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

Hamed Araab; Abbas Ahmadi; Mohammad Hossein Basiri

eess.SYOct 26, 2026

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

Authors: Hamed Araab, Abbas Ahmadi, Mohammad Hossein Basiri

Organizations: Department of Industrial Engineering and Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran · Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

Abstract

Connected and automated vehicles could allow reassigning lane directions and speed limits on every road frequently, but the benefit hinges on how traffic reroutes, and one-way roads can isolate junctions. We formulate network-wide dynamic lane allocation and directional speed limit control with one-way roads, lane clearing before each reversal, and a navigable graph kept strongly connected at all times. An action-resolution algorithm grounded in graph orientation theory admits a proposal closing a direction only if the network stays strongly connected and otherwise relaxes or reverts it, keeping all junctions mutually reachable within the model, even during clearing. All road controllers share one transformer whose attention, Global Endpoint Relation-Aware Spatio-Temporal Self-Attention (GERASTSA), spans all road-time tokens, biased by the endpoint relations between roads. It is pretrained on action-conditioned traffic forecasting and fine-tuned with per-road proximal policy optimization under a mixed reward that also credits neighboring roads and the network. On a 6 x 6 grid with commuter rush hours, the learned policy makes about two thirds of roads one-way in the peak direction and cuts daily delay by 90% against the initial configuration held fixed and by 85% against a tuned two-way load balancer. Restricted to two-way roads at test time, it gains only about as much as this balancer, whereas its learned speed limits add delay. Pretraining roughly halves the updates needed to surpass the fixed configuration. Of the ablations, only removing the relational bias or the spatial embedding clearly matters, multiplying delay about fivefold.

Figures & tables

Panel of Figure 1 — Fig. 1: An example network with $|\mathcal{J}|=7$ junctions and $|\mathcal{R}|=8$ roads. (a) Each stroke is one lane. Road $r_{5}$ (heavy) is the only bridge road, $\mathcal{R}_{\leftrightarrow}=\{r_{5}\}$ , so it has at least two lanes, and strong connectivity requires it to keep at least one open lane in each direction. (b) A strongly connected navigable arc set $\vec{\mathcal{R}}^{(t)}\in\mathcal{S}$ : arrows show the navigable arcs (solid: forward; dashed: backward), with one stroke per open lane $\bar{\ell}_{r,d}^{(t)}$ ; most roads are one-way, yet $\vec{G}^{(t)}$ is strongly connected. (c) One road controller per road; controllers of roads that share a junction are neighbors.

Fig. 2: Clearing two lanes of a road with

L_{r}=5

(lane 1, the first forward lane, at the bottom). When the target lanes

\hat{\ell}_{r}

drop below the active lanes

\ell_{r}

, lanes

\hat{\ell}_{r}+1,\dots,\ell_{r}

are closed to both directions (dark grey) while vehicles traveling in their old direction leave them. Clearing is atomic: once it completes, all of these lanes open at once to the backward direction (hatched; forward lanes are tinted) and

\ell_{r}=\hat{\ell}_{r}

. The open lanes

\bar{\ell}_{r,d}

below each state need not sum to

L_{r}

while the road is clearing.

Fig. 3: One decision step. The policy of the road controllers proposes an action

a^{(t)}

, consisting of proposed lanes and proposed normalized speed limits for every road. Action resolution rejects closing proposals that would break strong connectivity, relaxing them on multi-lane roads and reverting them on single-lane roads, yielding the next target lanes

\hat{\ell}^{(t+1)}

; proposed normalized speed limits are always accepted and become the next active normalized speed limits

u^{(t+1)}

. The traffic network applies the resulting active speed limits immediately, and each clearing road completes clearing once its clearing lanes are empty.

Fig. 4: Relations

\kappa(r_{5},\cdot)

on the controller graph of the example network, with

\Lambda_{\max}=2

(heavy border:

r_{5}

; shaded: roads adjacent to

r_{5}

; white: roads at hop distance at least

2

). Roads adjacent to

r_{5}

, with

\omega(r_{5},\mathrm{fwd})=(j_{3},j_{5})

, are told apart by the directions in which the two roads flow into their shared junction, e.g.

r_{2}

, with

\omega(r_{2},\mathrm{fwd})=(j_{2},j_{3})

, flows into

j_{3}

forward while

r_{5}

flows into it backward. Each relation

\kappa(r_{5},r)

selects the learned relational bias

\boldsymbol{B}_{\mathrm{R},h,\xi(\kappa(r_{5},r))}

of every head

h

Fig. 5: The GERASTSA block. Queries, keys, and values are split into

H

heads and flattened over the

WR

road–time tokens of each sample. The relational bias

B^{\prime}_{\mathrm{R}}

is gathered from the learned table

\boldsymbol{B}_{\mathrm{R}}

through the relation index matrix

\Xi

and shared across all window positions and samples, and the flattened mask

M^{\prime}

forbids attention as specified by

M

, which in the transformer is the mask of ( 32 ).

Fig. 6: The GERASTSA transformer. The histories

X^{\langle k\rangle}

are left-padded to the longest window length

W

, and the mask

M

of ( 32 ) is built from their window lengths

W_{k}

. The embedded input

Z^{[0]}

passes through

N

pre-norm layers, each mapping

Z^{[n-1]}

Z^{[n]}

with a GERASTSA block and a SwiGLU feedforward network in residual connections; a final layer normalization and a linear map produce the output

Y

Symbol	Hyperparameter	Value
Environment
$L_{\max}$	Maximum total lanes	$6$
$\varepsilon_{\mathrm{R}}$	Rerouting threshold	$0.1$
GERASTSA transformer
$F_{\mathrm{Y}}$	Output width	$128$
$F_{\mathrm{Z}}$	Model width	$128$

TABLE I: Hyperparameters of the experiments.

