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

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

Problem Statement
Edge intelligence enables AI inference at the network edge, offering low-latency solutions for applications like video analytics. However, the cost-efficiency and performance of these systems depend critically on the joint dimensioning of wireless and computational resources prior to deployment. Existing literature largely focuses on run-time resource allocation or employs simplified models that decouple radio access from computing infrastructure. These approaches often overlook end-to-end correlations in large-scale deployments and rely on average performance metrics, failing to address the strict tail-latency and inference accuracy constraints required by next-generation safety-critical applications. Furthermore, network planning often treats wireless and computing dimensions in isolation, ignoring the stochastic nature of user locations, traffic, and interference in realistic multi-cellular environments.

Methodology
The authors propose a unified stochastic framework to model and optimize the dimensioning of multi-cellular edge-intelligent systems. The methodology integrates three core components:

1. Stochastic Geometry for Network Topology: The spatial distribution of base stations and users is modeled using a homogeneous Poisson Point Process (PPP). This allows for the derivation of closed-form expressions for the ergodic uplink capacity in both noise-limited and interference-limited regimes. The model incorporates distance-proportional fractional power control, peak-power constraints, and inter-cell interference within a Poisson-Voronoi tessellation.
2. Queueing Theory and AI Workload Profiling: The end-to-end offloading delay is decomposed into uplink transmission time, queuing time at the edge server, and AI inference time. The arrival process is modeled as a Poisson process, and the server queue is treated as an M/D/1 system (Poisson arrivals, deterministic service). The service time is derived from empirical profiling of YOLOv5-based inference, showing a cubic dependence on frame resolution.
3. Joint Optimization Formulation: The authors formulate a non-convex optimization problem to minimize the total deployment cost (weighted sum of wireless bandwidth and computing capacity) while satisfying statistical Quality-of-Service (QoS) guarantees. These guarantees include strict tail-latency constraints (defined by a minimum success probability), coverage requirements for cell-edge users and large Voronoi cells, and minimum inference accuracy.

To solve the non-convex problem, the authors prove that it can be decomposed into a series of convex sub-problems. By fixing specific variables (such as the worst-case user distance and frame resolution) and utilizing epigraph representations for power constraints, they demonstrate that the problem admits a globally optimal solution with zero optimality gap under specific load conditions.

Key Contributions

• Unified Stochastic Framework: The paper introduces a tractable model that jointly captures spatial randomness, wireless transmission dynamics, and computational queueing for edge video analytics.
• Closed-Form Capacity Expressions: The authors derive ergodic capacity formulas for SIMO uplink transmissions under both noise-limited and interference-limited conditions, explicitly accounting for fractional power control and peak-power limits.
• Global Optimality in Non-Convex Planning: The work provides a theoretical proof that the complex, non-convex resource dimensioning problem can be solved globally by decomposing it into convex sub-problems, ensuring optimal cost-performance trade-offs without heuristic approximations.
• Design Guidelines for Densification: Through numerical evaluation, the paper identifies critical trade-offs in network densification. It reveals that while denser networks reduce transmission delays, they can increase per-request computing costs due to reduced statistical multiplexing at servers. Conversely, in interference-limited regimes, densification is only cost-effective if the frequency reuse factor scales proportionally with base station density; otherwise, it leads to severe interference and inefficiency.

Results
Numerical evaluations in both noise-limited and interference-limited regimes highlight distinct design behaviors:

• Noise-Limited Regime: Densification (increasing base station density) reduces the required bandwidth per frame due to shorter propagation distances. However, it increases the required computing capacity per server because smaller cells aggregate fewer users, reducing statistical multiplexing gains.
• Interference-Limited Regime: If the frequency reuse factor is kept constant while densifying the network, interference increases, negating the benefits of shorter links and leading to higher bandwidth requirements. Cost-efficient designs in this regime require a proportional scaling of the frequency reuse factor with base station density.
• Trade-offs: The analysis confirms a fundamental trade-off between wireless and computational efficiency. Smaller cells reduce transmission delay but increase computing costs, while larger cells exhibit the opposite trend. The optimal design depends heavily on the traffic intensity and the specific interference management strategy employed.

Significance
The paper claims to bridge a critical gap in the literature by shifting the focus from run-time optimization to the pre-deployment planning stage of edge-intelligent systems. By providing a rigorous stochastic framework that accounts for spatial randomness and strict tail-latency constraints, the work offers system designers principled guidelines for provisioning resources in 5G and beyond-6G networks. The ability to derive globally optimal solutions for joint wireless and computing dimensioning ensures that edge intelligence deployments can be both cost-effective and reliable, avoiding the pitfalls of under-provisioning or over-provisioning resources in large-scale, heterogeneous networks.