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Cooperative RSU Sleep Scheduling for Green V2I Corridors

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Cooperative RSU Sleep Scheduling for Green V2I Corridors

arXiv:2606.29609v1 [cs.NI] 28 Jun 2026

Yousef AlSaqabi

Abstract As vehicle-to-infrastructure (V2I) deployments scale, roadside units (RSUs) that consume 10–25 W continuously yet serve negligible traffic during off-peak hours represent a growing source of energy waste. Sleep scheduling can exploit the pronounced diurnal variation in urban traffic, but the WAVE service restoration overhead of up to 100 ms nearly exhausts the 3GPPTS 22.185 latency budget, making independent sleep decisions risky. This paper proposes a cooperative framework in which upstream RSUs share traffic detection signals with downstream neighbors via infrastructure-to-infrastructure links, enabling predictive wake-up that exploits spatial correlation between adjacent intersections. The framework is formulated as a constrained Markov decision process and decomposed into per-RSU subproblems solvable by value iteration. Four algorithms of increasing sophistication are evaluated on real hourly traffic data from four consecutive signalized intersections in Kuwait City, comprising a total of 762,050 vehicles over five days. The cooperative algorithm reduces corridor energy consumption by 59.5% relative to always-on operation while maintaining 99% latency compliance, and provides 7.7 percentage points of additional savings over independent per-RSU optimization at downstream RSUs with spatial correlation ρ ≥ 0.97. Extrapolated to a 200-RSU urban deployment, the cooperative approach yields an estimated 5.25 tonnes of CO2 reduction per year.

Index Terms Roadside unit (RSU), sleep scheduling, vehicle-to-infrastructure (V2I), green communications, cooperative scheduling, Markov decision process (MDP), energy efficiency, latency constraints.

I. I NTRODUCTION The radio access network accounts for the majority of energy consumption in wireless communication systems, with base stations alone responsible for an estimated 80% of total network power draw [1]. Y. AlSaqabi is with the Department of Electrical Engineering, Kuwait University, Kuwait City, Kuwait (e-mail: [email protected]). Manuscript received XXXX XX, 2026; revised XXXX XX, 2026.

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As vehicle-to-infrastructure (V2I) deployments scale, roadside units (RSUs) face an analogous challenge: commercial DSRC RSUs consume 10–25 W continuously [2]–[4], yet urban arterials exhibit diurnal peakto-trough ratios of 10:1–20:1 [5], meaning RSUs draw full power overnight to serve negligible traffic. In the cellular domain, sleep scheduling reduces energy consumption by 22–68% [6], [7]; translating these gains to V2I infrastructure is a natural step toward green roadside networks. RSU sleep scheduling, however, is fundamentally constrained by latency. The 3GPP TS 22.185 standard specifies a 100 ms latency budget for safety-critical cooperative awareness messages [8], while the WAVE Service Advertisement broadcast cycle under IEEE 1609.4 requires up to 100–150 ms for service restoration [9], nearly exhausting the entire budget. Cooperative scheduling, in which upstream RSUs share traffic detection information with downstream neighbors via infrastructure-to-infrastructure (I2I) signaling, transforms this tradeoff by providing advance warning of approaching traffic, enabling downstream RSUs to sleep more aggressively during confirmed low-traffic periods and wake preemptively when upstream traffic surges. Despite substantial progress in cellular base station sleep scheduling [6], [10]–[13] and a growing body of RSU-specific work [7], [14]–[16], three gaps remain. First, no existing framework integrates upstream vehicle detection with predictive downstream RSU wake-up; Han et al. [17] is the closest but considers only homogeneous Poisson traffic without MDP-based optimization. Second, publicly available traffic characterization from the Gulf region remains limited for V2I infrastructure design, despite distinctive commute patterns (Friday–Saturday weekend). Third, carbon footprint analysis for V2I infrastructure is entirely absent from the literature. This paper addresses these gaps with four contributions: 1) Cooperative corridor-aware RSU sleep scheduling (C1). We propose a cooperative MDP framework with upstream-downstream I2I signaling, achieving 59.5% corridor energy reduction with 99% latency compliance and 7.7 percentage points of additional savings over independent per-RSU optimization. 2) Comparative algorithm benchmarking (C2). We benchmark four algorithms of increasing sophistication (periodic, threshold, MDP, cooperative) on the same dataset, isolating the marginal value of adaptivity and cooperation. 3) Gulf-region traffic characterization (C3). We characterize hourly traffic from four intersections in Kuwait City (762,050 vehicles, five days), revealing a 14.8× corridor peak-to-trough ratio, 1.51×

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weekday-to-weekend contrast, and spatial correlations of 0.907–0.984. 4) Design guidelines and carbon footprint analysis (C4). Sensitivity analyses across latency SLA, wake-up delay, traffic volume, and RSU power class identify a critical boundary at 102 ms, and carbon footprint estimates project 5.25 tonnes CO2 reduction per year for a 200-RSU deployment. The remainder of this paper is organized as follows. Section II reviews related work. Section III presents the system model and traffic characterization. Section IV formulates the optimization problem. Section V describes the scheduling algorithms. Section VI presents the results and sensitivity analysis. Section VII concludes the paper. II. R ELATED W ORK A. RSU and Base Station Sleep Scheduling RSU sleep scheduling has received growing attention as V2I deployments scale. Sou [18] provided an early analytical model for optimal active RSU counts. Mostofi et al. [19] proposed the Flow Graph Sleep Scheduler, and Hammad et al. [20] established NP-completeness of offline green scheduling bounds. Khezrian et al. [14] extended this to multiple RSUs with a polynomial 2-approximation algorithm. Bhattacharya et al. [7] introduced six sleep cycle types achieving 68% energy savings via G/G/1/K Gvacation queueing. Ali et al. [15] proposed event-driven duty cycling for solar-powered RSUs, and Patra and Murthy [16] jointly optimized RSU placement and sleep scheduling with solar power. These works treat each RSU independently; none exploits upstream-downstream spatial correlation for cooperative scheduling. The cellular BS sleep mode literature provides the theoretical backbone. Wu et al. [6] surveyed sleep techniques comprehensively. Auer et al. [1] established the EARTH power model, and Debaillie et al. [21] defined four progressive sleep depth levels with wake-up latencies from 71 µs to ∼1 s. Niu et al. [10] introduced cell zooming, and Peng et al. [22] demonstrated up to 53% savings through network-wide sleep coordination. These works target omnidirectional cellular cells rather than the directional corridor topology of V2I.

B. Traffic-Aware and Cooperative Scheduling Wu et al. [11] derived the foundational traffic-aware sleep model, proving a critical threshold exists below which sacrificing delay does not yield energy savings. Liu et al. [12] proposed DeepNap using

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TABLE I: Comparison with Related Work Study Sou [18] Khezrian et al. [14] Ali et al. [15] Bhattacharya et al. [7] Patra & Murthy [16] Han et al. [17] Liu et al. [12] Wu et al. [13] This work

Coop. sched.

Real data

Corr.aware

Latencyconstr.

Gulf region

Carbon anal.

