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REVIEW 4 major objections 6 minor 30 references

A Model-Data Dual-Driven Resource Allocation Scheme for IREE Oriented 6G Networks

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A hybrid model-data scheduler is claimed to converge to the optimal integrated relative energy efficiency in 6G networks even when traffic data is incomplete.

desk verdict A useful algorithm and solid simulations, but the central convergence proof does not hold as written. read the letter →

arxiv 2506.03508 v1 pith:WLKZUYWV submitted 2025-06-04 cs.NI

Tao Yu , Simin Wang , Shunqing Zhang , Xiaojing Chen , Zi Xu , Xin Wang , Jiandong Li , Junyu Liu
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Sihai Zhang
This is my paper
classification cs.NI
keywords integratedrelativeenergyefficiencymodel-datadual-drivenLyapunovqueuegraphneuralnetworktrafficprediction6Gresourceallocationtraffic-capacitymismatchradialbasisfunction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that a hybrid model-data scheduler can maximize integrated relative energy efficiency (IREE) — a 6G energy metric that penalizes spatial-temporal mismatch between capacity and traffic — without ever holding a complete traffic map. The algorithmic claim is Theorem 2: under smoothness of the fine-tuning loss, the IREE value converges to the optimum as both iteration and time grow. The practical stake is that operators could allocate bandwidth and power from volunteered user reports and short traffic histories, yet track the full-information optimum closely; the reported gap is about 5.1–7.6%. If true, the result turns traffic prediction from a precondition into an optional accuracy booster, because a Lyapunov queue corrects prediction drift over the long run.

What carries the argument

The machinery is the pair of a Lyapunov virtual queue and a correction factor. Three virtual queues $Q^\zeta_\tau$, $Q^\kappa_\tau$, and $Q^\eta_\tau$ store the accumulated errors in the utility constraint, the JS divergence, and the transient IREE; correction factors $\nu^\zeta_\tau,\nu^\kappa_\tau,\nu^\eta_\tau\in[0,2]$ are meant to zero each queue residual at every slot, so transient optimization tracks the long-term optimum. Around them sits a recursive ADMM on the augmented Lagrangian. The data-driven partner is the GRAF network, which uses Fourier Graph Operator layers over the base-station adjacency graph to forecast bandwidth and power configurations and a radial-basis (RBF) layer to interpolate missing traffic while preserving spatial continuity.

What would settle it

Run MDDRA on a constructed traffic trace with a sudden demand surge after a long quiet period and check whether constraints (19)–(21) admit $\nu\in[0,2]$ at every slot; if a slot forces $\nu$ outside that interval and IREE stops tracking the full-information optimum, the claim fails. A cheaper check is to record the required $\nu$ values from the paper's own simulator and test whether they ever leave $[0,2]$.

Watch

Extended reading notes

Core claim

The central claim is that the MDDRA algorithm drives $\eta_T^{\mathrm{IREE}}$ to the optimal value, i.e., $\lim_{k,\tau\to\infty}\eta_T^{\mathrm{IREE}}=\eta_T^{*,\mathrm{IREE}}$ (Theorem 2), under dynamic traffic and incomplete spatial-temporal data. The argument couples a data-driven GRAF network, which predicts current traffic from incomplete reports using radial-basis interpolation and Fourier graph operators, with a model-driven Lyapunov queue that accumulates historical errors while correction factors force the transient allocation to satisfy long-term constraints. The paper also claims a universal approximation property for GRAF on spatially continuous, temporally autoregressive traffic, and reports IREE gains of 10.2–20.7% over purely data-driven or model-driven baselines in simulations.

Load-bearing premise

The load-bearing premise is that at every time step the correction factors $\nu^\zeta_\tau,\nu^\kappa_\tau,\nu^\eta_\tau$ can be chosen inside $[0,2]$ to drive the virtual-queue residuals exactly to zero; if any traffic sequence makes that infeasible, the claimed convergence to the optimal IREE has no proof.

