Driven by the rapid advancement of LLMs, researchers have increasingly explored integrating AI agents into vehicular networks [3,4,19,20]. To address the substantial computing demand of AI agents, the authors in [21] proposed a cloud-edge collaborative architecture that distributed multimodal LLM inference between edge servers and the cloud for intelligent driver assistance. Furthermore, the authors in [22] developed an Agent-as-a-Service paradigm, where AI agents autonomously performed computing and communication tasks, effectively reducing service latency for edge-assisted autonomous driving.

Given the high mobility of vehicles, AI agent migration across edge servers has emerged as a promising approach to maintain service continuity [5,23]. Specifically, the authors in [23] proposed a generative diffusion-based contract design to incentivize RSU participation in AI agent migration. To address security threats during AI agent migration, the authors in [5] developed a secure online migration framework with trust assessment, effectively mitigating network attacks while maintaining low migration latency. However, the above works focus on incentive mechanisms and migration security, while overlooking vehicle energy consumption, which critically constrains vehicles with limited resources across successive migrations in the IoVA.

Resource optimization in wireless networks typically involves long-term constraints (e.g., energy budgets and service quality guarantees) that conventional DRL methods fail to satisfy [18,24]. Constrained DRL (CDRL) methods address this limitation by formulating the problem as a CMDP, which extends the MDP with cumulative cost constraints [25]. Among CDRL methods, Lagrangian dual optimization is the most widely adopted approach, which solves the CMDP by converting constraints into penalty terms in the objective function [18,25]. For instance, the authors in [24] employed Lagrangian dual optimization to achieve near-optimal network capacity through joint UAV altitude control and channel access under energy harvesting constraints. Since Lagrangian dual methods may still produce infeasible actions during execution [18], recent studies have incorporated safety mechanisms to provide stronger constraint guarantees [26,27]. For instance, the authors in [28] embedded a safety layer that projects each action onto the feasible set to satisfy latency constraints for edge offloading. However, the above CDRL methods rely on flat state representations, which cannot capture the spatial relationships among interacting entities. When applied to IoVA scenarios with heterogeneous vehicles and RSUs under dynamic topologies, this limitation degrades the expressiveness and scalability of the learned policies.

We consider an IoVA system that consists of a set 𝒱={1,…,v,…,V} of V vehicles and a set ℰ={1,…,e,…,E} of E RSUs. Due to limited on-board computing capacity, AI agents are deployed on nearby RSUs for computation-intensive inference [9]. The service duration is discretized into T time slots. Each time slot is sufficiently short that the vehicle-RSU associations and channel conditions remain approximately constant [29]. At time slot t, vehicle v is associated with its serving RSU kv(t)∈ℰ, and the set of vehicles served by RSU e is denoted by 𝒱e(t)={v∈𝒱∣kv(t)=e}. The service process comprises uplink transmission, RSU-side inference, AI agent migration upon RSU handover, and downlink delivery.

In the communication phases, each vehicle exchanges data with its serving RSU through shared wireless bandwidth. Let Beu and Bed denote the total uplink and downlink bandwidth of RSU e, and let βv,eu(t) and βv,ed(t) denote the allocation ratios for vehicle v, subject to ∑v∈𝒱e(t)βv,eu(t)≤1 and ∑v∈𝒱e(t)βv,ed(t)≤1. Based on the Shannon-Hartley theorem, the uplink and downlink transmission rates can be expressed as (1)Rv,eup(t)=βv,eu(t)Beulog2⁡(1+pvu(t)hv,e(t)σe2),Rv,edw(t)=βv,ed(t)Bedlog2⁡(1+pedhv,e(t)σv2),where pvu(t) is the uplink transmit power of vehicle v at time slot t, ped is the fixed downlink transmit power of RSU e, hv,e(t) denotes the channel gain between vehicle v and RSU e at time slot t, and σe2 and σv2 represent the noise power at the RSU and the vehicle, respectively. In the uplink phase, the vehicle transmits environmental perception data of size Mvsen(t) and user instructions of size Mvins(t). In the downlink phase, the RSU returns structured actions of size Mvact(t) and textual outputs of size Mvtxt(t). The uplink and downlink communication latencies can be obtained as (2)Dv,eup(t)=Mvsen(t)+Mvins(t)Rv,eup(t),Dv,edw(t)=Mvact(t)+Mvtxt(t)Rv,edw(t).

