Distributed Federated Learning for Ultra-Reliable Low-Latency Vehicular Communications

I. INTRODUCTION

• Existing probabilistic queue-length controls can miss rare large-queue events, while EVT estimation needs scarce network-wide exceedance samples and sharing individual QSI incurs communication overhead.Such extreme queues can cause unacceptable latency for some VUEs.Source: §I · pp. 1–2
• For 100 VUE pairs, the proposed solution reduces VUEs with large queue lengths by 60.9% while reducing power consumption by two folds versus the average-queue reliability baseline.Compared with that baseline, it also reduces averages and fluctuations of extreme queue lengths by 28.6% and 33.2%, respectively.Source: §I · p. 2
• The proposed framework estimates queue-length tail distributions with EVT-based GPD parameters learned through distributed FL, then uses Lyapunov optimization to derive per-VUE allocation policies.VUEs share local models rather than queue samples; the approach accounts for FL communication over shared wireless resources and develops synchronous and asynchronous algorithms. It assumes threshold-exceeding queue samples are independently and identically distributed across VUEs.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM DEFINITION

• The system partitions VUE pairs into groups that reuse resource blocks with low-to-no mutual interference, while the RSU allocates blocks orthogonally across groups.Each VUE pair may use only the resource blocks assigned to its group.Source: §II · p. 3
• The objective is network-wide power minimization while maintaining queue stability and keeping each VUE’s probability of exceeding queue threshold q0 below ǫ.The paper treats queue lengths beyond q0 as extreme events because they correspond to worst-case network queuing latency.Source: §II · p. 3
• For each VUE, targets on the mean and second moment of queue exceedances help control extreme-queue fluctuations and allocate more power to users with larger queues.The targets are system-generated to help avoid infeasibility and instability, and their use supports identical tail distributions across vehicles for the analysis.Source: §II · pp. 3–4
• The optimization is difficult because decisions depend on future network states and the exceedance distribution is unknown; centralized solving would require costly network-wide CSI and QSI exchange.The paper therefore motivates a distributed solution with minimal coordination.Source: §II · p. 4

III. PROPOSED DISTRIBUTED FRAMEWORK USING EVT AND LYAPUNOV OPTIMIZATION

• The proposed solution decouples the objective and constraints over VUE pairs using network-wide statistics of queue lengths exceeding q0.Source: §III · p. 4

A. Modeling Extreme Queue Lengths Using Extreme Value Theory

• Under IID queue samples and a large threshold, excess queue lengths are modeled by a GPD whose first two moments are bounded and equivalent to the stated formulas only when ξ < 1/2.The GPD parameters are scale σ and shape ξ.Source: A. Modeling Extreme Queue Lengths… · p. 4
• With RSU assistance, each VUE pair can estimate ξ and σ locally without sharing queue-state information, decoupling and locally imposing the reliability constraints.Source: A. Modeling Extreme Queue Lengths… · p. 4

B. Lyapunov Optimization for Power Allocation

• Using EVT to model queue excesses and their first two moments, the authors recast the original optimization problem into an equivalent form.Source: B. Lyapunov Optimization for Power… · p. 4
• The reliability constraint is replaced by E[qu] ≤ ǫq0 using Markov’s inequality, and a virtual queue Ψu represents this time-average constraint for each VUE.Source: B. Lyapunov Optimization for Power… · p. 4
• Controlling the Lyapunov-drift upper bound ensures stability of both actual and virtual queues, while V tunes the queue-length versus optimal-solution-accuracy tradeoff.Source: B. Lyapunov Optimization for Power… · p. 4
• Adding a power penalty to expected drift yields drift-plus-penalty minimization; with CQI-based interference estimates, the minimization decouples across VUEs and its convex solution uses water-filling.The first two queue-tail moments affect the optimal power solution, motivating accurate GPD-parameter estimation.Source: B. Lyapunov Optimization for Power… · pp. 4–5

• Accurately estimating σ and ξ from network-wide queue-state samples is imperative because the optimal power allocation relies on the excess queue distribution.Source: §IV · p. 5
• A centralized model of queue lengths exceeding the threshold requires a central controller to compute and communicate with all VUEs at each time t.Source: §IV · p. 5

A. Queue Sampling via Block Maxima (BM)

• Each VUE samples at most one queue-length maximum per block when its queue exceeds threshold q0, with block length chosen to limit correlation and avoid undersampling.The method assumes independent queue-length samples across VUEs for EVT modeling.Source: A. Queue Sampling via Block Maxima (BM) · p. 5
• Each VUE independently performs queue sampling, so the number of collected samples can vary across VUEs; the sample set excludes zero.Fig. 2 illustrates the VUE sampling process.Source: A. Queue Sampling via Block Maxima (BM) · p. 5