✓

✓

✓ ✓ ✓

✓ ✓ ✓

✓ ✓

✓ ✓

✓

✓

deep Q-networks, and Wu et al. [13] developed DeepBSC combining spatio-temporal forecasting with actor-critic RL. Han et al. [17], [23] investigated cooperative BS sleep scheduling in one-dimensional vehicular networks, exploiting vehicular speeds to predict arrivals cooperatively. Their work is the closest precursor to ours but considers only homogeneous Poisson traffic without MDP-based optimization or real data. Zheng et al. [24] formulated cooperative BS sleeping as a constrained potential game, and Wu et al. [25] modeled cooperative sleep with vacation queues. None of these frameworks has been adapted to V2I corridors. Furthermore, publicly available traffic characterization from the Gulf region remains limited for V2I sleep scheduling design, and carbon footprint analysis for RSU infrastructure is entirely absent from the literature [6], [26]. Table I positions this work relative to the most closely related studies. III. S YSTEM M ODEL AND T RAFFIC C HARACTERIZATION This section presents the system model for cooperative RSU sleep scheduling along a V2I corridor. The model comprises five components: the corridor topology (Section III-A), the RSU power state model (Section III-B), the traffic arrival model parameterized from real Gulf-region data (Section III-C), the V2I latency model (Section III-D), and the cooperative information exchange model (Section III-E).

A. Corridor Topology and RSU Deployment Model We consider a corridor of K = 4 consecutive signalized intersections on the Second Ring Road, a major urban arterial in Kuwait City. The intersections are indexed k ∈ {1, 2, 3, 4} in the direction of predominant traffic flow. Intersections I1 through I3 are four-way signalized junctions and I4 is a three-way junction.

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Each intersection is equipped with one DSRC RSU providing IEEE 802.11p V2I communication services within its coverage zone. The corridor is modeled as a directed graph G = (V, E), where the vertex set V = {1, 2, . . . , K} represents the RSU-equipped intersections and the edge set E = {(k, k + 1) : k = 1, . . . , K − 1} represents the directed traffic flow and infrastructure-to-infrastructure (I2I) communication links between adjacent RSUs. Each RSU k can communicate with its immediate downstream neighbor k + 1 via a low-latency I2I backhaul link (wired Ethernet or dedicated wireless channel), enabling cooperative scheduling decisions as described in Section III-E. The inter-intersection spacing along the Second Ring Road is approximately 500–800 m, typical of signalized urban arterials. At prevailing corridor speeds of 40–60 km/h, the inter-RSU travel time is τk,k+1 ≈ 1–2 minutes. Since the scheduling time resolution is one hour (see Section III-C), a vehicle detected at RSU k during hour t is expected to arrive at RSU k + 1 within the same hour, allowing the upstream detection to inform the downstream scheduling decision for the current time slot.

B. RSU Power State Model Each RSU operates in one of three power states S = {A, I, S}: Active (A), fully operational with all subsystems powered, transmitting WSAs and serving V2I requests (Pa ); Idle (I), radio receiver powered but no active transmissions, vehicles served without wake-up delay (Pi ); and Sleep (S), nearly all subsystems deactivated except a minimal wake-up controller (Ps ). When an RSU transitions from Sleep to Idle or Active, it incurs a wake-up delay twake and consumes transition power Ptr . The transition energy per wake-up event is Etr = Ptr · twake .

(1)

The power consumption model builds on the EARTH project framework [1], whose pico cell (P0 = 6.8 W) and femto cell (P0 = 4.8 W) categories are the closest cellular analogues to DSRC RSUs [27]. The Cohda Wireless MK5 RSU draws 8–12 W total system power via PoE Class 3 [2]; dual-mode RSUs (Cohda MK6, Commsignia ITS-RS4) consume 15–25 W [3], [4]. We adopt the MK5 power envelope as the reference platform. Debaillie et al. [21] defined four progressive sleep depth levels with wake-up latencies from 71 µs (SM1) to ∼1 s (SM4). Onireti et al. [28] showed that activation power exceeds idle power by 1.2–1.5×, and Ashraf et al. [29] measured femtocell power at approximately 10 W active, 5 W idle, and 1 W in deep sleep.

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TABLE II: RSU Power State Parameters Parameter

Symbol

Active power Idle power Sleep power Transition power Wake-up delay Transition energy

Pa Pi Ps Ptr twake Etr

Value Source 8.4 W 5.3 W 0.15 W 10.0 W 2 ms 0.02 J

[2] [1], [29] [21] [28] [21] Eq. (1)

Table II lists the parameters used in this work. The active power of 8.4 W represents a typical MK5 operating point. The idle power of 5.3 W is estimated by scaling the EARTH pico zero-load ratio (P0 /Pmax ≈ 0.63) to the MK5 active power, consistent with the femtocell measurements in [29]; the sensitivity analysis in Section VI-E confirms robustness across RSU power classes. The sleep power of 0.15 W corresponds to a deep sleep mode where only a wake-up controller remains powered; the results are robust to sleep power values up to approximately 1 W. The wake-up delay of 2 ms reflects the SM2/SM3 boundary in [21], enabled by IEEE 802.11p’s association-free design. The transition power of 10.0 W applies the 1.2× Pa scaling from [28]. The instantaneous power consumption of RSU k at time slot t is    Pa , if sk (t) = A,     Pk (t) = Pi , if sk (t) = I,      P , if s (t) = S, s k

(2)

and the energy consumed by RSU k during time slot t of duration ∆ seconds is Ek (t) = Pk (t) · ∆ + nk (t) · Etr ,

(3)

where nk (t) is the number of sleep-to-active transitions during slot t. The total corridor energy over a P P scheduling horizon of T slots is Ecorridor = Tt=1 K k=1 Ek (t). C. Traffic Arrival Model with Gulf-Region Parameterization Vehicle arrivals at each intersection are modeled as a non-homogeneous Poisson process (NHPP) with a piecewise-constant rate function. For RSU k, the arrival rate during hour h ∈ {0, 1, . . . , 23} on day type (d)

d ∈ {weekday, weekend} is denoted λk (h). Within each hour, vehicle inter-arrival times are exponentially (d)

distributed with mean 1/λk (h). The NHPP with piecewise-constant rates is a standard model for urban

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TABLE III: Traffic Statistics by Intersection and Day Type Daily mean (veh)

Peak-to-trough ratio

Intersection Weekday Weekend Weekday

Weekend

I1 (4-way) I2 (4-way) I3 (4-way) I4 (3-way)

41,905 50,205 42,149 42,072

27,828 36,630 31,963 20,108

15.2× 13.7× 14.2× 24.6×

12.9× 12.2× 12.5× 14.4×

Corridor

176,332

116,528

14.8×

12.8×

intersection traffic in the V2X literature [17], [30] and naturally captures the diurnal periodicity that creates the sleep scheduling opportunity. (d)

The rate parameters λk (h) are estimated from a real traffic dataset collected at the four study intersections. The dataset consists of hourly directional vehicle counts over five consecutive days: August 15–19, 2025. In the Gulf calendar, Friday and Saturday constitute the weekend, and Sunday is the first working day. The five-day trace thus spans two weekend days (Friday, Saturday) and three weekdays (Sunday, Monday, Tuesday), providing both day types for parameterization. Each intersection records traffic from all approach directions (four directions for I1–I3, three for I4), yielding 15 directional streams and 1,800 hourly observations. The directional counts are aggregated to obtain the total intersection-level arrival rate (d)

λk (h) for each intersection, hour, and day type, producing 480 intersection-level hourly values used for NHPP parameterization. Table III summarizes the key traffic statistics. Three features of the Gulf-region traffic pattern are relevant to RSU sleep scheduling. First, the diurnal variation is pronounced. The corridor-level weekday peak-to-trough ratio is 14.8×, with trough hours (03:00–05:00) averaging approximately 500 vehicles/hour across the corridor and peak hours (19:00–20:00) exceeding 7,000 vehicles/hour. This ratio exceeds the 5:1 peak-to-trough commonly reported for cellular base station traffic in Western urban environments [31] and is consistent with the 10:1–20:1 range reported by the FHWA Traffic Monitoring Guide for urban arterials [5]. The pronounced trough creates a substantial window during which RSU sleep yields energy savings with minimal latency impact. Second, the weekday-weekend contrast is substantial. Weekday corridor traffic (176,332 vehicles/day) exceeds weekend traffic (116,528 vehicles/day) by a factor of 1.51×, reflecting the commuter-dominated character of the Second Ring Road. This contrast is most extreme at I4, where the weekday-to-weekend ratio reaches 2.09× (42,072 vs. 20,108 vehicles/day), consistent with its three-way geometry that channels

