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Probabilistic Caching in Wireless D2D Networks: Cache Hit Optimal vs. Throughput Optimal
Zheng Chen, Nikolaos Pappas, Marios Kountouris
TL;DR
The paper asks whether probabilistic caching should optimize cache hits or successfully served requests when D2D reliability matters. It uses stochastic geometry to approximate cache-aided throughput and numerically optimize caching probabilities, finding larger gains over cache-hit optimization in dense user regimes.
Problem
Conventional cache-hit optimization does not account for the reliability of D2D transmissions when placing content probabilistically.
Method
The paper uses stochastic geometry to derive a closed-form approximation of cache-aided throughput and numerically optimize caching probabilities.
Results
Cache-aided throughput is significantly improved over cache-hit optimization and MPC, with the gain more profound in dense user regimes.
Takeaways & Limitations
D2D content-delivery success probability is a critical factor alongside cache-hit probability when optimizing caching placement.
Takeaways & Limitations
The numerical optimization uses a content library of N = 20 files to avoid high complexity, although real content libraries are much larger.
Abstract
from arXiv · showhide
Departing from the conventional cache hit optimization in cache-enabled wireless networks, we consider an alternative optimization approach for the probabilistic caching placement in stochastic wireless D2D caching networks taking into account the reliability of D2D transmissions. Using tools from stochastic geometry, we provide a closed-form approximation of cache-aided throughput, which measures the density of successfully served requests by local device caches, and we obtain the optimal caching probabilities with numerical optimization. Compared to the cache-hit-optimal case, the optimal caching probabilities obtained by cache-aided throughput optimization show notable gain in terms of the density of successfully served user requests, particularly in dense user environments.
I. INTRODUCTION
The paper studies probabilistic caching in stochastic wireless D2D networks under cache-hit and cache-aided-throughput objectives. It models local service through self-caching or nearby devices and emphasizes D2D transmission reliability in caching decisions.
- Probabilistic placement is studied as an alternative to caching the most popular content everywhere in spatially distributed wireless networks.
- The cache-hit objective counts requests served locally by either the requesting device or neighboring devices within distance Rd.
- Cache-aided throughput measures the density of successfully served requests from a user’s own cache or nearby devices through D2D transmission.
- Users are modeled as a homogeneous PPP, with active requesters and inactive devices serving as potential D2D transmitters.
- Each device independently caches file fi with probability qi under geographic caching, producing file-specific device intensities qi(1−ρ)λu.
- A D2D cache hit occurs when a requested file is stored on a nearby device within Rd; otherwise, it is fetched through the cellular backhaul.
III. PERFORMANCE METRICS AND ANALYSIS
The paper distinguishes cache-hit probability from cache-aided throughput as its main performance metrics. Both account for self-requests, while cache-aided throughput additionally captures successful local service density.
- The paper defines cache-hit probability and cache-aided throughput as its two main performance metrics.
- Cache-hit probability is the probability that a random active user finds its requested file in local caches, including self-request and D2D cache-hit cases.
- Self-request service is handled without assistance from other devices.
1) Self-Request:
A self-request occurs when the requesting device can handle its request without assistance from other devices.
- 2) Self-Request:: A self-request is handled directly by the requesting device without assistance from other devices.
- 2) Self-Request:: Self-request service avoids reliance on nearby devices.
- 2) Self-Request:: The self-request case represents local handling at the user’s own device.
2) D2D Cache Hit:
D2D cache hits use nearby devices to locate requested files, and the overall cache-hit probability combines self-requests with D2D cache hits.
- 2) D2D Cache Hit:: The probability of finding a requested file nearby depends on its popularity order and the area size within distance Rd.
- 2) D2D Cache Hit:: The total cache-hit probability equals the sum of self-request probability and D2D cache-hit probability.
B. Cache-Aided Throughput
Cache-aided throughput measures the density of requests successfully handled by local caches, combining guaranteed self-service with reliability-limited D2D delivery. Its derivation averages file-specific D2D success over nearest-cache distances and the content library.
- Cache-aided throughput counts successfully and simultaneously handled local-cache requests per unit area.
- Self-requested files are served with probability one, whereas D2D cache hits depend on the received SINR.