Editorial extensions

If this is right

  • Operators could run bandwidth and power allocation for IREE maximization using only volunteered user location reports, without collecting complete spatial-temporal traffic data.
  • The 10.2% gain over greedy scheduling with predicted traffic and the 20.7% gain over scheduling with averaged historical traffic give a concrete split of what the long-term queue correction and the graph predictor each contribute.
  • The gap to complete-information benchmarks stays near 5.1% when current traffic is known and 7.6% for full ADMM, so the price of data incompleteness is bounded in the tested scenarios.
  • The design-principle result steers extra power budget toward roads with large speed limits and higher driving visibility, because those conditions raise the JS divergence faster than they raise network utility.
  • GRAF's spatial interpolation makes the gains persist as the sampling rate drops; at half the user reports the reported IREE advantage over graph or frequency baselines reaches 37.6%.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A finite-time version of Theorem 2 would be the natural next step: the asymptotic statement does not say how many slots an operator needs before the queue correction overtakes prediction error, and the numerical study uses $T=30$.
  • The feasibility of the correction factors inside $[0,2]$ can be tested adversarially; a constructed demand sequence that forces a factor outside that interval would reduce the guarantee from exact optimality to approximate tracking.
  • The same Lyapunov-plus-graph template transfers to other long-term network objectives such as latency, fairness, or carbon intensity whenever a transient metric and a mismatch term like the JS divergence can be defined.
  • Because GRAF trains on complete historical resource configurations rather than on sparse traffic readings, its learned topology abstraction may transfer to deployments with different traffic but similar base-station layouts.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a model-data dual-driven resource allocation (MDDRA) scheme for maximizing integrated relative energy efficiency (IREE) in 6G wireless networks under dynamic, partially observable traffic. The method combines a model-driven Lyapunov queue for long-term correction of cumulative mismatch errors with a data-driven Graph Radial Basis Fourier (GRAF) network for short-term traffic prediction under incomplete spatial data. The central theoretical claims are Theorem 1 (universal approximation property of GRAF) and Theorem 2 (convergence of MDDRA to the optimal IREE, i.e., lim_{k,τ→∞} ηT_IREE = ηT,*_IREE). Numerical experiments compare MDDRA against several baselines and report IREE gains of 10.2%–20.7%, as well as robustness to traffic incompleteness and real-world map data.

Significance. The problem addressed—energy-efficient resource allocation under incomplete and dynamically mismatched traffic—is timely and practically relevant. If the convergence guarantee (Theorem 2) were rigorously established, the MDDRA framework would be a useful contribution to 6G network optimization, particularly for scenarios where complete spatial-temporal traffic data are unavailable. The paper also includes a substantial simulation study, comparison with multiple baselines, and an extension to real-world maps, which are commendable. However, the central theoretical guarantee is not sound: the proof of Lemma 1 (Appendix B) relies on an invalid implication from non-positive Lyapunov drift to queue convergence, and the proof of Theorem 2 (Appendix D) assumes the very constraints it must prove. These are load-bearing gaps that the numerical experiments cannot compensate for. The paper does not provide reproducible code or machine-checked proofs, so the claimed convergence cannot be independently verified.

