Parameter settings and implementation details<\/p>\n
This subsection describes the hyperparameter configuration used in the experimental evaluation of the proposed SLIRA framework, along with the rationale behind their selection. Careful tuning of these parameters is essential to balance utility maximization, explainability, fairness, and computational efficiency in PSN environments. The learning rate \\(\\alpha\\) controlling the allocation update dynamics was set to \\(\\alpha =0.05\\). This value was selected to ensure stable convergence without oscillatory behavior in dynamic emergency scenarios. Smaller values led to slow adaptation, while larger values resulted in unstable allocation updates under bursty traffic conditions. The trade-off parameter \\(\\lambda\\), which balances allocation utility and explanation fidelity in the hybrid loss function, was chosen from the range \\(\\lambda \\in [\\text{0.1,1.0}]\\). Empirical tuning showed that \\(\\lambda =0.5\\) provides an effective compromise between performance and interpretability, preventing either objective from dominating the optimization process. The SHAP\u2013LIME fusion weight \\(\\gamma \\in [\\text{0,1}]\\) controls the relative contribution of global (SHAP) and local (LIME) explanations. Based on sensitivity analysis, \\(\\gamma =0.6\\) was selected, favoring global fairness awareness while retaining sufficient local adaptability for instance-specific allocation decisions.<\/p>\n
Fairness enforcement is governed by the tolerance threshold \\(\\delta\\), which limits disparities in allocation or explanation contributions between protected groups. In the experiments, \\(\\delta =0.05\\) was used, reflecting a strict but feasible fairness constraint consistent with public safety equity requirements. For SHAP computation, Monte Carlo sampling with \\(K=100\\) coalitions were employed, offering a favorable balance between explanation accuracy and runtime. LIME explanations were generated using \\(P=500\\) perturbations per instance, which provided stable local explanations without excessive computational overhead. Bayesian uncertainty estimation was implemented using variational inference with a diagonal Gaussian approximation. The optimization was run for 200 iterations per update cycle, which was sufficient to achieve convergence of posterior mean and variance estimates across all experiments. All solver-based experiments were conducted on an Intel Core i7 (3.2 GHz) workstation with 32 GB RAM running Ubuntu 22.04 LTS. The same network state trajectories and random seeds were used across solver-based and learning-based methods to guarantee controlled benchmarking conditions. The use of a high-precision convex solver ensures that the reported solver baseline reflects true near-optimal performance under the defined formulation.<\/p>\n
SLIRA: a SHAP-LIME hybrid framework for explainable and fair resource allocation<\/p>\n
SLIRA integrates SHAP (global explainability) and LIME (local interpretability) to create a hybrid model that enhances transparency, fairness, and adaptability in resource allocation. By optimizing both explanation fidelity and fairness constraints, SLIRA ensures that allocation decisions are justifiable and interpretable across different stakeholders. The framework refines LIME\u2019s proximity kernel to align perturbations with SHAP\u2019s global importance, enabling a more accurate assessment of feature contributions. Furthermore, SLIRA updates allocations using a SHAP-LIME hybrid gradient, balancing global fairness and local fidelity while minimizing overall loss functions. To maintain fairness and stability, SLIRA enforces demographic parties across protected groups by integrating SHAP-LIME contributions into allocation rules. The framework also employs Bayesian inference to quantify uncertainty, ensuring that decision-makers can assess confidence levels in allocation explanations. Additionally, sparsity constraints are introduced to limit the number of active features, making explanations more concise and interpretable. By tracking temporal consistency, SLIRA ensures that explanation quality remains stable over time, detecting and mitigating irregularities or adversarial behavior. SLIRA bridges the gap between local and global explainability, making it ideal for critical applications like public safety networks where transparency and adaptability are paramount. SLIRA jointly optimizes global fairness (SHAP) and local fidelity (LIME) using a hybrid loss function:<\/p>\n
$$g^{*} \\left( {x_{i} } \\right) = \\arg \\mathop {\\min }\\limits_{{g \\in {\\mathcal{G}}}} \\underbrace {{{\\mathcal{L}}\\left( {f,g,\\pi_{{x_{i} }} } \\right)}}_{{\\text{LIME loss}}} + {\\uplambda }_{1} \\underbrace {{{\\Omega }\\left( g \\right)}}_{{{\\text{Sparsity}}}} + {\\uplambda }_{2} \\underbrace {{\\mathop \\sum \\limits_{j} \\left( {\\phi_{ij}^{{{\\text{SHAP}}}} – \\phi_{ij}^{{{\\text{SLIRA}}}} } \\right)^{2} }}_{{\\text{SHAP consistency}}},$$<\/p>\n
\n (41)\n <\/p>\n
where: \\({\\upphi }_{ij}^{SHAP}\\): SHAP values from cooperative game theory. \\({\\upphi }_{ij}^{SLIRA}\\): SLIRA\u2019s explanation coefficients. \\({\\uplambda }_{1},{\\uplambda }_{2}\\): Regularization weights balancing sparsity and SHAP alignment.<\/p>\n
Modify LIME\u2019s proximity kernel \\({\\uppi }_{{x}_{i}}\\) to prioritize perturbations aligned with SHAP\u2019s global importance:<\/p>\n
$${\\uppi }_{{x_{i} }} \\left( z \\right) = \\exp \\left( { – \\frac{{D\\left( {x_{i} ,z} \\right)^{2} }}{{{\\upsigma }^{2} }}} \\right) \\cdot \\mathop \\sum \\limits_{j = 1}^{m} \\phi_{j}^{{{\\text{SHAP}}}} \\cdot \\left| {z_{j} – x_{ij} } \\right|,$$<\/p>\n
\n (42)\n <\/p>\n
where \\(D\\left({x}_{i},z\\right)\\) is the Euclidean distance and \\({\\upphi }_{j}^{SHAP}\\) scales weights by global feature importance. Update allocations using a SHAP-LIME hybrid gradient:<\/p>\n
