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Stochastic Modeling and Resource Dimensioning of Multi-Cellular Edge Intelligent Systems

Jaume Anguera Peris, Joakim Jaldén

TL;DR

This paper addresses the problem of dimensioning wireless and edge-computing resources for large-scale multi-cell edge-intelligent systems under spatial randomness and strict QoS guarantees. It develops a unified framework that combines stochastic geometry (PPP-based base-station layouts and Poisson-Voronoi cells), a SIMO uplink ergodic-capacity analysis in noise- and interference-limited regimes, a queueing model for end-to-end offloading, and a YOLOv5-based inference profile to capture accuracy vs. frame resolution. By formulating a non-convex joint optimization that minimizes deployment cost while enforcing tail-latency and accuracy constraints, the authors show that the problem can be decomposed into convex subproblems with global optimality under certain load conditions, and they derive design insights for densification and spectrum reuse. Numerical results reveal nuanced trade-offs: in noise-limited settings, densification mainly benefits the wireless path, while computing costs rise with smaller cells; in interference-limited settings, densification must be accompanied by proportional spectrum partitioning to achieve cost efficiency and fairness. Overall, the work provides a principled planning framework for cost-effective edge intelligence in 5G/6G networks, guiding operators on how to jointly allocate bandwidth and edge-computing capacity to meet statistical latency and accuracy requirements.

Abstract

Edge intelligence enables AI inference at the network edge, co-located with or near the radio access network, rather than in centralized clouds or on mobile devices. It targets low-latency, resource-constrained applications with large data volumes, requiring tight integration of wireless access and on-site computing. Yet system performance and cost-efficiency hinge on joint pre-deployment dimensioning of radio and computational resources, especially under spatial and temporal uncertainty. Prior work largely emphasizes run-time allocation or relies on simplified models that decouple radio and computing, missing end-to-end correlations in large-scale deployments. This paper introduces a unified stochastic framework to dimension multi-cell edge-intelligent systems. We model network topology with Poisson point processes, capturing random user and base-station locations, inter-cell interference, distance-based fractional power control, and peak-power constraints. By combining this with queueing theory and empirical AI inference workload profiling, we derive tractable expressions for end-to-end offloading delay. These enable a non-convex joint optimization that minimizes deployment cost under statistical QoS guarantees, expressed through strict tail-latency and inference-accuracy constraints. We prove the problem decomposes into convex subproblems, yielding global optimality. Numerical results in noise- and interference-limited regimes identify cost-efficient design regions and configurations that cause under-utilization or user unfairness. Smaller cells reduce transmission delay but raise per-request computing cost due to weaker server multiplexing, whereas larger cells show the opposite trend. Densification reduces computational costs only when frequency reuse scales with base-station density; otherwise, sparser deployments improve fairness and efficiency in interference-limited settings.

Stochastic Modeling and Resource Dimensioning of Multi-Cellular Edge Intelligent Systems

TL;DR

This paper addresses the problem of dimensioning wireless and edge-computing resources for large-scale multi-cell edge-intelligent systems under spatial randomness and strict QoS guarantees. It develops a unified framework that combines stochastic geometry (PPP-based base-station layouts and Poisson-Voronoi cells), a SIMO uplink ergodic-capacity analysis in noise- and interference-limited regimes, a queueing model for end-to-end offloading, and a YOLOv5-based inference profile to capture accuracy vs. frame resolution. By formulating a non-convex joint optimization that minimizes deployment cost while enforcing tail-latency and accuracy constraints, the authors show that the problem can be decomposed into convex subproblems with global optimality under certain load conditions, and they derive design insights for densification and spectrum reuse. Numerical results reveal nuanced trade-offs: in noise-limited settings, densification mainly benefits the wireless path, while computing costs rise with smaller cells; in interference-limited settings, densification must be accompanied by proportional spectrum partitioning to achieve cost efficiency and fairness. Overall, the work provides a principled planning framework for cost-effective edge intelligence in 5G/6G networks, guiding operators on how to jointly allocate bandwidth and edge-computing capacity to meet statistical latency and accuracy requirements.

Abstract

Edge intelligence enables AI inference at the network edge, co-located with or near the radio access network, rather than in centralized clouds or on mobile devices. It targets low-latency, resource-constrained applications with large data volumes, requiring tight integration of wireless access and on-site computing. Yet system performance and cost-efficiency hinge on joint pre-deployment dimensioning of radio and computational resources, especially under spatial and temporal uncertainty. Prior work largely emphasizes run-time allocation or relies on simplified models that decouple radio and computing, missing end-to-end correlations in large-scale deployments. This paper introduces a unified stochastic framework to dimension multi-cell edge-intelligent systems. We model network topology with Poisson point processes, capturing random user and base-station locations, inter-cell interference, distance-based fractional power control, and peak-power constraints. By combining this with queueing theory and empirical AI inference workload profiling, we derive tractable expressions for end-to-end offloading delay. These enable a non-convex joint optimization that minimizes deployment cost under statistical QoS guarantees, expressed through strict tail-latency and inference-accuracy constraints. We prove the problem decomposes into convex subproblems, yielding global optimality. Numerical results in noise- and interference-limited regimes identify cost-efficient design regions and configurations that cause under-utilization or user unfairness. Smaller cells reduce transmission delay but raise per-request computing cost due to weaker server multiplexing, whereas larger cells show the opposite trend. Densification reduces computational costs only when frequency reuse scales with base-station density; otherwise, sparser deployments improve fairness and efficiency in interference-limited settings.
Paper Structure (18 sections, 3 theorems, 38 equations, 5 figures, 2 tables)