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Fig. 1: Average hourly traffic profiles for intersections I1–I4 and the corridor aggregate, comparing weekday (solid) and weekend (dashed) patterns. Trough hours (02:00–05:00) offer the primary sleep scheduling window. The Gulf weekend (Friday–Saturday) shows lower overall volumes and a later, broader peak than weekdays. commuter flows from residential areas to the south. The scheduling algorithm must adapt to both day types to exploit the additional sleep opportunity on weekends. Third, I4 exhibits notably higher volatility than the four-way intersections. Its weekday peak-to-trough ratio of 24.6× is nearly double that of I2 (13.7×). This heterogeneity means that a uniform sleep policy across all RSUs is suboptimal; intersection-specific scheduling is necessary to exploit the varying sleep windows. The hourly traffic profiles for all four intersections are shown in Fig. 1. The weekday profiles exhibit a bimodal pattern with a morning ramp-up (07:00–09:00) and an evening peak (17:00–20:00), while the weekend profiles are unimodal with a later and broader peak (16:00–22:00). The spatial correlation between adjacent intersections is quantified by the Pearson correlation coefficient ρk,k+1 computed from the hourly aggregated traffic counts: ρ1,2 = 0.984,

ρ2,3 = 0.974,

ρ3,4 = 0.907.

(4)

The decreasing trend reflects increasing traffic dispersion along the corridor as vehicles enter and exit at intermediate cross-streets. These correlations serve as direct inputs to the cooperative scheduling model

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in Section III-E.

D. V2I Latency Model The end-to-end V2I service latency experienced by a vehicle depends on the current power state of the serving RSU. We decompose the latency into three additive components: L = Lwake + Ldisc + Ltx ,

(5)

where Lwake is the hardware wake-up delay, Ldisc is the WAVE service discovery delay, and Ltx is the 802.11p channel access and transmission delay. Wake-up delay Lwake : If the RSU is in Active or Idle state, Lwake = 0. If the RSU is in Sleep state and must transition to serve an arriving vehicle, Lwake = twake = 2 ms (Table II). Discovery delay Ldisc : After the RSU hardware is active, it must broadcast at least one WAVE Service Advertisement (WSA) on the control channel (CCH) before vehicles can discover its services. The IEEE 1609.4 synchronization interval is a fixed 100 ms period synchronized to UTC via GPS, divided into a 50 ms CCH interval and a 50 ms service channel (SCH) interval, each with a 4 ms guard interval [9]. The RSU broadcasts one WSA per synchronization interval (10 Hz rate). If the RSU awakens at a random point within the synchronization cycle, the expected time until the next WSA broadcast is uniformly distributed on [0, 100] ms. The discovery delay Ldisc is therefore modeled as a uniform random variable: Ldisc ∼ Uniform(0, TWSA ),

TWSA = 100 ms.

(6)

Transmission delay Ltx : Once service is established, the 802.11p EDCA mechanism governs channel access. Under low-to-moderate load, single-hop V2I latency is typically 2–8 ms [32], [33]. We adopt a fixed Ltx = 5 ms to represent the combined channel access and transmission delay. For a vehicle arriving at an RSU in Active or Idle state, the total latency is L = 0 + 0 + 5 = 5 ms, well within any practical latency budget. The binding constraint arises when a vehicle arrives at a sleeping RSU: the total service restoration window is Trestore = twake + TWSA = 2 + 100 = 102 ms.

(7)

Following 3GPP TS 22.185 [8], the latency constraint for safety-critical cooperative awareness messages is Lmax = 100 ms. A vehicle experiences a latency violation when L > Lmax , which occurs when

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Ldisc > Lmax − twake − Ltx = 93 ms. Given the uniform distribution of Ldisc , the per-vehicle violation probability during a restoration event is Pviol = Pr[L > Lmax ] =

102 − 95 Trestore − (Lmax − Ltx ) = = 0.069. Trestore 102

(8)

When RSU k is scheduled to Sleep during time slot t with arrival rate λk (t), the RSU cycles between sleep and brief restoration windows as vehicles arrive. The fraction of the hour spent in restoration windows is   λk (t) · Trestore frestore (t) = min 1, , 3600

(9)

where Trestore is in seconds (= 0.102 s). The expected number of latency violations per hour is Vk (t) = λk (t) · frestore (t) · Pviol .

(10)

This model captures the key property that sleeping during high-traffic hours is dramatically more costly than sleeping during low-traffic hours: at λ = 2,000 veh/hr (peak), Vk ≈ 7.8 violations/hr, while at λ = 50 veh/hr (trough), Vk ≈ 0.005 violations/hr, a ratio of approximately 1,500×. The system-level latency constraint requires that the overall violation rate across all vehicles and all RSUs over the evaluation horizon remain below a threshold ε: PT PK

k=1 PTt=1 PK t=1

Vk (t)

k=1 λk (t)

≤ ε,

(11)

with ε = 0.01 (99% compliance).

E. Cooperative Corridor Model The preceding subsections model each RSU independently. The key observation that motivates cooperative scheduling is that Trestore = 102 ms nearly exhausts the Lmax = 100 ms latency budget, leaving only a 7% margin (Eq. 8). An RSU acting independently must therefore be conservative about sleeping: it has no advance warning of approaching vehicles and cannot guarantee timely service if caught asleep during a traffic surge. Cooperative scheduling addresses this by enabling upstream RSUs to share traffic detection information with downstream neighbors, allowing downstream RSUs to sleep more aggressively during confirmed low-traffic periods and wake up preemptively when upstream traffic increases. The cooperative mechanism operates as follows. At the end of each time slot t, RSU k observes its

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realized arrival count λk (t) and transmits a binary signal uk (t) ∈ {Low, High} to the downstream RSU k + 1 via the I2I backhaul link. The signal is defined as

uk (t) =

  High,

if λk (t) > λ̃k (h),

 Low,

otherwise,

(d)

(12)

(d)

where λ̃k (h) is the median arrival rate at RSU k for hour h on day type d, computed from historical data. The binary encoding keeps the I2I signaling overhead minimal (one bit per time slot) and is robust to communication errors. The downstream RSU k + 1 incorporates uk (t) into its scheduling decision for the next time slot. When uk (t) = High, the downstream RSU shifts its traffic forecast upward, reflecting the spatial correlation between adjacent intersections. Specifically, the effective arrival rate used by RSU k+1 for sleep scheduling decisions is modulated as

λeff k+1 (t) =

  λk+1 (t) · (1 + ρk,k+1 · α),

if uk (t) = High,

 λ

if uk (t) = Low,

k+1 (t) · (1 − ρk,k+1 · α),

(13)

where α = 0.30 is a modulation parameter that controls the strength of the upstream influence. The correlation coefficient ρk,k+1 scales the modulation: at ρ1,2 = 0.984 (I1→I2), the upstream signal strongly influences the downstream decision, while at ρ3,4 = 0.907 (I3→I4), the influence is attenuated to reflect the weaker correlation. The cooperation gain arises through the following mechanism. When the upstream signal is Low, the downstream RSU has increased confidence that the current low-traffic period will persist, enabling it to enter or remain in Sleep with reduced risk of a latency violation. Without the upstream signal, the independent MDP (Section V-C) must hedge against the possibility of a sudden traffic surge by remaining in Idle during ambiguous hours. The cooperative algorithm resolves this ambiguity by providing corroborating evidence from the upstream neighbor. IV. P ROBLEM F ORMULATION This section formulates the cooperative RSU sleep scheduling problem as a constrained optimization over the corridor, characterizes its computational complexity, and motivates the decomposition into perRSU subproblems that underlies the algorithmic approaches in Section V.