$$A_{ij} \\left( {t + 1} \\right) = A_{ij} \\left( t \\right) + \\alpha \\left[ {\\gamma \\phi_{ij}^{{{\\text{SHAP}}}} \\left( t \\right) + \\left( {1 – \\gamma } \\right)\\phi_{ij}^{{{\\text{SLIRA}}}} \\left( t \\right)} \\right] – \\lambda \\frac{{\\partial {\\mathcal{L}}_{fi} }}{{\\partial A_{ij} }},$$<\/p>\n
\n (43)\n <\/p>\n
where: \\(\\upgamma \\in \\left[\\text{0,1}\\right]\\): Balances global vs. local explanations. \\({\\mathcal{L}}_{fi}\\): Fairness loss.<\/p>\n
Enforce fairness across protected groups \\({G}_{1},{G}_{2}\\) using combined SHAP-LIME contributions:<\/p>\n
$$\\left| {\\frac{1}{{\\left| {G_{1} } \\right|}}\\mathop \\sum \\limits_{{i \\in G_{1} }} \\left( {\\gamma \\phi_{ij}^{SHAP} + \\left( {1 – \\gamma } \\right)\\phi_{ij}^{SLIRA} } \\right) – \\frac{1}{{\\left| {G_{2} } \\right|}}\\mathop \\sum \\limits_{{i \\in G_{2} }} \\left( {\\gamma \\phi_{ij}^{SHAP} + \\left( {1 – \\gamma } \\right)\\phi_{ij}^{SLIRA} } \\right)} \\right| \\le \\delta$$<\/p>\n
\n (44)\n <\/p>\n
Model uncertainty via Bayesian fusion of SHAP and LIME:<\/p>\n
$$P\\left( {\\phi_{ij}^{{{\\text{SLIRA}}}} {\\text{|Data}}} \\right) = \\int {\\left[ {{\\upgamma }P\\left( {\\phi_{ij}^{{{\\text{SHAP}}}} {|}\\theta } \\right) + \\left( {1 – {\\upgamma }} \\right)P\\left( {\\phi_{ij}^{{{\\text{LIME}}}} {|}\\theta } \\right)} \\right]} \\;P\\left( {\\theta {\\text{|Data}}} \\right)d\\theta$$<\/p>\n
\n (45)\n <\/p>\n
Limit active features in explanations using:<\/p>\n
$${\\Omega }\\left( g \\right) = {\\uplambda }_{1} \\mathop \\sum \\limits_{j = 1}^{m} \\left| {\\phi_{ij}^{{{\\text{SLIRA}}}} } \\right| + {\\uplambda }_{2} \\mathop \\sum \\limits_{j = 1}^{m} \\left( {\\phi_{ij}^{{{\\text{SLIRA}}}} } \\right)^{2}$$<\/p>\n
\n (46)\n <\/p>\n
Track stability over time \\(t\\):<\/p>\n
$${\\text{Consistency}} = 1 – \\frac{1}{T}\\mathop \\sum \\limits_{t = 1}^{T} |{\\upgamma }\\phi_{ij}^{{{\\text{SHAP}}}} \\left( t \\right) + \\left( {1 – {\\upgamma }} \\right)\\phi_{ij}^{{{\\text{SLIRA}}}} \\left( t \\right) – \\phi_{ij}^{{{\\text{SLIRA}}}} \\left( {t – 1} \\right)|_{2}$$<\/p>\n
\n (47)\n <\/p>\n
Generate minimal changes \\(\\Delta {x}_{i}\\) to alter allocations, guided by both SHAP and LIME:<\/p>\n
$$\\Delta {x}_{i}^{*}=\\text{arg}\\underset{\\Delta {x}_{i}}{\\text{min}}|\\Delta {x}_{i}{|}_{1}+\\uplambda \\left|f\\left({x}_{i}+\\Delta {x}_{i}\\right)-f\\left({x}_{i}\\right)\\right|\\hspace{1em}s.t.\\hspace{1em}{\\upphi }_{ij}^{SLIRA}\\left({x}_{i}+\\Delta {x}_{i}\\right)\\ne {\\upphi }_{ij}^{SLIRA}\\left({x}_{i}\\right)$$<\/p>\n
\n (48)\n <\/p>\n
SLIRA presents a robust, interpretable, and fairness-aware resource allocation framework by integrating global and local explainability techniques. Its ability to optimize transparency, fairness, and adaptability makes it particularly suited for high-stakes environments like public safety networks. The framework\u2019s key advantages include enhanced interpretability, reduced bias in allocations, improved stability over time, and the ability to quantify uncertainty. By combining the strengths of SHAP and LIME, SLIRA sets a new standard for fair, explainable, and accountable AI-driven decision-making.<\/p>\n
The predictive model is designed to approximate the mapping from the network state to urgency-weighted allocation scores, rather than to directly output final allocations. This separation allows the system to replace repeated solver invocations with a single forward inference step, significantly reducing computational latency. Unlike solver-based approaches, the learning model can operate under partial observability and noisy measurements and can generalize from historical patterns to unseen operating conditions. Consequently, the predictive component provides a practical mechanism for real-time allocation guidance in PSNs, while the final allocation remains subject to explicit feasibility and fairness constraints. Algorithm 1 provides the complete operational specification of the SLIRA pipeline, detailing how predictive modeling, explainability, fairness regulation, and uncertainty quantification interact to produce interpretable resource allocation decisions. Starting from the observed network state \\(x\\left(t\\right)\\), the algorithm generates urgency-weighted allocation scores, computes global SHAP values and local LIME explanations, and fuses them into a unified attribution signal that directly regulates the allocation update rule. The updated allocation is then projected onto the feasible constraint set and supplemented with Bayesian uncertainty estimates to ensure confidence-aware operation. Together, these steps define a coherent, explanation-driven allocation mechanism tailored for dynamic and safety\u2013critical PSN environments.<\/p>\n
Algorithm 1![\"Algorithm](\"https:\/\/www.europesays.com\/ai\/wp-content\/uploads\/2026\/06\/41598_2026_43440_Figa_HTML.png\")
The alternative text for this image may have been generated using AI.<\/p>\n
SLIRA (SHAP\u2013LIME Integrated Resource Allocation) Pipeline<\/p>\n
The definition of \\(x\\left(t\\right)\\), \\({f}_{\\theta }\\left(x\\left(t\\right)\\right)\\), and the update rule leading to \\(A\\left(t\\right)\\) establishes the complete SLIRA pipeline. Unlike traditional solver-based or heuristic policies, SLIRA integrates prediction, explainability, fairness regulation, and constraint projection into a unified iterative mechanism. This explicit formulation ensures that the experimental results directly correspond to the defined model behavior and eliminates ambiguity regarding the origin of the final allocation decisions.<\/p>\n
Evaluation metrics<\/p>\n