In the computation phase, the RSU allocates its computing resources to the AI agents for inference [8]. Specifically, the AI agent first encodes the multimodal perception data into a joint representation of the driving environment and task intent. This representation is then processed in parallel during prefill to construct the Key-Value (KV) cache for the session. Based on this cache, the AI agent performs autoregressive decoding to generate the response. The encoding, prefill, and decode stages process data volumes of Mvenc(t), Mvpre(t), and Mvdec(t), respectively. Let αv,ealc(t) denote the fraction of computing resources of RSU e allocated to vehicle v, subject to ∑v∈𝒱e(t)αv,ealc(t)≤1, and let ωe and Ce denote the computational intensity in GPU cycles per unit of data and the processing speed of RSU e, respectively. The resulting inference latency is expressed as (3)Dv,epro(t)=ωe(Mvenc(t)+Mvpre(t)+Mvdec(t))αv,ealc(t)Ce.

Since the AI agent is deployed on the RSU, it must be migrated upon RSU handover to preserve service continuity [30]. Let e′=kv(t−1) denote the serving RSU at the previous time slot and define the migration indicator δvmig(t)=I[e′≠e], which equals 1 if a handover occurs and 0 otherwise. As the vehicle moves, the AI agent processes newly received perception data and user instructions at each time slot, appending new entries to the KV cache at a rate of Svkv per context token. The accumulated cache of Nvctx(t) context tokens is compressed via quantization with coefficient qv to reduce the transfer volume. Together with a fixed overhead Ωv covering the model parameters, runtime environment, and protocol data, the migration latency over the inter-RSU link with bandwidth Be,e′ is given by (4)Dv,e′→emig(t)=Nvctx(t)Svkvqv+ΩvBe,e′.

Thus, the end-to-end service latency for vehicle v at time slot t is given by (5)Dvtot(t)=Dv,eup(t)+Dv,epro(t)+δvmig(t)Dv,e′→emig(t)+Dv,edw(t).

In the IoVA, vehicles operate on limited onboard batteries while RSUs are grid-powered, we model only the vehicle-side energy consumption during uplink and downlink communication [11].

In the uplink phase, the vehicle transmits data to the serving RSU through its radio frequency chain [29]. Due to the limited amplifier efficiency, the power amplifier draws input power that exceeds the intended transmit power. The active transmit chain further consumes static circuit power from the supporting circuitry and a bandwidth-dependent dynamic component that arises from baseband signal processing across the allocated bandwidth. The resulting uplink energy consumption can be expressed as (6)Evup(t)=(pvu(t)ηvpa+pvus+κuBv,eu(t))Dv,eup(t),where ηvpa is the power amplifier efficiency, pvus is the uplink static circuit power, and κu is the bandwidth-dependent circuit power coefficient for the uplink chain.

In the downlink phase, the vehicle receives the service response without power amplification. The receive chain consumes a demodulation power pvd, a static circuit power pvds, and a bandwidth-dependent component κdBv,ed(t), yielding the downlink energy consumption (7)Evdw(t)=(pvd+pvds+κdBv,ed(t))Dv,edw(t).

Thus, the total energy consumption of vehicle v at time slot t is given by (8)Evtot(t)=Evup(t)+Evdw(t).