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A. Corridor Sleep Scheduling Problem Consider the corridor of K RSUs over a scheduling horizon of T time slots, each of duration ∆ = 3,600 s (one hour). At each time slot t, a scheduling policy π selects the power state sk (t) ∈ S = {A, I, S} for each RSU k, based on available information including the current time of day, recent traffic observations, and (for the cooperative policy) upstream signals from neighboring RSUs. The corridor sleep scheduling problem is:

T

minimize {sk (t)}

subject to

K

1 XX Ek (t) T t=1 k=1 PT PK k=1 Vk (t) ≤ ε, PTt=1 PK t=1 k=1 λk (t) sk (t) ∈ S,

(14a) (14b)

∀ k, t,

sk (t) = S ⇒ sk (t−1) ∈ {I, S},

(14c) ∀ k, t,

(14d)

where Ek (t) is the energy consumed by RSU k during slot t (Eq. 3), Vk (t) is the expected number of latency violations (Eq. 10), and λk (t) is the vehicle arrival rate. The objective (14a) minimizes the timeaveraged total corridor energy consumption. Constraint (14b) enforces the corridor-level latency SLA: the fraction of vehicles experiencing latency above Lmax = 100 ms must not exceed ε = 0.01. Constraint (14c) restricts each RSU to the three defined power states. Constraint (14d) encodes state transition feasibility: an RSU can only enter Sleep from Idle or Sleep (not directly from Active), reflecting the requirement that the RSU must first complete any ongoing transmissions before shutting down the radio. The violation count Vk (t) depends on both the scheduling decision sk (t) and the traffic realization λk (t), which is a random variable at decision time (the scheduler decides sk (t) before observing the arrivals during slot t). This makes (14) a stochastic optimization problem. In the cooperative setting, the scheduler for RSU k + 1 additionally observes the upstream signal uk (t) (Eq. 12) before deciding sk+1 (t + 1), providing partial information about the traffic state.

B. Complexity Analysis Problem (14) is computationally intractable for exact solution due to three sources of complexity. First, the joint state space grows exponentially with the corridor length. The scheduling decision for each RSU involves |S| = 3 choices per time slot. Over K RSUs and T time slots, the total number of

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joint schedules is 3KT . For the study corridor (K = 4, T = 120 slots over 5 days), this yields 3480 ≈ 10229 candidate schedules, ruling out exhaustive search. Second, the latency constraint (14b) couples the decisions across RSUs and time slots. A violation budget consumed by one RSU during one time slot reduces the budget available to other RSUs in other slots. This coupling prevents decomposition into independent per-RSU subproblems without relaxation. Third, the traffic arrivals λk (t) are stochastic and only partially predictable from historical patterns and upstream signals. The scheduler must make decisions under uncertainty about the current slot’s traffic realization, which introduces the exploration-exploitation tradeoff characteristic of sequential decision problems. These features place the problem in the class of constrained multi-agent Markov decision processes (CMDPs), which are PSPACE-hard in general [24], [34]. Even for a single RSU, the constrained MDP with a long-run average cost constraint requires solving a linear program over the state-action occupancy measures, with complexity polynomial in the state space size but exponential in the number of constraints when multiple SLA levels are considered.

C. Decomposition and Algorithmic Approach To make the problem tractable, we adopt a two-level decomposition. At the first level, the corridor-level constraint (14b) is relaxed into per-RSU constraints by allocating the violation budget uniformly across RSUs: PT

PTt=1

Vk (t)

t=1 λk (t)

≤ ε,

∀ k.

(15)

This relaxation is conservative (it implies the corridor-level constraint but not vice versa) and enables each RSU to be scheduled independently, reducing the joint problem to K single-RSU subproblems. In practice, the corridor-level metric (14b) is the primary compliance criterion, as it permits one RSU to consume more violation budget if others consume less; per-intersection violation rates are reported for transparency in Section VI-C. At the second level, each single-RSU subproblem is formulated as a constrained MDP. The state of RSU k at time slot t is
xk (t) = ℓk (t), sk (t − 1), h(t) ,

(16)

where ℓk (t) ∈ {1, . . . , B} is the quantized traffic level (obtained by discretizing the observed arrival rate

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into B bins based on the empirical distribution at intersection k), sk (t−1) ∈ S is the previous power state, and h(t) ∈ {0, . . . , 23} is the hour of day. The resulting state space has |Xk | = B × |S| × 24 = 3 × 24 × B states. With B = 5 bins (quintile-based discretization), this yields |Xk | = 360 states per RSU, which is small enough for exact solution via value iteration. For the cooperative extension, the state is augmented with the upstream signal:
(t) = ℓk (t), sk (t − 1), h(t), uk−1 (t) , xcoop k

(17)

where uk−1 (t) ∈ {Low, High} is the binary signal from the upstream neighbor (Eq. 12). This doubles the state space to |Xkcoop | = 720 states, still tractable for value iteration. The Lagrangian relaxation of the per-RSU constraint (15) converts the constrained MDP into an unconstrained MDP with a modified reward function: Rk (x, a) = −P (a) · ∆ − βk · Vk (x, a),

(18)

where P (a) is the power consumption in action a ∈ S, Vk (x, a) is the expected violation count (Eq. 10) given the traffic level encoded in state x, and βk ≥ 0 is the Lagrange multiplier (violation penalty weight) that trades off energy savings against latency compliance. The optimal βk is the value for which the resulting unconstrained MDP policy achieves exactly ε violation rate on the training data; it is found via binary search (see Section V-C). This decomposition yields four scheduling approaches of increasing sophistication, each adding one capability: (1) a periodic fixed schedule that ignores real-time traffic entirely, (2) a threshold-based reactive policy that uses local observations, (3) an MDP-based adaptive policy that optimally plans for a single RSU, and (4) a corridor-aware cooperative policy that incorporates upstream information via I2I signaling. These are detailed in the following section. V. S CHEDULING A LGORITHMS This section presents four scheduling algorithms of increasing sophistication for the RSU sleep scheduling problem formulated in Section IV. The algorithms are organized as a progression: each successive method adds one capability over the previous, enabling a controlled evaluation of the marginal value of adaptivity (Algorithms 2 and 3) and cooperation (Algorithm 4). Table IV summarizes the key characteristics of each algorithm.