To explicitly address whether learning-based allocation is necessary given the availability of efficient solvers, we benchmark the proposed SLIRA framework against direct solver-based optimization under identical conditions. While the solver achieves optimal utility in static scenarios, its performance degrades under dynamic and uncertain conditions due to repeated re-optimization overhead and sensitivity to imperfect state information. SLIRA maintains comparable utility with significantly lower runtime, while additionally providing fair consistency, explainability, and uncertainty awareness. These results demonstrate that the value of the proposed approach lies not in exceeding solver optimality, but in delivering deployable, transparent, and risk-aware allocation decisions in real-time PSN environments.<\/p>\n
SLIRA is benchmarked against (i) a direct solver-based optimizer (ii) a black-box AI baseline that predicts allocation scores followed by feasibility projection, and (iii) explainability ablations such as SHAP-only and LIME-only post-hoc explanations. Performance is evaluated using utility\/QoS, fairness gaps, explanation fidelity and stability, uncertainty calibration, and runtime. Results are reported as mean\u2009\u00b1\u2009standard deviation with 95% confidence intervals across multiple seeds, and relative (%) improvements are computed to quantify performance gains. The benchmark comparison includes solver-based methods, baseline AI approaches, explainable AI variants, and the proposed SLIRA framework, all evaluated under identical Public Safety Network scenarios.<\/p>\n
Table 2<\/a> presents a comprehensive comparison of classical optimization-based methods, heuristic and learning-based approaches, post-hoc explainable AI models, and the proposed SLIRA framework for resource allocation in Public Safety Networks. The evaluated methods differ in their allocation mechanisms, ranging from direct convex optimization solvers and priority-based heuristics to learned AI models with and without explainability and uncertainty awareness. The results demonstrate that direct solver-based approaches achieve optimal utility under static conditions but incur higher computational costs and provide no interpretability. Greedy heuristics offer minimal runtime overhead at the expense of substantially reduced utility and fairness. Black-box AI models closely match solver performance with significantly lower runtime but lack transparency and fairness guarantees. Incorporating post-hoc explainability (SHAP or LIME) improves interpretability reporting without materially affecting allocation behavior or fairness. In contrast, the proposed SLIRA framework achieves a strong balance between performance, fairness, explainability, and stability. While maintaining utility within 2% of the optimal solver, SLIRA reduces the fairness gap by more than 40% relative to solver-based methods and exhibits superior temporal stability. The full SLIRA model further provides uncertainty awareness through Bayesian inference, enabling confidence-calibrated decisions with modest additional computational overhead that remains suitable for real-time deployment.<\/p>\n Table 2 Comparative benchmarking of resource allocation strategies in public safety networks<\/p>\n The comparison highlights a crucial distinction: while the solver baseline provides mathematically optimal allocations in static, perfectly known environments, it cannot adapt rapidly to dynamic PSN states without incurring repeated computational overhead. The black-box AI model provides lower-latency inference but lacks transparency and introduces higher fairness variability. SLIRA maintains near-optimal utility while delivering significantly improved fairness consistency and much higher temporal stability. Furthermore, SLIRA uniquely provides interpretable, feature-attributed decisions and uncertainty quantification, which are essential for operational accountability in PSNs. Thus, the added value of SLIRA is not in outperforming solvers in static utility, but in enabling deployable, accountable, and robust allocation decisions in dynamic and uncertain settings.<\/p>\n In addition to absolute performance values, we compute relative improvements (%) for each method with respect to the direct solver baseline. This reporting strategy provides a clearer assessment of trade-offs introduced by explainability and uncertainty modeling. For example, we quantify the percentage reduction in fairness disparity, the percentage gain in temporal stability, and the relative change in utility, which is typically below 2% for SLIRA. Percentage-based metrics make explicit the benefits of explanation-regulated updates and highlight cases where SLIRA provides substantial stability and fairness gains despite small differences in raw utility.<\/p>\n The results in Tables 2<\/a> and 3<\/a> show that SLIRA delivers a strong balance between performance and interpretability. While the direct solver achieves the highest utility under static conditions, SLIRA remains within 1\u20132% of this value while achieving substantially improved fairness (over 40% reduction in fairness gap) and significantly enhanced temporal stability (over 30% gain). Furthermore, SLIRA demonstrates markedly higher explainability and fidelity due to the fusion of global and local attributes. The consistency of these gains across multiple runs, as reflected by narrow confidence intervals, confirms that SLIRA improves transparency and stakeholder interpretability without compromising allocation performance. These findings directly substantiate the claims made in the introduction and validate the effectiveness of explanation-regulated decision-making.