This paper contains 18 sections, 3 theorems, 38 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Our contribution
  3. Document organization
  4. Network model
  5. Base station deployment and user association
  6. Uplink transmission model
  7. Performance insights and design guidelines
  8. End-to-end offloading model
  9. Resource-dimensioning problem
  10. Quality-of-service requirements
  11. Optimization problem
  12. Theoretical analysis
  13. Numerical results
  14. Noise-limited system
  15. Interference-limited system
  16. ...and 3 more sections

Key Result

Lemma 2.1

Consider a noise-limited uplink transmission in a single-input multiple-output system with $M \geq 1$ receiver antennas at the base station. Let a user at distance $r$ (in kilometers) from its serving base station transmit with power $\ell(r, \alpha, \epsilon) = \min(P r^{\alpha \epsilon}, \bar{P})$ where $E_i(x) = \int_1^\infty \exp(-xt)/t^i\, dt$ is the generalized exponential integral function

Figures (5)

  • Figure 1: (a) Cumulative distribution function of the normalized distance between any user and its associated base station, and best-fit approximations to the cumulative distribution functions of the normalized maximum distance squared \ref{['eq:cdf_normalized_maxDistance']} and the normalized area of the Voronoi cells in two dimensions \ref{['eq:cdf_normalized_area']}, taken from peris2024extreme and ferenc2007size, respectively. (b) Multi-cell system with reuse factor $\delta=1$, where the user of interest is located at the Voronoi cell of the base station on the right, and the interfering users are located elsewhere. The straight lines show the different distances $r$, $r_z$, and $d_z$ defined in Section \ref{['sec:system-model_ULtransmission']}. The dashed lines show the signal of interest (blue) and the interfering signals (red) at one of the $M$ antennas at the receiver, characterized by the different Rayleigh fading coefficients of the channel $|g|^2$, and $|g_z|^2$, respectively.
  • Figure 2: (a)-(f) Ergodic capacity for the noise-limited and the interference-limited systems as a function of the distance $r$ between any randomly selected user and its serving base station. Figure (a) analyzes the effect of the power control coefficient $\epsilon$ while taking into consideration the distribution of $r$. Figure (b) evaluates the ergodic capacity for different number of receiver antennas $M$. Figure (c) analyzes the effect of the density of base stations $\lambda_{\mathrm{b}}$ for a constant reuse factor $\delta$ while taking into consideration the distribution of the maximum distance between cell-edge users and their serving base station $r_{\max}$. Figure (d) evaluates the ergodic capacity for different $\lambda_{\mathrm{b}}$ and $\delta$, with proportional ratios of $\lambda_{\mathrm{b}}/\delta$. Finally, Figures (c) and (d) analyzes the effect of $\epsilon$ for different $\lambda_{\mathrm{b}}$ and $\delta$ while taking into consideration the distribution of $r_{\max}$.
  • Figure 3: End-to-end offloading timeline for a video-analytics task. Parameters in red correspond to the wireless and computing resources that need to be optimized to satisfy the network, user, and video analytic requirements. Parameters in blue represent (from left to right) the uplink, waiting, and service times of the end-to-end offloading process.
  • Figure 4: (a)--(b) Optimal wireless and computing resources per frame, optimal server load, and total cost of the resource-dimensioning (in millions) per unit area for a noise-limited system as a function of the density of base stations per unit area $\lambda_{\mathrm{b}}$. (c) Effect of the trade-off parameter $\beta_1$ on the optimal resources for a noise-limited system with density $\lambda_{\mathrm{b}}=2$ BS/km$^2$. (d) Optimal offloading parameters $r$, $A$, and $s$ for which the optimal $B$ and $H$ satisfy all the statistical QoS requirements. In all cases, the results are compared for different traffic intensities $\lambda$, with Figure (d) yielding the same results for any $\lambda$.
  • Figure 5: (a)--(b) Optimal wireless and computing resources per frame for an interference-limited system as a function of the density of base stations per unit area $\lambda_{\mathrm{b}}$. Figures (a) and (b) analyze the effect of having a constant reuse factor $\delta$, or adjusting $\delta$ in proportion to $\lambda_{\mathrm{b}}$, respectively. All the results are also compared for different traffic intensities $\lambda$.

Theorems & Definitions (8)

  • Lemma 2.1: Noise-limited system
  • proof
  • Lemma 2.2: Interference-limited system
  • proof
  • Remark 1
  • Lemma 4.1
  • proof
  • Remark 2