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TABLE IV: Summary of Scheduling Algorithms Property

PFS THR MDP COOP

Real-time adaptation Time-of-day awareness Multi-slot optimization Upstream I2I signal Awake state States per RSU

✓

✓ ✓ ✓

A —

I 360

✓

A —

✓ ✓ ✓ ✓ I 720

A. Algorithm 1: Periodic Fixed-Schedule (PFS) The periodic fixed-schedule algorithm assigns each RSU a predetermined sleep/wake schedule based on the average hourly traffic profile. The schedule is computed offline, separately for weekday and weekend day types, and does not adapt to real-time traffic conditions. (d)

For each RSU k and day type d, the algorithm constructs the schedule as follows. Let λ̄k (h) denote the average arrival rate at RSU k during hour h on day type d, computed from the historical traffic data. (d)

The 24 hourly slots are sorted in ascending order of λ̄k (h). Starting from the lowest-traffic hour, slots are greedily assigned to Sleep until adding the next slot would cause the expected violation rate to exceed (d)

the SLA threshold ε. Formally, the sleep set Hk ⊆ {0, 1, . . . , 23} is the largest set such that P (d) Vk (h) h∈Hk ≤ ε, P23 (d) λ̄ (h) h=0 k

(19)

(d)

where Vk (h) is the expected violation count for hour h computed from Eq. (10) using λ̄k (h). All hours (d)

not in Hk are assigned to the Active state. The algorithm uses Active (not Idle) as its awake state because the schedule is precomputed without knowledge of which state minimizes energy. It has no tunable parameters beyond the SLA constraint ε and serves as a lower bound on the performance of adaptive approaches. It represents the simplest operationally deployable strategy: a network operator configures a fixed sleep window (e.g., 00:00–08:00) based on average traffic statistics.

B. Algorithm 2: Threshold-Based Reactive (THR) The threshold-based algorithm makes reactive sleep/wake decisions using the most recent traffic observation. At the beginning of each time slot t, RSU k observes the realized arrival count from the previous

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slot, λk (t − 1), and applies a threshold rule with hysteresis:    S, if sk (t−1) ̸= S and λk (t−1) < λth ,     sk (t) = A, if sk (t−1) = S and λk (t−1) > 1.5 λth ,      s (t−1), otherwise, k

(20)

where λth is the sleep threshold and the factor of 1.5 on the wake-up threshold provides hysteresis to prevent rapid cycling between sleep and active states during transitional traffic periods. The threshold λth is the sole tunable parameter. It is determined by grid search over the range [50, 1000] veh/hr in steps of 50, selecting the value that minimizes corridor energy while maintaining ε ≤ 0.01 on the training trace. Like the periodic algorithm, the threshold algorithm uses Active as its awake state. The threshold approach improves over the periodic schedule by adapting to real-time traffic: it can exploit unexpected low-traffic periods (e.g., a quiet weekday evening) that the fixed schedule cannot anticipate. However, it has two limitations. First, it uses only local information from the previous time slot and cannot anticipate future traffic trends or exploit upstream correlation. Second, the one-hour lag between observation and decision means the algorithm reacts to traffic changes rather than predicting them, leading to suboptimal decisions during rapid transitions between peak and trough periods.

C. Algorithm 3: MDP-Based Adaptive (MDP) The MDP-based algorithm formulates single-RSU scheduling as a Markov decision process and solves it via value iteration, yielding a policy that is optimal for each RSU independently (without cooperation). This algorithm instantiates the per-RSU decomposition described in Section IV-C. 1) State, Action, and Transition Model: The state of RSU k at time slot t is xk (t) = (ℓk (t), sk (t−1), h(t)) as defined in Eq. (16). The traffic level ℓk (t) ∈ {1, . . . , B} is obtained by discretizing the previous hour’s arrival count into B = 5 bins, with bin edges set at the quintiles of the empirical arrival rate distribution at intersection k. The quintile-based binning ensures that each bin is equally populated in the training data, providing balanced transition probability estimates across all traffic levels. The action set is A = {A, I, S}, corresponding to the three power states. At each time slot, the policy selects an action ak (t) ∈ A that determines the RSU’s power state for the upcoming slot. The transition probabilities Pr[ℓk (t+1) = j | ℓk (t) = i, h(t) = h] capture how the traffic level evolves from one hour to the next. These probabilities are estimated from the 5-day trace by counting, for each

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(i, h) pair, the empirical frequency of transitioning to each bin j at hour h+1. Laplace smoothing (adding a count of one to each transition) is applied to avoid zero probabilities, which is necessary given the limited sample size (at most 5 observations per (i, h) pair). The sensitivity of the results to the discretization granularity, which implicitly governs the smoothing influence, is evaluated in Section VI-D. The hour-ofday component h(t) transitions deterministically: h(t + 1) = (h(t) + 1) mod 24. 2) Reward Function and Penalty Calibration: The reward function follows the Lagrangian formulation in Eq. (18): Rk (x, a) = −P (a) · ∆ − βk · Vk (x, a),

(21)

where P (a) ∈ {Pa , Pi , Ps } is the power consumption of action a, ∆ = 3,600 s is the slot duration, and Vk (x, a) is the expected violation count computed from Eq. (10) using the representative arrival rate for the traffic bin encoded in x. When a ∈ {A, I}, the RSU is awake and Vk = 0. When a = S, violations are incurred according to the traffic-proportional model. The penalty weight βk controls the energy-latency tradeoff and must be calibrated so that the resulting policy achieves exactly the target violation rate ε = 0.01. A higher βk produces a more conservative policy (less sleep, fewer violations); a lower βk produces a more aggressive policy (more sleep, more violations). We determine βk via binary search over the range [0, 108 ]. At each iteration, value iteration is run to convergence, the resulting policy is evaluated on the training trace, and the violation rate is compared to ε. The search terminates after 40 iterations, yielding βk values that produce violation rates within 0.1 percentage points of the target. 3) Value Iteration: The optimal policy is obtained by solving the Bellman equation " # X Pr[x′ | x, a] V ∗ (x′ ) , V ∗ (x) = max R(x, a) + γ a∈A

(22)

x′

with discount factor γ = 0.99. Convergence (defined as maxx |Vn+1 (x) − Vn (x)| < 10−6 or policy stability) is reached within 200–400 iterations, taking less than one second per RSU on commodity hardware. The MDP algorithm uses Idle (not Active) as its preferred awake state, because Pi < Pa while both states yield zero violations. The simpler baselines (PFS and THR) use Active by design, forgoing this 3.1 W per-hour saving.

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D. Algorithm 4: Corridor-Aware Cooperative (COOP) The cooperative algorithm is the primary contribution of this work. It extends the single-RSU MDP with upstream traffic information, enabling downstream RSUs to make better-informed sleep decisions by exploiting the spatial correlation between adjacent intersections. 1) State Augmentation: For downstream RSUs (k ≥ 2), the state is augmented with the upstream signal as defined in Eq. (17):
(t) = ℓk (t), sk (t−1), h(t), uk−1 (t) , xcoop k where uk−1 (t) ∈ {Low, High} is the binary upstream signal (Eq. 12). This doubles the state space to |Xkcoop | = 5 × 3 × 24 × 2 = 720 states. The head-of-corridor RSU (k = 1) has no upstream neighbor and uses the standard 360-state MDP from Algorithm 3. 2) Modified Transition and Reward Model: The upstream signal modifies the MDP in two ways. First, the transition probabilities are conditioned on the upstream signal. When uk−1 (t) = High, the probability mass over next-hour traffic bins shifts toward higher values, reflecting the spatial correlation: if the upstream RSU observed above-median traffic, the downstream RSU is likely to experience elevated traffic as well. The shift magnitude is proportional to the correlation coefficient ρk−1,k . Formally, the cooperative transition probability is coop

Pr [ℓ′ = j | ℓ, h, u] ∝ Pr[ℓ′ = j | ℓ, h] · wj (u),

(23)

where the weight wj (u) shifts probability toward higher (lower) bins when u = High (u = Low), scaled by ρk−1,k , followed by renormalization. Second, the reward function modulates the violation cost based on the upstream signal. When the RSU considers sleeping, the expected violation count is evaluated at an effective arrival rate (Eq. 13) that is adjusted upward (if u = High) or downward (if u = Low) by a factor of ρk−1,k · α with α = 0.30. This makes sleeping more costly when the upstream RSU reports high traffic (the downstream RSU should prepare for incoming vehicles) and less costly when the upstream RSU reports low traffic (the downstream RSU can sleep with greater confidence). 3) Solution and Complexity: The cooperative MDP is solved by the same value iteration procedure as Algorithm 3 (Eq. 22), with the state space expanded to 720 states. The penalty weight βk is re-calibrated independently for each downstream RSU via binary search, since the upstream information changes the