<\/p>\n Table 3 Relative performance gains of explainable and SLIRA-based allocation methods compared to the solver baseline<\/p>\n Table 3<\/a> summarizes the relative (percentage-based) performance changes of learning-based and explainable allocation strategies with respect to the direct solver baseline, providing a clearer interpretation of trade-offs between efficiency, fairness, stability, and explainability. Negative values in Utility Change (%) indicate minor reductions relative to solver optimality, while positive values in Fairness Gap Reduction and Temporal Stability Gain reflect improvements over the baseline. The results show that black-box AI and post-hoc explainable AI methods (SHAP and LIME) achieve utility levels close to the solver, with only marginal performance degradation (\u2264\u20091.6%), but offer limited improvements in fairness and temporal stability. In contrast, the proposed SLIRA framework demonstrates a substantially different behavior: although it incurs a slightly larger utility deviation (\u2212\u20091.9%), it achieves a dramatic reduction in fairness disparity (\u2212\u200940.2%) and a significant improvement in temporal stability (+\u200931.5%). Moreover, SLIRA uniquely provides regulatory grade explainability, where explanations actively govern allocation decisions rather than serving as post-hoc diagnostics.<\/p>\n I.<\/p>\n Standardized Evaluation Metrics: To ensure a rigorous and reproducible experimental validation, we adopt a set of standardized and well-defined evaluation metrics that jointly capture allocation performance, fairness, stability, explainability, and computational efficiency. Allocation performance is quantified using normalized system utility, defined as the aggregate weighted satisfaction of user demands relative to the maximum achievable value under capacity constraints. Fairness is evaluated through the inter-group allocation gap, measured as the absolute difference in mean resource allocation between protected user groups, which directly reflects distributional equity. Temporal stability is assessed by computing the consistency of allocation and explanation patterns across consecutive time steps, capturing the robustness of decisions under dynamic network conditions. Explainability quality is evaluated through explanation fidelity and sparsity metrics, which measure how accurately surrogate explanations approximate the predictive model while remaining interpretable. Finally, computational efficiency is reported as the average per-step runtime, enabling a direct comparison between solver-based, learning-based, and explainability-regulated approaches. All metrics are formally defined prior to result presentation to avoid ambiguity and to facilitate reproducibility.<\/p>\n II.<\/p>\n Relative and Percentage-Based Performance Improvements: Beyond reporting absolute metric values, we emphasize relative and percentage-based improvements to provide a clearer interpretation of the trade-offs introduced by explainability and uncertainty modeling. For each metric, the performance of learning-based and explainable approaches is normalized with respect to the direct solver baseline, which serves as a reference upper bound for static optimality. Relative changes are expressed as percentage gains or losses, allowing direct comparison across heterogeneous metrics such as utility, fairness gap, and stability. This reporting strategy highlights that while black-box and explainable AI approaches incur only marginal utility degradation (typically below 2%), the proposed SLIRA framework achieves substantial relative improvements in fairness and temporal stability, far exceeding those of post-hoc explainable baselines.<\/p>\n III.<\/p>\n Uncertainty and Variability Analysis: To account for stochasticity in traffic demand, channel conditions, and learning processes, all experiments are conducted over multiple independent simulation runs with different random seeds. Reported results correspond to the mean and standard deviation of each metric, and confidence intervals are provided where appropriate. This variability analysis ensures that observed improvements are statistically meaningful rather than artifacts of a single realization. In addition, SLIRA uniquely incorporates Bayesian uncertainty modeling, enabling explicit quantification of confidence in both allocation decisions and explanation coefficients. The posterior variance of allocations is analyzed alongside performance metrics, revealing that higher uncertainty correlates with volatile network states and congestion events. This uncertainty-aware evaluation provides an additional layer of robustness assessment that is absent in solver-based and black-box AI methods, which produce deterministic outputs without confidence estimates.<\/p>\n IV.<\/p>\n Interpretation and Experimental Credibility: The combination of standardized metrics, relative performance reporting, and uncertainty analysis substantially strengthens the credibility of the experimental validation. Rather than relying on isolated performance snapshots, the evaluation demonstrates consistent trends across multiple runs and diverse scenarios. Importantly, the results show that SLIRA preserves near-optimal allocation efficiency while delivering statistically significant improvements in fairness consistency and temporal stability, supported by reduced variability and calibrated uncertainty estimates. These findings directly substantiate the claim that explainability in SLIRA is not merely descriptive but operational, enabling more robust and accountable decision-making in dynamic public safety network environments.<\/p>\n To provide a standardized and reproducible basis for comparison, we evaluate all approaches using a set of well-defined metrics that capture allocation performance, fairness, interpretability, and stability. (1) Utility: the normalized system utility, defined as the weighted sum of satisfied user demands relative to the solver-optimal benchmark. (2) Fairness gap: the absolute difference in average allocation between protected user groups. (3) Temporal stability: the average correlation between consecutive allocation matrices, measuring robustness under dynamic conditions. (4) Explainability fidelity: the agreement between the predictive model and its local surrogate explanations (LIME) and the consistency of global attributions (SHAP). (5) Runtime: the average per-step computational latency. These metrics allow us to quantify the contribution of explainability and uncertainty modeling beyond raw allocation quality.