B. RSU-Centric GPD Parameter Estimation

• MLE estimates the GPD tail parameters d = [σ, ξ] by fitting the GPD to the network queue samples through log-likelihood optimization.The negative log-likelihood is summed over samples, and its feasible parameter set requires σ > 0, ξ < 1, and 1 + ξQ/σ ≥ 0 for every sample Q.Source: B. RSU-Centric GPD Parameter Estimation · p. 5
• Because the likelihood is smooth and sums over queue samples, its gradient with respect to the GPD parameters can be derived for an individual sample.The paper states the derivative coefficient for a sample in Proposition 2.Source: B. RSU-Centric GPD Parameter Estimation · p. 5
• SVRGD iteratively estimates the optimal GPD parameters from queue samples, after which the RSU shares them with all VUEs.The procedure uses a predefined positive step size and stochastic variance-reduced gradients.Source: B. RSU-Centric GPD Parameter Estimation · pp. 5–6
• CEN requires VUEs to upload local queue samples to the RSU over reused V2V resource blocks, adding wireless overhead that can degrade URLLC performance.As VUE density and sample size increase, RSU access congestion can increase network latency.Source: B. RSU-Centric GPD Parameter Estimation · pp. 5–6
• Because centralized uploading risks congestion and latency, distributed MLE that avoids sharing VUE-local samples with the RSU or other VUEs is needed.CEN is the paper's name for RSU-centric GPD parameter estimation.Source: B. RSU-Centric GPD Parameter Estimation · pp. 5–6

C. FL-Based GPD Parameter Estimation

• Each VUE locally evaluates its GPD estimate and gradient, then shares its learning model with the RSU for network-wide averaging.The shared model includes the local gradient and parameter estimates, sample count, and maximum queue length; the latter helps determine the domain needed for SVRGD.Source: C. FL-Based GPD Parameter Estimation · p. 6
• VUEs use SVRGD with step size δu = δ/Ku to evaluate local gradients and GPD parameters [27].Updates use local and global copies of the parameters and gradients, processing each local QSI sample.Source: C. FL-Based GPD Parameter Estimation · p. 6
• In sync-FL, VUEs upload together after interval Tf ≫ w, which may improve global-gradient accuracy but degrades VUE-RSU data rates and delays V2V communication.The RSU averages the local models and sends the global model back to the VUEs.Source: C. FL-Based GPD Parameter Estimation · p. 6
• In async-FL, each VUE uploads after collecting a predefined number of new QSI samples, and the RSU averages its model with existing models before returning the update.Because multiple VUEs are unlikely to share models simultaneously, upload and download delays are described as very small.Source: C. FL-Based GPD Parameter Estimation · p. 6

D. Cost of Communication with the RSU

• RSU learning communications reuse V2V communication resource blocks, adding latency to ongoing V2V communication and creating an additional cost for URLLC applications.The paper models the upload and download time for queue samples or learning models as additional V2V delay.Source: D. Cost of Communication with the RSU · p. 7
• In CEN, VUE u incurs an additional V2V delay of (JQ ˆKu/ru0 + Jd/r0u) to upload new queue samples and download GPD parameters.The RSU schedules VUEs over resource blocks already allocated for their V2V communication links.Source: D. Cost of Communication with the RSU · p. 7
• In sync-FL, VUE u incurs uplink and downlink delays of (JΥ + Jd + JQ)/ru0 and (JΥ + Jd + JQ)/r0u, respectively; async-FL is expected to have lower delays.Async-FL VUEs access the RSU independently, which can reduce interference and increase uplink and downlink rates relative to sync-FL.Source: D. Cost of Communication with the RSU · p. 7

• The 250 m × 250 m, nine-intersection Manhattan setup uses VUE pairs at 60 kmph, 50 m apart, 60 RBs, p0 = 10 W maximum power, and 500 kbps Poisson arrivals.Each road has two lanes, each 4 m wide per direction; RB allocation per group is adopted from and.Source: §V · p. 7
• Fig. 4 compares CEN and async-FL on accuracy of GPD parameter estimation.The supplied caption gives the comparison scope but no accuracy values or winner.Source: Figure 4 · p. 8
• Gradient values and GPD parameters are assumed to be 16 bits each, while the rest of the parameter values are presented in Table I.Source: §V · p. 8

A. Centralized vs distributed GPD parameter estimation

• For U = 20, 60, and 100, async-FL's estimated GPDs were almost equivalent to CEN's.The estimates were compared with the original samples plotted alongside the estimated distributions.Source: A. Centralized vs distributed GPD… · p. 8
• Async-FL exchanged 27% less data than CEN at U = 28 and up to 79% less at U = 100.Reliability was slightly lower than CEN for U < 72 and higher for U > 72. At U = 20, async-FL exchanged more data because VUEs uploaded and downloaded both parameters and gradients, while CEN efficiently used the small sample set.Source: Figure 5 · p. 8, A. Centralized vs distributed GPD… · pp. 8–9
• With one SVRGD iteration, async-FL cost was 66.6%, 47.1%, and 40.4% higher than CEN for U = 20, 40, and 60, respectively.Two iterations gave FL lower cost and higher accuracy than CEN; beyond two iterations, async-FL cost was about 0.5% higher at U = 20 and 0.5% lower at U = 100. More samples lowered cost, and additional iterations reduced it rapidly at first, then insignificantly.Source: A. Centralized vs distributed GPD… · p. 8