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Algorithm 1 Corridor-Aware Cooperative RSU Sleep Scheduling Input: Traffic traces {λk (t)}, correlations {ρk,k+1 }, SLA ε Output: Per-RSU policies {πk } 1: // Offline: Policy computation 2: for k = 1 to K do

Compute bin edges from quintiles of {λk (t)} 4: Estimate transition probabilities from training trace 5: if k = 1 then 6: Solve 360-state MDP via value iteration (Alg. 3) 7: else 8: Augment state with upstream signal (|X | = 720) 9: Modify transitions and rewards using ρk−1,k , α 10: Solve 720-state cooperative MDP via value iteration 11: end if 12: Calibrate βk via binary search to achieve ε 13: Store policy πk : Xk → A 14: end for 3:

15: // Online: Distributed execution 16: for each time slot t = 1, 2, . . . , T do

for k = 1 to K do 18: Observe ℓk (t), sk (t−1), h(t) 19: if k ≥ 2 then 20: Receive upstream signal uk−1 (t) 21: end if
22: sk (t) ← πk xk (t) 23: Compute uk (t) and send to RSU k+1 (if k < K) 24: end for 25: end for 17:

// Table lookup

energy-violation tradeoff. In practice, the cooperative βk values are lower than the independent MDP values (e.g., 238 vs. 309 for I2), indicating that the upstream signal substitutes for some of the violation penalty pressure: the cooperative policy can achieve the same compliance level with less conservatism because it has better information. The computational cost of the cooperative algorithm is modest. Value iteration over 720 states with 3 actions requires 720 × 3 = 2,160 Bellman updates per iteration, converging in comparable iteration counts to the 360-state MDP. The I2I communication overhead is one binary message per RSU pair per time slot (K − 1 = 3 messages per hour for our corridor). The policy computation is performed offline; at runtime, each RSU executes a simple table lookup indexed by its current state, requiring O(1) time per decision. The overall corridor scheduling overhead therefore scales linearly with K, making the approach applicable to longer corridors without architectural changes.

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Algorithm 1 summarizes the cooperative scheduling procedure for a corridor of K RSUs. The offline policy computation phase (lines 1–14) completes in under one minute for the entire corridor on commodity hardware. The dominant cost is the βk binary search, which requires approximately 40 iterations of value iteration per RSU. The online execution phase (lines 15–21) involves only table lookups and binary message exchanges, with negligible computational overhead. VI. R ESULTS AND A NALYSIS This section evaluates the four scheduling algorithms on the 5-day traffic trace from the four-intersection corridor described in Section III-A. We compare energy savings, latency compliance, cooperation gain, sensitivity to system parameters, and carbon footprint reduction. A. Simulation Setup The simulation replays the 5-day hourly traffic trace (762,050 total vehicles across 4 intersections and 120 time slots) through each scheduling algorithm. The RSU power parameters follow Table II, with the latency constraint Lmax = 100 ms and violation threshold ε = 0.01. The always-on (AO) baseline, in which all RSUs remain in the Active state continuously, serves as the reference for energy savings calculations, consuming 3,628,800 J (1,008 Wh) per RSU over the 5-day period. For the MDP and cooperative algorithms, the traffic arrival rates are discretized into B = 5 bins per RSU (quintile-based), yielding 360-state and 720-state MDPs respectively. Transition probabilities are estimated from the same 5-day trace used for evaluation. This overlap between training and evaluation data means the reported MDP and cooperative savings represent upper bounds on deployable performance. The 5day trace is insufficient for a statistically meaningful train-test split given the weekday/weekend partition (holding out one weekend day leaves only a single weekend training day). The traffic scaling analysis in Section VI-E3 provides indirect evidence of generalizability by showing that retrained policies maintain consistent performance across a 12× range of traffic intensities, and the strong diurnal periodicity of urban arterial traffic suggests that temporal generalization is plausible. All results are deterministic (fixed trace, no stochastic sampling) and fully reproducible. B. Energy Savings Comparison Table V and Fig. 2 present the 5-day energy consumption and percentage savings for each algorithm. The cooperative algorithm achieves 59.50% corridor-level energy savings over the always-on baseline,

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TABLE V: Energy Savings vs. Always-On Baseline (5-Day Total) Algorithm

I1

I2

I3

I4 Corridor

Periodic 36.8% 39.3% 34.4% 39.3% Threshold 36.8% 33.5% 31.9% 45.8% MDP 61.9% 49.7% 49.7% 61.4% Cooperative 61.9% 57.3% 57.3% 61.4%

37.4% 37.0% 55.7% 59.5%

Fig. 2: Energy savings by algorithm and intersection. The cooperative algorithm achieves 59.5% corridorlevel savings, with the cooperation gain concentrated at I2 and I3 (downstream RSUs with ρ ≥ 0.97). reducing total corridor energy from 14,515,200 J to 5,878,692 J. This represents an improvement of 22.1 percentage points over the best simple baseline (Periodic, 37.43%) and 3.83 percentage points over the independent MDP (55.67%). The results reveal a clear hierarchy. The two simple baselines (PFS and THR) achieve comparable corridor-level savings (37.4% and 37.0%) by exploiting the overnight low-traffic window, but through different mechanisms: PFS follows a fixed schedule while THR reacts to observed traffic dips. The threshold algorithm shows higher per-intersection variance, achieving 45.8% at I4 (whose extreme 24.6× peak-to-trough ratio creates long low-traffic windows) but only 31.9% at I3. The MDP nearly doubles the corridor savings to 55.7% through two mechanisms. First, it discovers that the Idle state (Pi = 5.3 W) is the energy-optimal awake mode, strictly dominating Active (Pa = 8.4 W) while maintaining zero latency violations during awake hours. The MDP and cooperative policies never select the Active state, operating exclusively in Idle and Sleep (Table VI). This renders the transition constraint (14d) non-binding and confirms that Idle is the optimal awake mode for RSU scheduling. The simple baselines use Active as their awake state by design (Section V-A), forgoing 3.1 W of savings during every awake hour. Second, the MDP optimally times its sleep periods using the traffic bin and

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TABLE VI: Power State Distribution (Hours over 5-Day Trace, per RSU) Active / Idle / Sleep (hours) Algorithm