<\/p>\n Computational complexity and runtime analysis<\/p>\n This section provides a rigorous computational analysis of the proposed SLIRA framework in comparison with solver-based re-optimization methods. Specifically, we present (i) a formal asymptotic complexity derivation that characterizes the theoretical scaling behavior of both approaches, (ii) an empirical runtime decomposition that isolates the computational contribution of each component within the SLIRA pipeline, and (iii) a log-scale scaling visualization that illustrates divergence in growth rates as the problem dimension increases. The primary objective of this analysis is to clarify the structural reason why SLIRA achieves lower per-step latency, even though it incorporates Bayesian uncertainty estimation and Monte Carlo\u2013based explainability techniques (SHAP and LIME), which may initially appear computationally intensive. While these components introduce additional processing steps, their computational cost scales linearly with feature dimension and remain bounded due to fixed sampling sizes. In contrast, solver-based approaches require repeated convex re-optimization at each decision epoch, incurring cubic complexity in the number of allocation variables.<\/p>\n Theoretical asymptotic complexity analysis<\/p>\n Let \\(U\\) denote the number of users, \\(R\\) denote the number of resources, and \\(F\\) denote the feature dimension. The total number of allocation decision variables is defined as \\(N=UR\\). The direct solver baseline computes allocations by solving the constrained utility maximization problem defined in Eqs.\u00a0(22<\/a>)\u2013(23<\/a>). Interior-point methods for convex optimization exhibit worst-case computational complexity \\(O({N}^{3})=O((UR{)}^{3})\\), primarily due to repeated matrix factorization and Newton-step updates required during each iteration. In dynamic Public Safety Network (PSN) environments where re-optimization is performed at every time step \\(T\\), the total computational complexity becomes \\(O(T(UR{)}^{3})\\). This cubic dependence on the decision variable dimension leads to rapidly increasing runtime as the system scale grows.<\/p>\n In contrast, SLIRA decomposes the allocation procedure into structured and computationally lighter stages. The predictive forward inference step has complexity \\(O(UR)\\). SHAP-based Monte Carlo sampling, with fixed \\(K=100\\), incurs complexity \\(O(KF)\\), while LIME local surrogate fitting, with fixed \\(P=500\\), contributes \\(O(PF)\\). Variational Bayesian uncertainty estimation scales as \\(O(\\mid \\theta \\mid )\\), where \\(\\mid \\theta \\mid\\) denotes the number of model parameters. Finally, the explanation-driven allocation update and projection step has complexity \\(O(UR)\\). Because \\(K\\) and \\(P\\) are fixed constants independent of system size, the dominant scaling term becomes \\(O(UR)\\). Consequently, under dynamic operation across \\(T\\) time steps, the total computational complexity of SLIRA is \\(O(TUR)\\), which grows linearly with the number of allocation variables.<\/p>\n Formally, the asymptotic comparison satisfies \\({\\text{lim}}_{N\\to \\infty }\\frac{O(N)}{O({N}^{3})}=0\\), demonstrating that SLIRA grows asymptotically slower than solver-based re-optimization as system dimension increases.<\/p>\n Importantly, Bayesian inference and Monte Carlo sampling in SLIRA operate on feature attribution and learned score surfaces rather than on combinatorial allocation search. Therefore, their computational cost scales linearly with feature dimension and remains independent of the cubic growth associated with convex re-optimization over allocation variables. This structural distinction explains why SLIRA achieves lower per-step latency despite incorporating uncertainty modeling and explainability mechanisms. Figure\u00a03<\/a> presents a log\u2013log scaling comparison between solver-based convex optimization \\(O({N}^{3})\\) and the SLIRA framework \\(O(N)\\). The horizontal axis represents the number of decision variables \\(N=UR\\), while the vertical axis shows normalized computational cost on a logarithmic scale. On the log\u2013log plot, the solver-based optimization curve exhibits an approximate slope of 3, confirming its cubic scaling behavior \\(O({N}^{3})\\), while the SLIRA curve exhibits an approximate slope of 1, confirming its linear scaling \\(O(N)\\). As the number of decision variables \\(N\\) increases, the divergence between the two curves becomes increasingly pronounced, illustrating how solver-based approaches experience rapid runtime escalation under large-scale Public Safety Network configurations. In contrast, SLIRA maintains controlled and predictable growth due to its linear dependence on system dimension. This visualization clearly demonstrates that the observed runtime advantage of SLIRA arises from fundamental structural differences in computational complexity rather than from minor constant-factor optimizations.<\/p>\n Fig. 3 Asymptotic Computational Complexity Scaling of Solver-Based Optimization versus SLIRA<\/p>\n Per-step runtime decomposition<\/p>\n To complement the asymptotic analysis and provide practical insight into computational behavior, this subsection presents a detailed per-step runtime decomposition of the SLIRA framework. Rather than reporting only aggregate latency, the computational contribution of each operational component within the allocation pipeline is isolated and quantified, including predictive inference, SHAP computation, LIME surrogate fitting, Bayesian uncertainty estimation, and the explanation-driven projection step. To provide further transparency, we report a detailed per-step latency breakdown.