B. Performance Evaluation

• Async-FL’s power reductions versus CEN and sync-FL are negligible at U = 20, reach 31.6% at U = 42, and remain around 35% for U > 42.QSO uses the least power but is reliability-oblivious; QSR uses less power than the proposed methods for U < 40, but becomes the most power-consuming method beyond U = 80.Source: B. Performance Evaluation · p. 9
• At U = 100, the proposed methods’ average queuing latency is up to three times QSR’s, although QSR has higher worst-case queue lengths than CEN and sync-FL for U ≤68 and async-FL for U ≤100.All three proposed methods have similar average queue lengths, while QSR yields the lowest average latency; FP and QSO have the highest worst-case latencies.Source: B. Performance Evaluation · p. 9, Figure 7 · p. 10
• At U = 100, async-FL reduces worst-case latencies by 7.5%, 21.7%, and 29% versus QSR, CEN, and sync-FL, respectively.Across proposed methods, worst-case latency reductions versus QSR are about 40.3% at U = 20 and 17.3% at U = 68.Source: B. Performance Evaluation · pp. 9–10, Figure 7 · p. 10
• At U = 100, async-FL reduces outages by about 60.9%, 36%, and 35.9% versus QSR, CEN, and sync-FL, respectively.Asynchronous sharing reduces communication delays; for U ≥84, async-FL also shows lower queue lengths and outages than CEN and sync-FL.Source: Figure 7 · p. 10, B. Performance Evaluation · p. 10
• Async-FL reduces average extreme queue lengths by about 28.6%, 41.9%, and 19.5% versus QSR, CEN, and sync-FL, respectively.For U > 44, async-FL has the lowest mean and fluctuations of queue lengths exceeding q0; at U = 100, fluctuation reductions are about 33.2%, 38%, and 47.1% versus QSR, CEN, and sync-FL.Source: Figure 8 · p. 10, B. Performance Evaluation · p. 11
• At vTx-vRx distances of 20 m, 50 m, and 80 m, async-FL reduces transmit power by 3.2%, 18.2%, and 43.1% versus QSR, respectively.Async-FL reduces worst-case queue lengths by 1.1%, 5.2%, and 5.8% at those distances; its average queue length is 1.2% lower at 20 m and 29.4% lower at 80 m, while QSR is 67% lower at 50 m.Source: Figure 9 · p. 10, B. Performance Evaluation · p. 11

C. Impact of finite block length

• Higher VUE speeds increase worst-case queuing latency and queue outages because shorter coherence times and block lengths lower achievable rates.Source: C. Impact of finite block length · p. 11
• For ε = .5, higher power consumption yields lower average queuing latency, while system performance degrades as ε decreases.Source: C. Impact of finite block length · p. 11
• The finite-block-length evaluation considers 40 VUEs at 40, 60, and 80 km/h, corresponding to block lengths of 800, 534, and 400 bits.Source: C. Impact of finite block length · p. 11

VI. CONCLUSIONS

• The proposed method reduces queue-threshold extreme events compared with systems imposing probabilistic constraints on average queue lengths.Source: §VI · p. 12
• The study formulates network-wide power minimization subject to URLLC constraints characterized by the tail distribution of queue lengths above a predefined threshold.Source: §VI · p. 12
• VUEs estimate the network-wide queue-tail distribution locally with RSU assistance, avoiding the sharing of actual queue-length samples.Source: §VI · p. 12
• The distributed transmit-power and resource-allocation procedure combines extreme-value theory and federated learning with Lyapunov optimization.Source: §VI · p. 12
• The accuracy of federated tail modeling relies on IID queue-length samples; studying non-IID training data is left for future work.Source: §VI · p. 12

APPENDIX A PROOF OF PROPOSITION 1

• The proof first considers the one-slot Lyapunov drift ΔLt = L(Ξ(t + 1)) − L(Ξ(t)).Source: Appendix A · p. 12
• Applying ([q+a−r]+)^2 ≤ q^2+(a−r)^2+2q(a−r) yields bounds (24), with M1 = q0 + σ/(1 − ξ) and M2 = 2σ^2/(1−ξ)(1−2ξ).Source: Appendix A · p. 12
• When the queue-exceeding indicator 1_t is one, the queue is nonempty and q_u(t + 1) = q_u(t) + a_u(t)−r_u(t) > 0.Under this condition, the proof uses the untruncated queue update instead of (3).Source: Appendix A · p. 12
• Queue stability bounds the quadratic terms #a1–#a4 by Δ0, while control-independent terms #b1 and #b2 are denoted by Δu for each VUE.Combining bounds (24)–(26) in (23) concludes the proof.Source: Appendix A · p. 12

APPENDIX B PROOF OF PROPOSITION 2

• Appendix B begins by finding the gradient of g_d(Q).Source: Appendix B · p. 12
• Appendix B then calculates the gradient of f_d(Q).Source: Appendix B · p. 12