I1

I2

I3

I4

Always-On 120/0/0 120/0/0 120/0/0 120/0/0 Periodic 75/0/45 72/0/48 78/0/42 72/0/48 Threshold 75/0/45 79/0/41 81/0/39 64/0/56 MDP 0/71/49 0/95/25 0/95/25 0/72/48 Cooperative 0/71/49 0/80/40 0/80/40 0/72/48

hour-of-day information, sleeping more aggressively during confirmed low-traffic hours than the fixed periodic schedule. The cooperative algorithm adds 3.83 percentage points at the corridor level by enabling I2 and I3 to sleep 15 additional hours each compared to the independent MDP (40 vs. 25 sleep hours). These additional sleep hours, saved at the difference between Idle and Sleep power (5.3 − 0.15 = 5.15 W), account for approximately 277,800 J per RSU, or 7.7% of the always-on baseline. I1 and I4 show identical performance under MDP and cooperative scheduling: I1 because it has no upstream neighbor, and I4 because the weaker correlation (ρ3,4 = 0.907) with 5-bin discretization is insufficient to change any policy decision (see Section VI-D). Fig. 3 shows the weekday-weekend breakdown. All algorithms achieve greater savings on weekends due to lower traffic volumes (116,528 vs. 176,332 daily corridor vehicles). The threshold algorithm benefits most from weekends (I4 weekend savings: 69.5%) because the reduced traffic more frequently falls below λth . The cooperative gains over MDP are concentrated during weekdays at I2 (+6.8 pp) and I3 (+8.5 pp), where the upstream signal provides the most value during the higher-traffic and more variable weekday periods. Fig. 4 shows the power state schedule for a representative weekday (Sunday, August 17). The periodic algorithm sleeps during a contiguous block (hours 0–8), fixed across all RSUs. The threshold algorithm shows fragmented sleep patterns that lag traffic by one hour. The MDP uses Idle during moderate-traffic hours and Sleep during the trough, producing a clean two-state partition. The cooperative algorithm extends sleep at I2 and I3 into the transitional hours (7–9), where the upstream signal provides confidence that traffic has not yet surged. On Gulf weekend days, all algorithms sleep more extensively due to lower traffic volumes. The MDP and cooperative algorithms extend their sleep windows from approximately 8 hours (weekday) to 12–14 hours, while the threshold algorithm sleeps most aggressively at I4, exploiting the extremely low weekend traffic

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Fig. 3: Energy savings by day type. All algorithms save more on weekends (Gulf Friday–Saturday). Cooperative gains over MDP are concentrated on weekdays at I2 and I3, where upstream information resolves traffic ambiguity during higher-volume periods.

Fig. 4: RSU power state schedule for Sunday, August 17 (weekday). PFS sleeps during a fixed overnight block. THR fragments sleep across low-traffic periods. MDP partitions the day into Idle and Sleep without using Active. COOP extends sleep at I2 and I3 into transitional hours via upstream signaling. at this three-way intersection (20,108 daily vehicles vs. 42,072 on weekdays). The MDP and cooperative algorithms adapt to both day types automatically through the hour-of-day state component. C. Latency Compliance Analysis Table VII and Fig. 5 report the per-intersection and corridor-level latency violation rates. All four algorithms satisfy the corridor-level SLA constraint (ε = 0.01), with violation rates ranging from 0.60% (MDP) to 0.93% (Threshold).

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TABLE VII: Latency Violation Rates (%) Algorithm

I1

I2

I3

I4 Corridor

Periodic 0.82 0.96 0.86 0.90 Threshold 0.87 0.75 0.91 1.28 MDP 0.96 0.31 0.37 0.85 Cooperative 0.96 0.76 0.90 0.85

0.89 0.93 0.60 0.86

Fig. 5: Corridor-level latency violation rates by algorithm, with the ε = 1% SLA threshold (dashed line). All algorithms are compliant at the corridor level. The MDP uses its violation budget most conservatively (0.60%), while the cooperative algorithm trades violation headroom for additional energy savings (0.86%). The threshold algorithm violates the per-intersection constraint at I4 (1.28%), although the corridor-level rate (0.93%) remains compliant. This demonstrates that a single threshold is too blunt for heterogeneous corridors: λth cannot simultaneously optimize sleep at I4 (peak-to-trough 24.6×) and I2 (13.7×) without over-sleeping at the more volatile intersection. As noted in Section IV-C, the corridor-level metric (14b) is the primary compliance criterion; per-intersection rates are reported for transparency. The MDP achieves the lowest corridor violation rate (0.60%), using its violation budget conservatively. The cooperative algorithm has a higher violation rate (0.86%) because it sleeps more aggressively at I2 and I3, deliberately trading violation headroom for energy savings. This is the correct behavior: the cooperative algorithm has better information (the upstream signal) and can therefore operate closer to the SLA boundary with confidence. I1 shows identical violation rates for MDP and cooperative (0.96%) because the head-of-corridor RSU uses the same policy in both algorithms.

D. Benefit of Corridor Cooperation Table VIII summarizes the per-RSU cooperation gain (cooperative savings minus MDP savings). I2 and I3 each gain 7.66 percentage points over the independent MDP, while I1 (no upstream neighbor) and I4

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TABLE VIII: Per-RSU Cooperation Gain (Cooperative vs. MDP) RSU Upstream (ρ) I1 I2 I3 I4

MDP COOP Gain (pp)

— (head) 61.9% 61.9% I1 (ρ = 0.984) 49.7% 57.3% I2 (ρ = 0.974) 49.7% 57.3% I3 (ρ = 0.907) 61.4% 61.4%

0.00 +7.66 +7.66 0.00

(ρ = 0.907) show zero gain. The cooperation gain at I2 and I3 corresponds to 15 additional sleep hours per RSU over the 5-day trace (40 vs. 25 for the MDP), translating to 277,818 J (77.2 Wh) of energy savings per RSU. The identical gain at I2 and I3 is a consequence of the limited training data. With five days and medianbased thresholding, the upstream signal is High for exactly 2 out of 5 days (40%) for every hour at both I2 and I3. This uniform signal distribution, combined with the 5-bin quantization, produces identical cooperative policies despite different traffic profiles (bin edges and βk values differ between I2 and I3, but the policy argmax is the same). With a longer training trace, the upstream signal distribution would vary by hour and likely produce differentiated policies. The zero gain at I4 reflects a discretization limitation. With ρ3,4 = 0.907 and modulation parameter α = 0.30, the reward adjustment (±0.907 × 0.30 = ±0.27) is insufficient to flip any action decision in the 5-bin MDP. When the discretization is refined to 10 bins, a small positive gain of 1.02% appears, confirming that the cooperative mechanism operates at I4 but below the resolution threshold of the 5-bin policy. Fig. 6 examines the interaction between cooperation gain and policy granularity. The cooperation gain for I2 peaks at 5 bins (+7.66%) and diminishes at higher bin counts as the independent MDP becomes more effective on its own. This finding has a practical implication: cooperation is most valuable when individual RSUs operate with limited state resolution, which is the realistic case for deployed systems with constrained memory and computation. This pattern is expected: at coarse resolutions, the per-RSU MDP cannot distinguish transitional traffic hours from confirmed low-traffic hours, and the upstream signal provides genuinely new information that resolves this ambiguity. At fine resolutions, the MDP’s richer state representation captures these distinctions internally, reducing the marginal value of external cooperation. We also evaluated the sensitivity of the cooperation gain to the spatial correlation ρ by sweeping ρ ∈ [0.5, 1.0] with βk re-calibrated at each value. The gain is invariant across this range for I2 and

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Fig. 6: Cooperation benefit as a function of MDP state granularity. Left: MDP (dashed) vs. cooperative (solid) energy savings. Right: additional savings from cooperation. The cooperation gain peaks at moderate granularity (3–5 bins) and diminishes as the independent MDP approaches optimality at finer resolutions. I3, because the βk binary search compensates for changes in ρ: as ρ increases, the cooperative signal becomes more informative, so βk decreases to maintain the same violation rate, and the net policy on the trace remains unchanged. This is a robustness finding: the cooperation gain is insensitive to correlation estimation error, which is important for deployments where ρ may be imprecisely known. The corridor-level cooperation gain of 3.83 percentage points reflects the dilution inherent in a short corridor: only 2 of 4 RSUs (I2 and I3) benefit from upstream information, while I1 (head node) and I4 (weak correlation at the 5-bin resolution) do not. On a longer corridor of K RSUs with comparable spatial correlations, K − 1 downstream RSUs would receive upstream signals, and the corridor-level gain would approach the per-RSU gain of 7.7 percentage points as the head-node dilution diminishes. For example, on a 10-RSU corridor, the head node constitutes only 10% of the fleet rather than 25%, and the fraction of RSU pairs with ρ ≥ 0.97 would determine the aggregate benefit. The linear scaling of I2I signaling overhead (Section V-D) ensures that extending the framework to longer corridors introduces no architectural barriers. Similarly, the identical policies at I2 and I3 and the zero gain at I4 are artifacts of the 5-day training set: with a longer trace, the median-based upstream threshold would vary by hour, producing differentiated signal distributions at I2 and I3 and enabling the cooperative mechanism to resolve finer traffic distinctions at I4. E. Sensitivity Analysis We evaluate the sensitivity of the cooperative algorithm to four system parameters: the latency SLA, the hardware wake-up delay, the traffic volume, and the RSU power class. These sweeps serve dual purposes:

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Fig. 7: Energy savings vs. latency SLA threshold Lmax . A sharp knee at Lmax ≈ 102 ms (the WSA restoration boundary) separates the constrained regime (Lmax < 107 ms, where sleep scheduling is a non-trivial optimization) from the unconstrained regime (Lmax ≥ 120 ms, where near-universal sleep is feasible). they characterize the design space for V2I sleep scheduling and they validate the robustness of the power model parameters adopted in Section III-B. 1) Latency SLA: Fig. 7 shows the corridor-level energy savings as a function of the latency budget Lmax . A sharp transition occurs at Lmax ≈ 102 ms, corresponding to the service restoration window Trestore = twake + TWSA = 102 ms. Below this threshold, every sleeping RSU incurs a nonzero violation probability (Eq. 8), and the algorithm must carefully select which hours to sleep. Above 120 ms, Pviol = 0 because the entire restoration window fits within the latency budget, and the RSU can sleep during every hour with no violation risk, yielding 98.1% savings (limited only by transition energy costs). At the most restrictive SLA of 50 ms, Pviol = 55.9% and the algorithm barely sleeps, achieving only 36.9% savings. This result identifies a fundamental hardware-level boundary for RSU sleep scheduling: the optimization problem is non-trivial only when Lmax < Trestore + Ltx ≈ 107 ms. The 3GPP TS 22.185 SLA of 100 ms falls just below this boundary, making it the most challenging and practically relevant operating point. The advanced driving requirements of TS 22.186 (3–100 ms) would tighten the constraint further, reinforcing the scope limitation discussed in Section III-D. 2) Wake-Up Delay: Energy savings degrade gracefully as the hardware wake-up delay increases: from 60.7% at twake = 1 ms to 49.7% at 10 ms and 36.9% at 100 ms. The WSA discovery cycle (100 ms) dominates the restoration window, so even a 50× increase in twake reduces savings by only 20 percentage points. At twake = 100 ms, the restoration window reaches 200 ms, exceeding the SLA entirely and

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precluding sleep. This confirms that the assumed twake = 2 ms (Section III-B) is not a critical parameter choice: the results are qualitatively similar for any twake ≤ 20 ms. 3) Traffic Volume Scaling: To evaluate robustness to traffic intensity changes, all arrival rates are multiplied by a scaling factor ranging from 0.25× to 3.0×. Two scenarios are compared: a fixed policy (trained at 1.0× and applied without retraining) and a retrained policy (MDP re-solved at each traffic level). The fixed policy degrades when traffic departs from the training volume. At 0.25× volume, it over-sleeps and massively violates the SLA (5.95% violation rate). At 3.0× volume, it under-sleeps and achieves only 47.5% savings. In contrast, retrained policies maintain approximately 59.5% savings across the entire 0.25×–3.0× range with consistent violation rates of 0.86–0.87%. This demonstrates that the MDP formulation is robust when re-parameterized, and highlights the importance of periodic policy retraining as traffic patterns evolve. Since the MDP solver converges in under one second per RSU, retraining can be performed daily or weekly with negligible computational cost. 4) RSU Power Class: Energy savings increase with the RSU power class: from 59.5% at Pa = 8.4 W (MK5-class) to 82.99% at 20 W and 86.4% at 25 W (MK6-class). This is because Ps (0.15 W) is fixed while Pa grows, increasing the sleep-to-active power ratio. The absolute energy saved scales linearly from 2,399 Wh to 10,367 Wh over the 5-day period. This confirms that the cooperative scheduling approach generalizes across RSU hardware classes, with greater absolute benefit for higher-power multi-radio units. F. Carbon Footprint and Deployment Cost Reduction Table IX translates the energy savings into annual carbon dioxide reduction using Kuwait’s grid emission factor of 0.6 kg CO2 /kWh. The cooperative algorithm saves an average of 26.3 kg CO2 per RSU per year, totaling 105.1 kg CO2 for the 4-RSU study corridor. Extrapolated to a hypothetical 200-RSU deployment across Kuwait City (a moderate scale for a smart-city V2I network), the cooperative algorithm reduces emissions by 5.25 tonnes CO2 per year, a 59% improvement over the 3.31 tonnes achieved by the periodic baseline. While these figures are modest in absolute terms, they represent a lower bound on the achievable reduction for three reasons. First, the 8.4 W MK5-class RSU is at the low end of the commercial power range; dual-mode RSUs (15–25 W) would yield proportionally greater savings. Second, the 5-day trace captures only summer traffic patterns in Kuwait; winter months with different commute patterns may offer additional sleep opportunities. Third, the single-sleep-depth model does not exploit lighter sleep modes

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TABLE IX: Annual Carbon Footprint Reduction Per RSU (avg) Algorithm Periodic Threshold MDP Cooperative

200-RSU city

kWh/yr kg CO2 /yr kWh/yr t CO2 /yr 27.6 27.2 41.0 43.8

16.5 16.4 24.6 26.3

5,509 5,448 8,193 8,756

3.31 3.27 4.92 5.25

(e.g., SM1/SM2 from [21]) that could save energy during moderate-traffic hours when deep sleep is too risky. VII. C ONCLUSION This paper presented a cooperative RSU sleep scheduling framework for energy-efficient V2I corridors, validated with real traffic data from four signalized intersections in Kuwait City. The cooperative algorithm reduced corridor energy consumption by 59.5% relative to always-on operation while maintaining 99% latency compliance (violation rate 0.86%), and provided 7.7 percentage points of additional savings over independent per-RSU optimization at downstream RSUs with spatial correlation ρ ≥ 0.97. The MDP-based algorithms discovered that the Idle state is the energy-optimal awake mode, yielding 3.1 W of additional savings per awake hour compared to simple baselines. Annualized over a 200-RSU deployment, the cooperative approach reduces CO2 emissions by 5.25 tonnes per year. The sensitivity analysis identified a fundamental design boundary at Lmax ≈ 102 ms (the WAVE service restoration window), below which sleep scheduling is a non-trivial optimization. The cooperative policy was robust to correlation estimation error and to traffic volume changes when periodically retrained. The Gulf-region traffic characterization revealed a corridor-level peak-to-trough ratio of 14.8× (reaching 24.6× at the most volatile intersection) and spatial correlations of 0.907–0.984, confirming both the opportunity and the challenge for RSU sleep scheduling in the region. Future work includes extending the evaluation to longer traffic datasets for proper train-test separation, refining the scheduling granularity to capture sub-hourly dynamics such as signal-induced platoons, and incorporating multiple sleep depth levels and realistic 802.11p channel models. Evaluating the framework under C-V2X and integrating renewable energy sources represent natural extensions toward comprehensive green V2I infrastructure management.

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