We aim to optimize the resource allocation in the IoVA to minimize the cumulative service latency across all vehicles while satisfying per-vehicle energy budget constraints. However, increasing the transmit power of a vehicle reduces its latency but raises its energy consumption, while allocating more bandwidth to one vehicle limits the resources available to others. To balance these competing objectives, we jointly determine the computing resource allocation ratio αv,ealc(t), the uplink and downlink bandwidth allocation ratios βv,eu(t) and βv,ed(t), and the vehicle transmit power pvu(t), collectively denoted as 𝒜={αv,ealc(t),βv,eu(t),βv,ed(t),pvu(t)}v∈𝒱,e∈ℰ,t∈𝒯. The optimization problem can be formulated as (9a)min𝒜∑t=1T∑v=1VDvtot(t) (9b)s.t.∑v∈𝒱e(t)αv,ealc(t)≤1,∀e∈ℰ, ∀t∈𝒯, (9c)∑v∈𝒱e(t)βv,eu(t)≤1, ∑v∈𝒱e(t)βv,ed(t)≤1,∀e∈ℰ, ∀t∈𝒯, (9d)pvu(t)∈[0,p¯vu],∀v∈𝒱, ∀t∈𝒯, (9e)kv(t)∈ℰvcom,∀v∈𝒱, ∀t∈𝒯, (9f)∑t=1TEvtot(t)≤Evbud,∀v∈𝒱.

Constraints (9b,c) ensure that the computing and bandwidth allocation ratios assigned by each RSU do not exceed unity. Constraint (9d) bounds the uplink transmit power of each vehicle in its feasible range, where p¯vu denotes the maximum transmit power. Constraint (9e) restricts the serving RSU of each vehicle to its communicable RSU set ℰvcom. Constraint (9f) imposes that the cumulative energy consumption of each vehicle over the entire service period does not exceed its energy budget Evbud.

The resource allocation problem in the IoVA involves a non-convex objective, temporally coupled energy constraints, and non-stationary system dynamics, which render conventional approaches intractable. We therefore reformulate it as a CMDP [25], characterized by the tuple ⟨𝒮,𝒜,r,c,γ⟩, where 𝒮 is the state space, 𝒜 is the action space, r is the reward function, c is the cost function, and γ∈(0,1] is the discount factor. The detailed definitions are as follows: (1)

State space: At each time slot t, the CDRL agent observes the system state s(t)={hv,e(t),kv(t), mv(t),Nvctx(t),E^v(t)}v∈𝒱,e∈ℰ, which encompasses channel gains, RSU associations, service data volumes, KV cache sizes, and cumulative energy consumption. Here, mv(t) collects all service data volumes of vehicle v defined in Section 3.1, and E^v(t)=∑τ=1t−1Evtot(τ) tracks the energy consumed up to time slot t.

(10a)maxπJ(π)=Eπ[∑t=1Tγt−1r(t)] (10b)s.t.Jcv(π)=Eπ[∑t=1Tγt−1cv(t)]≤Evbud,∀v∈𝒱.

We consider an IoVA system in which vehicles travel along a road segment at speeds of 30 to 120 km/h and are served by uniformly deployed RSUs. The initial positions of vehicles are randomly distributed along the road, and each vehicle maintains a constant speed throughout each episode. Channel gains between each vehicle and RSU combine a distance-dependent path loss with exponent α=3.76 and Rayleigh small-scale fading [14]. The uplink sensing and instruction data volumes range over [1,15] and [0.02,0.625] MB, respectively, while the downlink actuation and text response volumes range over [0.001,0.05] and [0.004,0.2] MB, respectively. The inference data volumes range over [0.1,6.25] MB across the encoding, prefill, and decoding stages, and the context token counts range over [1024,8192]. The detailed simulation parameters are summarized in Table 1.

For the GCPPO algorithm, the actor and critic networks share a two-layer bidirectional GAT encoder. All algorithms are implemented in PyTorch and trained for 5×105 environment steps on an NVIDIA RTX 4090 GPU with 5 random seeds. Each algorithm’s final policy is evaluated on 20 test episodes per seed, and the mean and standard deviation of each performance metric are computed over the resulting 100 episodes. The GCPPO algorithm completes training in 17.87 min. During inference, it takes 1.44 ms on average to generate a joint resource allocation decision.

To validate the effectiveness of the proposed GCPPO algorithm in the IoVA, we compare it with the following baseline algorithms:

CPO [34]: Constrained Policy Optimization (CPO) solves the CMDP via trust region updates with linearized cost constraints, providing first-order feasibility guarantees.