major comments (4)
  1. [Appendix B, Eqs. (30)-(31)] The proof of Lemma 1 assumes that for each time slot τ there exists a correction factor νκ_τ ∈ [0,2] such that ξ(τ) − κτ/T = −νκ_τ Qκ_τ (Eq. 30). This is an additional feasibility assertion, not a consequence of the traffic model or constraints (19)-(22). For a given Qκ_τ, the required value is νκ_τ = (κτ/T − ξ(τ))/Qκ_τ, and nothing in the paper guarantees this lies in [0,2], especially when Qκ_τ is near zero or has the opposite sign. Even granting that such ν exists, the Lyapunov drift argument is invalid: from Qκ_{τ+1} = (1−νκ_τ)Qκ_τ, the drift ΔQκ_τ = [(1−νκ_τ)²−1](Qκ_τ)² is non-positive, but non-positive drift does not imply convergence to zero. For example, νκ_τ = 0 gives zero drift while Qκ_τ is constant, and νκ_τ = 2 gives Qκ_{τ+1} = −Qκ_τ, which never converges. A contraction argument with the scaling factor bounded away from 1, or an independent residual-convergence argument, is needed and is absent. Thus Lemma 1, which underpins the queue-stability part of Theorem 2, is unproven.
  2. [Appendix D, Part A] The proof of Theorem 2 is circular. In Appendix D, after listing the first-order conditions, the authors state: 'At the same time, we should satisfy the constraints (19), (20) and (21).' They then claim that the ADMM update rules 'easily obtain (19) according to (39), obtain (21) according to (41) and obtain (20) according to (38).' However, these derivations assume that the constraint equalities hold in the first place. For instance, obtaining (20) from the stationarity condition in (38) requires substituting the very equality ξ(τ)+νκ_τ Qκ_τ = κτ/T that the proof is supposed to establish. Similarly, the claim that Adam converges to a bounded region (Ref. [54]) does not imply that the constraints (19)-(21) become feasible; it only gives stationarity of the unconstrained augmented Lagrangian. The existence of ν∈[0,2] satisfying all three nonlinear constraints simultaneously is never proven, and the argument does not establish the queue convergence that the optimality statement depends on.
  3. [Theorem 2 and Appendix D, Part B] The final step of the proof, Eq. (44), constructs an increasing sequence {ηT,τ_IREE} and argues that 'according to Appendix B, we can guarantee the optimality of the IREE when τ → ∞.' Since Appendix B's Lemma 1 is invalid, this optimality guarantee is unsupported. Moreover, the theorem's hypothesis 'lim_{k→∞} Λ(ητ,(k)_IREE) = 0' is itself a convergence assumption that is never established; it is exactly the kind of statement the proof should deliver. The footnote (Footnote 8) weakens the claim by saying the convergence 'still hold[s] in many practical scenarios,' but no sufficient conditions for practical convergence are provided. Therefore, the central claim of the paper, lim_{k,τ→∞} ηT_IREE = ηT,*_IREE, lacks a valid proof.
  4. [Appendix C, Theorem 1] The universal approximation result in Theorem 1 is a composition of known results: the RBF approximation property from Ref. [11] and the universal approximation of recurrent networks from Ref. [53], with an error bound that additionally depends on the unproven assumption that the FGO block can learn the autoregressive dynamics of the RBF parameters with bounded errors ε2, ε3 (Eq. 34). The paper does not provide a new approximation theorem, only a re-statement of existing results in a specific architecture. Since this theorem is presented as a contribution, the authors should either make precise the new element (e.g., the architectural constraint of FGO layers) or explicitly label the result as a corollary of prior work.
minor comments (6)
  1. [Abstract and Section I] The acronym IREE is used in the abstract before the metric is formally introduced in Section II-B. Please define the acronym and give a one-sentence description in the introduction to help readers not familiar with Ref. [24].
  2. [Section IV-C, Eq. (27) and Algorithm 1] The GRAF network is described as predicting traffic demands D(L,τ), but Eq. (27) defines CT(L,τ), the network capacity. The mechanism by which the network output is converted to a traffic prediction (Algorithm 1, line 3) is not specified. Please clarify the relationship between CT(L,τ) and D(L,τ) in the forward pass.
  3. [Section IV-B, Eq. (24)] The sentence 'in (24) we make some equivalent transformations on (21) to ensure the quadratic nature of κτ' is unclear. The quadratic nature of κτ in the penalty term is already apparent from the expression; please rephrase to explain why the particular form of the transformed constraint is chosen.
  4. [Table IV] In the row for Baseline 4, 'Aaveraged historical traffic' contains a typo; it should read 'Averaged historical traffic.'
  5. [Section V-A and Figure 5] The performance gap between MDDRA and Baseline 2 is attributed to 'prediction error of the GRAF network,' but no direct measurement of this prediction error in terms of IREE is provided. A quantitative decomposition of the gap (e.g., prediction error vs. queue tracking error) would strengthen the analysis.
  6. [Section IV-D, Footnote 8] The footnote 'Although the above convergence analysis relies on idealized traffic assumptions... the proposed MDDRA scheme can still converge in many practical scenarios as discussed in Section V' overstates the evidence: Section V shows numerical convergence for specific instances, which does not substitute for the missing theoretical guarantees. The authors should note that the practical convergence is empirical rather than proven.

Circularity Check

2 steps flagged · score 7.0 of 10

Theorem 2's convergence to optimal IREE assumes, rather than proves, the exact solvability of the queue-residual constraints (19)-(21), and imports the per-slot convergence from the authors' own [11, Theorem 3] under a hypothesis that restates the convergence itself; the empirical evaluation remains independent.