- The throughput expression incorporates the request density ρλu and the D2D success probability for each requested file.
- For a requested file, the nearest device caching it is characterized by distance di, with D2D service restricted to di ≤ Rd.
- The D2D success probability is derived for a target SINR using interference’s Laplace transform and the file-specific D2D-distance density.
- Substituting the distance distribution and success expression yields cache-aided throughput averaged over all files.
IV. OPTIMIZATION OF PROBABILISTIC CACHING PLACEMENT
The paper studies probabilistic caching probabilities under two distinct objectives: maximizing local cache-hit probability and maximizing cache-aided throughput.
- Caching probabilities q = [q1, . . . , qN] are optimized separately for cache-hit maximization and cache-aided throughput maximization.
A. Cache Hit Maximization
Cache-hit maximization is formulated as a constrained optimization over file caching probabilities, with each probability bounded between zero and one. The objective is concave, enabling a KKT-based solution involving the Lambert W function.
- The cache-hit optimization maximizes the cache-hit probability subject to 0 ≤ qi ≤ 1 for every file.
- The cache-hit objective is strictly concave in the caching probabilities.
- The constrained solution is obtained by applying the Karush-Kuhn-Tucker conditions to a Lagrangian formulation.
- The resulting caching probabilities use the Lambert W function together with the bounds qi ∈ [0,1].
B. Cache-aided Throughput Maximization
Throughput maximization uses an approximation because the exact throughput expression makes the optimal caching probabilities difficult to obtain numerically. The resulting non-convex problem is solved with Simulated Annealing.
- The exact throughput expression makes optimal caching probabilities difficult to obtain, even with numerical methods.
- The paper approximates the D2D success probability for each file using the underlying distance-distribution analysis.
- The approximation produces a closed-form expression for cache-aided throughput.
- The resulting optimization problem is non-convex and is solved numerically with Simulated Annealing.
V. NUMERICAL AND SIMULATION RESULTS
Numerical and simulation results compare cache-hit-optimal and throughput-optimal probabilistic caching in sparse and dense environments. Accounting for D2D reliability improves cache-aided throughput, with the largest gains in dense settings.
- Simulation setup: The evaluation uses user densities λu = [10−4, 10−3]/m2, Zipf parameters γ = {0.5, 1.2}, cache capacity Md = 2, and a library of N = 20 files.The D2D searching distance is Rd = 75 m, and 50% of users request files while the remaining users can transmit them.
- Optimal caching probabilities: In sparse environments, throughput-optimal and cache-hit-optimal caching probabilities are very close.The comparison plots optimal caching probabilities against file popularity order.
- Optimal caching probabilities: In dense environments, throughput optimization assigns higher probabilities to the most popular files than cache-hit optimization.For example, the throughput-optimal q⋆3 is much higher than the cache-hit-optimal value.
- Interpretation: Dense-user interference produces very low D2D success probability, making self-requests more important than cache-assisted D2D transmission.This explains the more selfish caching tendency observed under throughput optimization.
- Scope: The study uses N = 20 files because the real content library is much larger and larger libraries would increase optimization complexity.The authors note that this choice is made to avoid high optimization complexity.
- Throughput comparison: Throughput-optimal caching significantly improves simulated cache-aided throughput over cache-hit optimization and MPC, especially for dense users.With dense users and γ = 1.2, MPC performs better than cache-hit-optimal caching.
VI. CONCLUSIONS
The conclusion contrasts cache-hit probability with cache-aided throughput, defined as the density of successfully served user requests. It emphasizes that content-delivery success probability should inform caching placement alongside cache-hit probability.
- Objectives: The paper studies probabilistic caching placement with two objectives: maximizing cache-hit probability and maximizing cache-aided throughput.Cache-aided throughput is defined as the density of successfully served user requests.
- Metric: Cache-aided throughput measures the density of successfully served user requests by local caches.This distinguishes it from cache-hit probability as an objective for placement optimization.
- Takeaway: The main conclusion is that content-delivery success probability is a critical factor in optimal caching placement for wireless D2D networks.The conclusion places delivery reliability alongside cache-hit probability when improving throughput performance.