<\/p>\n Table 4<\/a> provides a detailed decomposition of SLIRA\u2019s per-step runtime across its principal computational stages, including predictive inference, SHAP-based global attribution, LIME-based local surrogate fitting, Bayesian uncertainty estimation, and the explanation-driven projection step. This breakdown makes explicit how total latency is distributed within the framework and reveals that no single component disproportionately dominates the overall computational budget. Although SHAP and LIME introduce additional processing through Monte Carlo sampling and local perturbation modeling, their computational costs remain bounded because the sampling sizes (\\(K\\) and \\(P\\)) are fixed constants independent of system dimension. As a result, their contribution scales linearly with feature dimension rather than with the number of allocation variables. In contrast, the solver baseline performs full convex re-optimization at every decision epoch, requiring repeated matrix factorizations and Newton-step updates whose complexity grows cubically with the number of decision variables. This structural requirement leads to substantially higher per-step latency, particularly as system size increases. The runtime decomposition therefore demonstrates that Bayesian inference and Monte Carlo-based explainability mechanisms introduce only modest linear overhead within SLIRA and do not constitute the dominant source of computational cost.<\/p>\n Table 4 Per-step latency breakdown (U\u2009=\u200950, R\u2009=\u200920).Empirical scaling behavior<\/p>\n To validate the theoretical complexity analysis, runtime growth was measured across progressively increasing system dimensions. The results indicate that solver-based runtime exhibits super linear growth once the number of users exceeds approximately \\(U>40\\), reflecting the cubic dependence on allocation variables. In contrast, SLIRA\u2019s runtime increases approximately linearly with system size, consistent with the derived asymptotic behavior. Even under large-scale configurations, SLIRA maintains stable per-step latency below 15\u00a0ms, demonstrating predictable and controlled scaling. These empirical observations confirm that the observed speed advantage is not incidental or implementation-specific but structurally grounded in the computational architecture of the framework. The primary reason SLIRA achieves lower runtime lies in replacing repeated convex re-optimization with a computational pipeline composed of a single forward inference step, fixed cost explainability mechanisms, and linear projection operations. Solver-based approaches repeatedly perform matrix inversion and Newton-step updates whose computational burden scales cubically with the number of allocation variables. By contrast, SLIRA operates on a learned urgency-weighted score surface and applies explanation-regulated updates without solving a full optimization problem at each time step. Consequently, the runtime benefit emerges from architectural design and complexity order differences rather than from omission of Bayesian or Monte Carlo components.<\/p>\n Simulation scenario and PSN modeling assumptions<\/p>\n To evaluate the effectiveness, interpretability, and fairness of the proposed SLIRA framework, a realistic yet controllable PSN simulation environment was constructed. The simulation is designed to emulate operational conditions commonly encountered in emergency response scenarios, such as natural disasters, large public events, and multi-agency crisis coordination, where communication resources are limited and demand fluctuates rapidly.<\/p>\n The simulated PSN consists of a centralized radio access network serving a set of emergency users \\(\\mathcal{U}=\\{{u}_{1},{u}_{2},\\dots ,{u}_{N}\\}\\), where \\(N\\in \\{\\text{20,30,50}\\}\\) depending on the experiment. The available communication resources \\(\\mathcal{R}=\\{{r}_{1},{r}_{2},\\dots ,{r}_{M}\\}\\) represent shared bandwidth blocks, with \\(M=5\\). Each resource \\({r}_{j}\\) is associated with a finite capacity \\({C}_{j}\\), reflecting spectrum and infrastructure limitations typical of PSNs during congestion.<\/p>\n Users are divided into heterogeneous emergency classes, including police, fire services, medical responders, and command units. Each user \\({u}_{i}\\) is characterized by:<\/p>\n I.<\/p>\n A time-varying demand \\({d}_{i}(t)\\), representing required data rate or communication load,<\/p>\n II.<\/p>\n A priority level \\({p}_{i}\\), reflecting mission criticality and role hierarchy,<\/p>\n III.<\/p>\n A protected group attribute (used only for fairness evaluation, not decision input).<\/p>\n Priority levels are normalized to ensure comparability across agencies and are dynamically updated in response to emergency escalation or de-escalation phases.<\/p>\n Emergency traffic is modeled using stochastic burst processes to capture sudden surges in communication demand, such as those observed during disaster onset or major incidents. Specifically, user demands follow a mixed distribution combining baseline Poisson arrivals with bursty spikes governed by a heavy-tailed process. This modeling choice reflects the unpredictable and highly dynamic nature of PSN traffic.<\/p>\n Time is discretized into allocation intervals \\(t=1,\\dots ,T\\), where SLIRA updates allocations iteratively based on both predicted utility and explanation-guided feedback. This enables the framework to adapt to evolving network conditions while maintaining interpretability and fairness constraints.<\/p>\n All experiments are conducted using synthetic data generated under the above assumptions. While real PSN datasets are typically unavailable due to confidentiality and security restrictions, the simulation parameters are chosen to closely align with values reported in public safety communication standards and prior literature. The use of synthetic data allows systematic control over network scale, demand variability, and fairness stress-testing while ensuring reproducibility.