In Fig. 2, we present the training performance of GCPPO and the baseline algorithms. As shown in Fig. 2a, GCPPO achieves the highest converged reward and converges in 1×105 training steps, substantially faster than all baselines. Among the constrained baselines, CPO and PPO-Lag plateau at lower rewards, while SAC-Lag exhibits high variance due to the instability of off-policy Lagrangian updates. Fig. 2b illustrates the cost curves under an energy budget of 200 J. GCPPO maintains its cost consistently below the energy constraint after initial training, whereas CPO converges below the threshold but adopts a more conservative policy that limits reward improvement. In contrast, SAC-Lag frequently exceeds the budget. Fig. 2c depicts the convergence trajectories in the reward-cost plane, where GCPPO converges to the upper-left corner of the feasible region, achieving the highest reward while satisfying the energy budget. The superior performance of GCPPO is attributed to the combined effect of the bidirectional GAT, which improves reward through topology-aware allocation, and the Lagrangian dual mechanism, which constrains the trajectory in the feasible region.

In Fig. 3, we present the evaluation results on independent test episodes. As shown in Fig. 3a, GCPPO achieves the lowest average system latency, reducing it by 36.0% over SAC-Lag and by approximately 4% over CPO and PPO-Lag. Fig. 3b shows that GCPPO matches CPO in energy consumption while consuming 20.9% less than SAC-Lag. As illustrated in Fig. 3c, GCPPO achieves a constraint satisfaction rate of 96.4%, substantially outperforming PPO-Lag and SAC-Lag. Although DAPA attains the highest satisfaction rate of 99.2%, this comes at a 76.6% increase in system latency. These results indicate that the bidirectional GAT encoder enables GCPPO to exploit the vehicle-RSU topology for effective resource allocation, while the Lagrangian dual mechanism maintains energy feasibility without sacrificing latency performance.

Fig. 4 illustrates the impact of the energy budget on GCPPO in the IoVA. As the budget increases from 160 to 240 J, the converged reward improves from approximately −1500 to −1200, and the constraint satisfaction rate rises from 90.8% to 98.1%. This is because a more relaxed budget allows the CDRL agent to allocate higher transmit power for latency reduction without exceeding the energy limit. Under the tightest budget of 160 J, the Lagrangian multipliers automatically increase, yielding a more energy-conservative policy that trades higher latency for constraint satisfaction.

Figs. 5 and 6 illustrate the impact of wireless bandwidth and vehicle transmit power in the IoVA, respectively. As bandwidth increases from 20 to 120 MHz, both system latency and energy consumption decrease across all algorithms, since higher bandwidth improves the transmission rate, thereby reducing communication time and the associated energy expenditure. Conversely, increasing the transmit power from 0.1 to 0.5 W reduces system latency but simultaneously raises energy consumption. Under both parameter sweeps, GCPPO consistently achieves the lowest normalized average latency, outperforming the strongest baseline by approximately 12% in the bandwidth sweep. This advantage grows under resource-scarce conditions, where topology-aware allocation via the bidirectional GAT yields the largest gains. In contrast, SAC-Lag consumes approximately 80% more normalized energy than GCPPO in the power sweep, indicating that its off-policy Lagrangian enforcement cannot effectively regulate the growing energy cost.

In Fig. 7, we evaluate the scalability of all algorithms as the number of vehicles increases from 20 to 100. We quantify it using the scalability exponent α, estimated via least-squares linear regression in log-log space, where per-vehicle metrics scale as O(Vα) with the number of vehicles V. An exponent below 1.0 indicates sub-linear growth, meaning that per-vehicle metrics grow more slowly than the network size.

As shown in Fig. 7a, GCPPO achieves the lowest latency scalability exponent of 0.91, indicating sub-linear growth in per-vehicle latency as the network expands. CPO, PPO-Lag, and SAC-Lag also achieve sub-linear exponents, while DAPA and Random exhibit super-linear growth. For energy consumption, Fig. 7b shows that GCPPO attains the lowest exponent of 0.60, significantly outperforming SAC-Lag and Random, both of which approach or exceed linear growth. The sub-linear scaling of GCPPO is attributed to the bidirectional GAT encoder, which generalizes allocation decisions to larger vehicle populations, and the Lagrangian multiplier updates, which adaptively tighten the energy penalty as network density increases.