment · p. 11
• Vehicles account for congestion and mean velocity when evaluating routes, rerouting when the next direction is closed or a cheaper route clears the threshold.The strongly connected navigable graph ensures a vehicle rerouting because a direction closed can reach its destination junction.Source: A. Environment · p. 11

• The self-supervised multi-horizon task forecasts congestion, density, and normalized velocity for every road and direction, while also training the model to respond to lane allocations and speed limits.Training episodes come from a random behavior policy, with action resolution exposing the data to accepted, rejected, and relaxed proposals.Source: B. Pretraining · p. 12
• The encoder uses 561,600 parameters and a maximum 150-minute history window of 960 road–time tokens; after pretraining, its regressor is discarded.Only the encoder initializes fine-tuning.Source: B. Pretraining · p. 12
• Forecasts are conditioned on the lane allocations and active speed limits that take effect between the history and each forecast horizon.The regressor receives the action context and forecasts each horizon separately as a residual on current values; encoder and regressor jointly minimize mean squared error.Source: B. Pretraining · p. 12

C. Fine-Tuning

• Fine-tuning is an RL task in which the model proposes lane counts and normalized speed limits to maximize return.Source: C. Fine-Tuning · p. 12

1) Reward:

• Each road’s mixed reward combines its own trip-and-delay reward with neighboring-road and network mean rewards, weighted by nonnegative coefficients summing to one.The own reward credits completed trips and charges delay, including waiting and travel below nominal speed.Source: 1) Reward · p. 13
• With the own-reward weight set to zero, a road’s reward enters its mixed reward only through the network mean, discouraging gains from shedding traffic onto other roads.The network share is 0.7/60 in the reported experiments.Source: 1) Reward · p. 13

2) Policy and Value Networks:

• Separate actor and critic networks use GERASTSA transformers initialized from the pretrained encoder, with per-road heads for values, lane proposals, and directional speeds.The lane head masks inadmissible lane counts; speed heads produce truncated-normal normalized speed limits, with offsets shifted near nominal early in fine-tuning.Source: 2) Policy and Value Networks · p. 13

Per-Road PPO

• Each road acts as a PPO agent with its own probability ratio and advantages, while all roads share the actor and critic parameters.The shared actor observes the whole network.Source: 3) Per-Road PPO · pp. 13–14
• Advantages use truncated generalized advantage estimation from mixed road rewards and critic values, with recursion stopping at rollout and episode boundaries.Episode ends are time-limit truncations that bootstrap from the critic’s next-time-step value.Source: 3) Per-Road PPO · p. 13
• Each road’s probability ratio compares its current-policy action probability with the probability under the data-collecting policy.Source: 3) Per-Road PPO · p. 13
• The combined objective maximizes a clipped policy surrogate and critic value regression, with entropy bonuses for lane and speed distributions.The speed entropy bonus covers open directions only.Source: 3) Per-Road PPO · pp. 13–14

A. Effect of Pretraining

• 47 updates: pretraining reaches the approximate baseline-crossing point, versus 86 updates without pretraining; after 100 updates, delay is 374 versus 911 veh·h.The pretrained run’s final return is 17,653 veh·h, versus 17,112 veh·h without pretraining.Source: A. Effect of Pretraining · p. 14

B. Learned Policy

• 89.5 ± 1.3%: the learned policy reduces daily delay from 3,565 to 374 veh·h against the fixed configuration, and has 85% less delay than the load balancer.Its return is 14.5% higher than the load balancer’s; Table III reports performance over 32 evaluation days.Source: B. Learned Policy · p. 15, Table III · p. 16
• About 40 of 60 roads become one-way in each rush hour, and the policy keeps peak-direction congestion at or below 0.19.It rarely lowers speed limits during rush hours; the mean normalized limit stays above 0.96.Source: B. Learned Policy · p. 15

C. Restricted Policies

• Two-way restrictions leave 2,368–2,843 veh·h of delay, while speed-only control raises delay 7.9 ± 1.5% against the baseline.These tests measure what the trained policy retains under restrictions, not what a policy trained under them could achieve.Source: C. Restricted Policies · pp. 15–16

D. Ablations

• Removing relational bias or spatial embedding multiplies delay by about 4.7 or 5.0, to 1,742 or 1,862 veh·h, respectively.Both variants also have more rejected closing proposals than the full model; the no-relational-bias encoder forecasts worse, while removing spatial embedding does not worsen forecast error.Source: D. Ablations · p. 16
• Collapsed relations, undirected spatial embedding, and no temporal embedding incur 547, 516, and 552 veh·h of delay, against 374 veh·h for the full model.Although their final returns are within about 1% of the full model, evaluation and pretraining evidence agree only for the temporal embedding.Source: D. Ablations · pp. 16–17

VII. DISCUSSION

• Pretraining roughly halved updates to surpass the fixed configuration; without it, the policy needed about twice as many updates and retained more than twice the delay after 100 updates.The forecasting task predicts how congestion, density, and velocity on every road evolve under intervening lane allocations and speed limits.Source: §VII · pp. 17–18
• Rush-hour reallocations raised peak-direction capacity to 155 and 159 of 200 lanes (versus 100); mean travel time still fell by a third despite detours.About two thirds of roads became one-way in the peak direction during each rush hour.Source: §VII · p. 18
• Learned speed limits cost return: holding them nominal at test time removes more than half of the remaining delay.The authors leave open whether speed limits can help in a simulator with the congestion mechanisms on which they act.Source: §VII · p. 18
• Action resolution rejected only four proposals from 16:00 to 19:30; most rejections occurred at morning rush onset and at night.Because every grid road has at least two lanes, rejected proposals are relaxed to keep one lane open.Source: §VII · p. 19
• Removing relational bias or spatial embedding raises policy delay to almost five times or five times full-model delay, respectively.Without spatial embedding, forecasting error is unchanged; without relational bias, closing proposals are rejected four times as often.Source: §VII · p. 19
• Endpoint-relation, direction-of-spatial, and temporal ablations leave final delay at 1.4–1.5 times full-model delay, but only temporal effects are corroborated earlier.The discussion notes that the grid’s uniform orientation may let traffic features substitute for endpoint relations.Source: §VII · p. 19, §VIII · p. 20
• The evaluation uses one synthetic 6×6 grid and one training run per variant; all-token attention scales quadratically, limiting direct use on city networks with thousands of roads.The authors propose training across multiple networks and testing transfer to unseen, including real, road networks.Source: §VII · pp. 19–20

VIII. CONCLUSION

• Daily delay fell 90% against the fixed initial configuration and 85% against a tuned load balancer that keeps every road two-way.On the 6×6 grid, the policy also reduced mean travel time by 32% against the fixed initial configuration.Source: §VIII · p. 20