Feature	Value	Count
Road length	$D_{r}/\max_{r^{\prime}\in\mathcal{R}}D_{r^{\prime}}$	1
Total lanes	$L_{r}/L_{\max}$	1
Nominal speed limit	$s_{r,d}^{(0)}/\max_{(r^{\prime},d^{\prime})\in\mathcal{R}\times\mathcal{D}}s_{r^{\prime},d^{\prime}}^{(0)}$	2
Bridge indicator	$\mathds{1}(r\in\mathcal{R}_{\leftrightarrow})$	1
Congestion	$c_{r,d}^{(t)}$	2
Density	$\bar{c}_{r,d}^{(t)}$	2

TABLE II: Input features of road

r

at time step

t

Fig. 7: Return against the PPO update when fine-tuning from the pretrained encoder and from an untrained one. (a) Greedy policy on the

8

days evaluated during fine-tuning (shaded: standard error). (b) Mean return of the training episodes that end in each update, under sampled actions; until update

18

(shaded), these episodes began under the baseline of the warm-up, and the drops at updates

5

and

6

and at updates

12

14

mark the policy taking over the evening and the morning rush hour. Dotted: mean return of the baseline on the days of (a).

Policy	Return	Return change (%)		Delay	Trips	Travel time	Adm. wait	Removed	Rejected
	( $10^{3}$ veh·h)	vs. baseline	vs. full model	(veh·h)	( $10^{3}$ )	(min)	(s)
Baseline	$14.36\pm 0.04$		$-18.6\pm 0.3$	$3565\pm 43$	$107.58\pm 0.07$	$5.20\pm 0.02$	$25.4\pm 0.6$	$583\pm 23$	$0$
Load balancer	$15.41\pm 0.03$	$+7.3\pm 0.2$	$-12.7\pm 0.2$	$2524\pm 29$	$107.62\pm 0.07$	$4.61\pm 0.02$	$39.0\pm 0.7$	$535\pm 17$	$0$
Full model	$17.65\pm 0.01$	$+22.9\pm 0.3$		$374\pm 9$	$108.16\pm 0.07$	$3.52\pm 0.01$	$3.1\pm 0.1$	$0$	$161\pm 2$
Untrained encoder	$17.11\pm 0.03$	$+19.1\pm 0.3$	$-3.1\pm 0.2$	$911\pm 29$	$108.14\pm 0.07$	$3.88\pm 0.02$	$6.7\pm 0.8$	$13\pm 4$	$211\pm 16$
Lane-only	$17.85\pm 0.01$	$+24.3\pm 0.3$	$+1.1\pm 0.1$	$174\pm 7$	$108.16\pm 0.07$	$3.410\pm 0.005$	$2.8\pm 0.1$	$0$	$154\pm 1$

TABLE III: Performance on the

32

evaluation days: means and standard errors over the days, with changes in return paired by day. Load balancer: the heuristic baseline of Section VI-B ; full model: the learned policy; untrained encoder: the full model fine-tuned without pretraining; the six rows from lane-only on: the full model restricted at test time (Section VI-C ); the last five rows: the ablations (Section VI-D ). Removed: vehicles removed from gridlocked queues by the safeguard; rejected: closing proposals rejected by action resolution, both per day.

Fig. 8: Metrics per decision step over the day under the baseline and the learned policy, averaged over the

32

evaluation days: (a) delay, (b) completed trips, (c) vehicles on the network, (d) one-way roads, (e) mean normalized speed limit over all roads and directions, and (f) closing proposals rejected by action resolution. Dotted verticals mark 08:00 and 17:30, the times shown in Fig. 9 .

Fig. 9: Congestion and open lanes of every road and direction at 08:00 and 17:30 under the baseline and the learned policy, averaged over the $32$ evaluation days. Each direction of a road is drawn on its right-hand side, with its luminance giving the congestion and its width the open lanes, so that a one-way road shows a single stroke. North is up; C and R mark the corners of the commercial and the residential zone.

Fig. 10: Ablations of the GERASTSA transformer against the full model. (a) Return of the greedy policy against the PPO update on the

8

days evaluated during fine-tuning (shaded: standard error); dotted: mean return of the baseline on the same days. (b) Validation MSE of pretraining against the pretraining step.

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Intelligent Transportation Systems apply sensing, communication, AI, and optimization to make transport networks safer and more efficient.

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Open paper AskPDF arXiv

We present a traffic-signal control interface in which a shared graph neural network assigns scores to individual traffic movements. Each junction converts these scores into its own variable-sized set of legal signal phases using a deterministic incidence matrix. Directed corridor nodes provide traffic context, while movement nodes represent controlled input-to-output paths through junctions. Typed mean aggregation produces one scalar per movement; phase definitions and signal timing remain outside the learned network. This makes graph size and junction-specific action count independent of the learned parameter shapes. PPO experiments evaluate the interface on unseen synthetic grid geometries, altered signal coverage, and five heterogeneous city graphs. The policies retained performance across unseen geometries within the synthetic grid family, while changes in signal coverage exposed sensitivity to a signal-coverage distribution shift. A single trained city-policy instance executed across all five city graphs, with heterogeneous outcomes. These results provide feasibility evidence rather than a general estimate of transfer to arbitrary road networks.

Abstract

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