  1. fitted input called prediction [Problem 4 constraints (19)-(22); Appendix B (Proof of Lemma 1), Eqs. (30)-(31); Appendix D Part A.]
    "For the constraint (16), we can define a queue Qκ_τ = Σ_{t=0}^{τ−1}(ξ(t) − κt/T) and a correction factor νκ_τ ∈ [0, 2] such that ξ(τ) − κτ/T = −νκ_τ Qκ_τ. ... ∆Qκ_τ = [(1−νκ_τ)^2 − 1](Qκ_τ)^2 ≤ 0. Since (Qκ_τ)^2 ≥ 0, we have lim_{τ→∞}Qκ_τ = 0, which means that (16) is satisfied with large enough τ."

    The queue convergence that Lemma 1 and Theorem 2 depend on is obtained by postulating correction factors ν ∈ [0,2] that force the residual equalities (19)-(21) at every step; no existence proof is given (the needed ν = (κτ/T − ξ(τ))/Qκ_τ need not lie in [0,2] and is undefined when Qκ_τ = 0). The drift calculation only yields |Qκ_{τ+1}| = |1−νκ_τ||Qκ_τ| ≤ |Qκ_τ|; with ν = 0 the drift is zero but Q never converges, and with ν = 2 Q merely alternates, so ∆Q ≤ 0 does not imply Q → 0. Convergence holds only if the residual-forcing constraints are assumed exactly solvable, the very property the theorem must prove.

  2. self citation load bearing [Theorem 2 statement; Appendix D Part B (Proof of Theorem 2).]
    "If the loss function −Λ(ητ,(k)_IREE) satisfies the (L0,L1) smoothness and lim_{k→∞} Λ(ητ,(k)_IREE) = 0, then ηT_IREE converges to the optimal IREE value, i.e., lim_{k,τ→∞}ηT_IREE =ηT,∗_IREE . ... According to Theorem 3 in [11], if the loss function −Λ(ητ,(k)_IREE) satisfies the (L0,L1) smoothness and lim_{k→∞} Λ(ητ,(k)_IREE) = 0, ητ_IREE will converge to a stationary point ητ,∗_IREE at each time stamp τ."

    Reference [11] is the authors' own prior paper (T. Yu, ... S. Zhang, X. Chen, X. Wang, 'IREE Oriented Green 6G Networks,' JSAC 2024), so the per-slot convergence step is imported from a same-author source. The load-bearing hypothesis lim_{k→∞} Λ(ητ,(k)_IREE) = 0 stated in Theorem 2 is identical to the hypothesis of the imported [11, Theorem 3]; in the Dinkelbach-type iteration the vanishing of this value gap is the convergence-to-optimality condition itself, so the theorem's hypothesis already contains the result the proof must deliver. With the Appendix B bridge also unproven, Theorem 2's conclusion is an assumption plus a self-citation, not a derivation. The same [11] also supplies the RBF step of Theorem 1 (Eq.

full rationale

The argument chain for the central claim (Theorem 2: lim_{k,τ→∞} ηT_IREE = ηT,∗_IREE) is: Theorem 2 ← Lemma 1 ← Appendix B ← constraints (19)-(21), with Appendix D supplying the per-slot stationarity step. Each link is an assumed input rather than a derived property. Appendix B postulates νκ_τ ∈ [0,2] that force the queue residual to zero at every step (Eq. (30) is constraint (20) verbatim), and then concludes lim Qκ_τ = 0 from a drift inequality that only shows non-increase; ν = 0 or ν = 2 gives ∆Q ≤ 0 without convergence, so the conclusion requires exactly the feasibility that was assumed. Appendix D then asserts that the ADMM dual updates 'easily obtain' (19)-(21) from the stationarity conditions, which does not follow, and imports the per-slot convergence from the authors' own [11, Theorem 3] under the same hypothesis that Theorem 2 states (lim Λ = 0); since the vanishing of Λ is the convergence-to-optimality condition in disguise, the theoretical guarantee is an assumption and a self-citation restated, not a derivation. The authors' own response letter confirms this structure by attributing the convergence guarantee to 'Constraints (19-22),' the very equalities whose exact solvability is the open question. Theorem 1's universal-approximation bound is a lighter concern: it is a triangle-inequality assembly of [11]'s RBF result (self-cited) and [53]'s RNN universal approximation (external), repackaging known theorems rather than reducing circularly, and it is not the load-bearing step for convergence. The numerical evaluation is externally grounded (FEDformer, GCN, FourierGNN, and ADMM baselines, plus the OpenStreetMap real-map test) and is not circular. Because the paper's advertised advantage — guaranteed convergence to optimal IREE under incomplete traffic data — reduces at its proof-critical steps to the assumed feasibility of the correction-factor constraints and to a same-authors' theorem whose hypothesis contains the convergence, while the empirical content remains independent, the circularity is substantial but not total (score 7).