<\/p>\n The AI-based prediction model estimates demand urgency and allocation utility from observable network state features, including current load, historical demand trends, and priority indicators. SHAP and LIME explanations are then computed on top of these predictions to regulate allocation updates, enforce fairness, and provide human-interpretable justifications.<\/p>\n The chosen simulation framework balances realism and analytical clarity. It is sufficiently rich to reflect real PSN challenges such as congestion, priority conflicts, and emergency dynamics\u2014while remaining interpretable and computationally tractable for explainable AI analysis. This design allows a focused evaluation of SLIRA\u2019s core contributions: transparent decision-making, fairness-aware resource allocation, and uncertainty-informed adaptation under high-stakes conditions.<\/p>\n Computational complexity analysis<\/p>\n Computational efficiency is a critical requirement for resource allocation in PSNs, where decisions must be made under strict real-time constraints. This section analyzes the computational complexity of the proposed SLIRA framework and compares it with standalone SHAP- and LIME-based explainability approaches. SHAP computes feature attributions using cooperative game theory, which has an exponential worst-case complexity \\(\\mathcal{O}({2}^{n})\\) with respect to the number of features \\(n\\). Such complexity is impractical for large-scale or real-time PSN deployments. To address this, the proposed framework adopts Monte Carlo SHAP sampling, reducing the computational cost to \\(\\mathcal{O}(K\\cdot n)\\), where \\(K\\) is the number of sampled coalitions. This approximation preserves explanation fidelity while significantly reducing runtime. LIME, on the other hand, constructs local surrogate models by generating perturbed samples around each instance. Its complexity scales as \\(\\mathcal{O}(P\\cdot n)\\), where \\(P\\) is the number of perturbations. While LIME is computationally efficient for local explanations, it lacks global consistency and may require repeated evaluations for dynamic network states. SLIRA integrates SHAP and LIME in a unified framework while maintaining tractable computational complexity.<\/p>\n SLIRA amortizes the cost of global SHAP computations across multiple allocation intervals, avoiding redundant recalculations at every time step. As a result, the marginal per-iteration complexity of SLIRA approaches that of LIME while retaining global explainability. The allocation update step, including SHAP\u2013LIME gradient computation and fairness constraint enforcement, scales linearly with the number of users \\(U\\) and resources \\(R\\), yielding a complexity of \\(\\mathcal{O}(U\\cdot R)\\). Bayesian uncertainty estimation is performed using variational inference, which adds a modest overhead that scales linearly with the number of model parameters and does not dominate the overall runtime. Compared to standalone SHAP, SLIRA significantly reduces runtime while providing richer interpretability and fairness guarantees. Compared to LIME, SLIRA introduces a moderate additional cost due to global explanation alignment but achieves superior stability, fairness consistency, and uncertainty awareness. This trade-off is acceptable in PSN environments, where decision justification and reliability are as critical as raw computational speed.<\/p>\n Dataset and resource description<\/p>\n This study evaluates SLIRA framework using a synthetic, yet realistic dataset designed to emulate operational conditions in Public Safety Networks (PSNs). Due to security, confidentiality, and availability constraints associated with real PSN data, synthetic data are commonly adopted in the literature to enable controlled experimentation while preserving realism. The dataset parameters and assumptions are chosen in accordance with typical public safety communication scenarios reported in prior studies. The simulated PSN consists of a set of emergency users \\(\\mathcal{U}=\\{{u}_{1},{u}_{2},\\dots ,{u}_{N}\\}\\), where \\(N\\in \\{\\text{20,30,50}\\}\\) depending on the experiment. Users represent heterogeneous public safety entities, including police units, fire services, medical responders, and command-and-control personnel. Each user is characterized by a time-varying traffic demand, a priority level reflecting mission criticality, and observable network state features used by the AI predictor. The available resources \\(\\mathcal{R}=\\{{r}_{1},{r}_{2},\\dots ,{r}_{M}\\}\\) correspond to shared communication resources such as bandwidth blocks, time\u2013frequency resource units, or logical network slices in LTE\/5G public safety systems. In the simulations, \\(M=5\\), and each resource \\({r}_{j}\\) has a finite capacity \\({C}_{j}\\), representing spectrum and infrastructure limitations under congested emergency conditions. Traffic demand is modeled as a stochastic process combining baseline communication activity with bursty emergency-driven surges. This captures realistic PSN behavior, where sudden incidents lead to sharp increases in data and voice traffic. Priority levels are normalized and dynamically adjusted to reflect changes in emergency severity, escalation, or resolution phases. These demand and priority signals are used as inputs to the AI-based prediction model, which estimates allocation urgency and utility. The dataset also includes protected group attributes used exclusively for fairness evaluation and monitoring. These attributes are not provided as inputs to the allocation model, ensuring that fairness constraints are enforced through explainability-driven regulation rather than direct discrimination. All experiments are conducted over multiple steps to evaluate dynamic adaptation, explanation stability, and uncertainty behavior.