Assumptions & free parameters 4 free parameters · 6 assumptions · 1 invented entities

The central claims rest on the traffic model, the Lyapunov feasibility assumption, and imported approximation theorems. Several key assumptions are stated without proof, and the simulation parameters are not fully disclosed.

free parameters (4)
  • Empirical exponents μ1, μ2, θ1, θ2 = μ1=2.05, μ2=21.11, θ1=1, θ2=1
    These power-law exponents in the traffic convection-diffusion model (Eqs. 2-3) are set to literature values rather than derived; the numerical IREE results and design principles depend on them.
  • Sinusoid superposition parameters (amplitudes, frequencies, phases) = not specified in the paper
    Equation (5) models traffic as a sum of sinusoids with per-location amplitudes dM_i(L), frequencies φ_i(L), and phases φ0_i(L). These values are never given in the manuscript, so the synthetic traffic traces cannot be reproduced from the paper alone.
  • Normalized equilibrium speed Ve and anticipation time Ta = varied over [0,1] ranges
    The design principles recommending extra power for high speed limits and high visibility are derived from sweeps over Ve and Ta (Fig. 7). These are varied ad hoc and are not fitted to real data in the main text.
  • GRAF network hyperparameters = 3 FGO layers, 1 FC, 1 RBF layer, 10000 epochs
    The network architecture in Table I is chosen by hand; no sensitivity analysis is provided, so the reported ANRMSE gains are tied to these specific settings.
assumptions (6)
  • domain assumption Traffic demand D(L,τ) is ergodic over time.
    Assumed in Section II-B and used in Footnote 8 to justify convergence; if traffic is non-stationary, the Lyapunov queue analysis does not hold.
  • domain assumption The convection-diffusion equation (1) describes the spatio-temporal evolution of user density in the evaluation area.
    Used in Section II-A to generate traffic; the authors acknowledge in Footnote 8 that this is a simplified model.
  • ad hoc to paper The inequality √(Cτ/C_tot)+√(Dτ/D_tot) ≤ 1 holds in Appendix A for the JS divergence convexity step.
    Step (a) in Appendix A relies on this bound to lower-bound IREE; no derivation is given and it is not obvious that it holds for arbitrary capacity and traffic distributions.
  • standard math The RBF network from [11] can approximate any continuous traffic function to error ε1.
    This is the universal approximation premise imported from the authors' prior work, used in the proof of Theorem 1 (Appendix C).
  • ad hoc to paper The FGO block can learn the autoregressive dynamics of the RBF network parameters with bounded error ε2, ε3.
    Theorem 1 assumes the Fourier Graph Operator predicts the next bandwidth/power allocation from history; this is asserted but not proven as an approximation bound for the specific FGO architecture.
  • ad hoc to paper A non-positive Lyapunov drift of the virtual queues implies the queues converge to zero.
    Appendix B uses this implication to prove Lemma 1; it is mathematically invalid without further conditions (a non-increasing nonnegative sequence need not tend to zero).
invented entities (1)
  • GRAF network
    purpose: A graph neural network combining Fourier Graph Operator layers and a Radial Basis Function layer to predict traffic and output resource allocations from incomplete traffic data.
    The network is an architectural invention of this paper; no external benchmark or theoretical result outside the paper establishes its effectiveness beyond the simulations shown here.

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Cite this review

Pith. "Pith review of A Model-Data Dual-Driven Resource Allocation Scheme for IREE Oriented 6G Networks." pith.science (2026). https://pith.science/paper/WLKZUYWV

@misc{pith2026250603508,
  author       = {Pith},
  title        = {Pith review of: A Model-Data Dual-Driven Resource Allocation Scheme for IREE Oriented 6G Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WLKZUYWV}},
  note         = {Machine review of arXiv:2506.03508}
}
read the original abstract

The rapid and substantial fluctuations in wireless network capacity and traffic demand, driven by the emergence of 6G technologies, have exacerbated the issue of traffic-capacity mismatch, raising concerns about wireless network energy consumption. To address this challenge, we propose a model-data dual-driven resource allocation (MDDRA) algorithm aimed at maximizing the integrated relative energy efficiency (IREE) metric under dynamic traffic conditions. Unlike conventional model-driven or data-driven schemes, the proposed MDDRA framework employs a model-driven Lyapunov queue to accumulate long-term historical mismatch information and a data-driven Graph Radial bAsis Fourier (GRAF) network to predict the traffic variations under incomplete data, and hence eliminates the reliance on high-precision models and complete spatial-temporal traffic data. We establish the universal approximation property of the proposed GRAF network and provide convergence and complexity analysis for the MDDRA algorithm. Numerical experiments validate the performance gains achieved through the data-driven and model-driven components. By analyzing IREE and EE curves under diverse traffic conditions, we recommend that network operators shall spend more efforts to balance the traffic demand and the network capacity distribution to ensure the network performance, particularly in scenarios with large speed limits and higher driving visibility.

Figures

Figures reproduced from arXiv: 2506.03508 by the authors.

Figure 1
Figure 1. An illustrative example of wireless networks and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Overview of the proposed MDDRA scheme. The orange boxes represent the data-driven component, i.e. the architecture [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Convergence and IREE performance comparison [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: An illustration of the simulation scenario, which encompasses an area [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: The long-term IREE performance using different [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The ξ τ and Qκ τ dynamics. The virtual queue Qκ τ can effectively capture the changes in ξ τ caused by the dynamic nature of traffic. data. These two comparisons highlight the benefits of inte￾grating model-driven and data-driven methods in the proposed scheme. Given t…
Figure 7
Figure 7. Figure 7: Numerical results for the network capacity, JS divergence, EE and IREE versus normalized equilibrium speed and [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: IREE versus Nτ U /M under different data-driven com￾ponents [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: The long-term IREE using proposed MDDRA scheme [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 1
Figure 1. Figure 1: Validation of sinusoidal traffic model against the actual measured tr [PITH_FULL_IMAGE:figures/full_fig_p021_1.png]
Figure 2
Figure 2. Figure 2: Visualizing OpenStreetMap (OSM) [19] with real-world measur [PITH_FULL_IMAGE:figures/full_fig_p023_2.png]
Figure 3
Figure 3. Figure 3: Convergence and IREE performance comparison among different trai [PITH_FULL_IMAGE:figures/full_fig_p024_3.png]
Figure 4
Figure 4. Figure 4: The long-term IREE performance using different schemes. T [PITH_FULL_IMAGE:figures/full_fig_p025_4.png]
Figure 5
Figure 5. Figure 5: The ξ τ and Qκ τ dynamics. The virtual queue Qκ τ can effectively capture the changes in ξ τ caused by the dynamic nature of traffic. Through the proposed IREE maximization scheme, we can allocate the network resources more energy-efficiently to meet the traffic requir…
Figure 6
Figure 6. Figure 6: Numerical results for the network capacity, JS divergence, E [PITH_FULL_IMAGE:figures/full_fig_p027_6.png]
Figure 7
Figure 7. Figure 7: The long-term IREE using proposed MDDRA scheme under the t [PITH_FULL_IMAGE:figures/full_fig_p028_7.png]
Figure 8
Figure 8. Figure 8: Comparison among EE, AEE and IREE given in [14]. (a) EE is a smooth sur [PITH_FULL_IMAGE:figures/full_fig_p029_8.png]
Figure 9
Figure 9. Figure 9: IREE versus Nτ U /M under different data-driven components. and provide more practical suggestions to reduce the computational burden or communication overhead. (a) Synergy between Model-Driven and Data-Driven Components. As surveyed and discussed in Q1, the proposed M…
Figure 10
Figure 10. Figure 10: Overview of the proposed MDDRA scheme. The orange boxes repr [PITH_FULL_IMAGE:figures/full_fig_p034_10.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.