<\/p>\n Cost of SLIRA versus SHAP and LIME: time complexity and runtime considerations<\/p>\n In PSNs, computational efficiency is a critical design requirement, as resource allocation decisions must be generated under strict latency and reliability constraints. This subsection analyzes the computational cost of the proposed SLIRA framework and compares it with standalone SHAP- and LIME-based explainability methods, highlighting the trade-offs between runtime complexity and explainability performance.<\/p>\n Standalone SHAP computes feature attributions based on cooperative game theory, which exhibits exponential worst-case complexity \\(\\mathcal{O}({2}^{n})\\) with respect to the number of features \\(n\\). Such complexity is prohibitive for real-time PSN deployment. To mitigate this issue, SLIRA employs Monte Carlo sampling\u2013based SHAP approximations, reducing the computational cost to \\(\\mathcal{O}(K\\cdot n)\\), where \\(K\\) denotes the number of sampled coalitions. This approximation preserves global explanation fidelity while significantly reducing runtime. LIME, in contrast, generates local explanations by fitting surrogate models around individual instances using perturbed samples. Its complexity scales as \\(\\mathcal{O}(P\\cdot n)\\), where \\(P\\) is the number of perturbations. While LIME is computationally efficient for local interpretability, it lacks global consistency and often requires repeated recalculations in dynamic environments such as PSNs.<\/p>\n where global SHAP sampling and local LIME perturbations are executed in parallel. Importantly, SLIRA amortizes the cost of SHAP computations across multiple allocation intervals by reusing global explanations when network conditions evolve smoothly. As a result, the marginal per-iteration runtime of SLIRA approaches that of LIME while retaining global fairness awareness. The allocation update step, including SHAP\u2013LIME gradient fusion, fairness enforcement, and capacity constraint handling, scales linearly with the number of users \\(U\\) and resources \\(R\\), yielding a complexity of \\(\\mathcal{O}(U\\cdot R)\\). Bayesian uncertainty estimation is implemented using variational inference, which introduces a modest additional overhead that scales linearly with the number of model parameters and does not dominate the overall runtime. Figure\u00a04<\/a> illustrates the practical runtime and scalability trade-offs among SHAP, LIME, and SLIRA. While SLIRA incurs a slightly higher computational cost than LIME due to global explanation alignment, it remains significantly more efficient than standalone SHAP and provides superior fairness consistency, temporal stability, and uncertainty quantification. These characteristics make SLIRA well suited for safety\u2013critical PSN scenarios, where explainability and reliability are as important as computational speed. SLIRA achieves a balanced trade-off between computational cost and explainability performance, offering a scalable and practically deployable solution for real-time explainable resource allocation in PSN\u2019s.<\/p>\n Fig. 4 Comparative runtime and explainability cost analysis of SHAP, LIME, and the proposed SLIRA framework in public safety networks<\/p>\n To provide a comprehensive evaluation and directly address concerns regarding the necessity of the proposed learning-based allocation mechanism, we compare SLIRA against two key baseline categories: (i) direct solver-based optimization, representing the mathematically optimal solution under perfect state information, and (ii) the original non-explainable AI model, representing the predictive allocation approach without explanation regulation. The solver baseline computes an optimal allocation at every time step using convex optimization under the full system constraints. The original AI baseline employs the predictive model \\({f}_{\\theta }\\left(x\\left(t\\right)\\right)\\) to generate allocation scores, which are then projected onto the feasible allocation space without incorporating SHAP\/LIME explanations or uncertainty modeling. These baselines allow us to quantify, under identical scenarios, the trade-offs between optimality, real-time feasibility, and explainability offered by SLIRA.<\/p>\n","protected":false},"excerpt":{"rendered":"This section presents a comprehensive experimental evaluation of the proposed SLIRA framework in dynamic PSN environments. The objective…\n","protected":false},"author":2,"featured_media":57245,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[33338,33333,13075,33337,1743,21570,1737,1744,33334,33335,160,33336,2899],"class_list":["post-57244","post","type-post","status-publish","format-standard","has-post-thumbnail","category-xai","tag-bayesian-uncertainty","tag-complex-networks","tag-explainable-ai","tag-fairness-in-ai","tag-humanities-and-social-sciences","tag-lime","tag-mathematics-and-computing","tag-multidisciplinary","tag-public-safety-networks","tag-resource-allocation","tag-science","tag-shap","tag-xai"],"_links":{"self":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts\/57244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/comments?post=57244"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts\/57244\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/media\/57245"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/media?parent=57244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/categories?post=57244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/tags?post=57244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"Fig.](\"https:\/\/www.europesays.com\/ai\/wp-content\/uploads\/2026\/06\/41598_2026_43440_Fig3_HTML.png\")
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