D2D vs Infrastructure Delivery

Two Delivery Paradigms

Having established the Θ(M/N)\Theta(M/N) scaling for D2D caching, we now compare it against infrastructure-based delivery (cellular base station, possibly with MAN caching). This comparison reveals when D2D is preferable: typically in dense, local, low-mobility scenarios; when it is not: typically in sparse or long-range scenarios where D2D neighbor density is too low.

The design implication is that neither paradigm is universally better. Real 6G networks will likely combine the two: cellular infrastructure for low-density regions and wide-area coverage, with D2D caching offloading dense local traffic.

Theorem: D2D vs Infrastructure Throughput

For the D2D caching network with nn users, cache MM, library NN, and protocol interference model:

TD2D(n,M)β€…β€Š=β€…β€ŠΞ˜(M/N),Tinfra(n,M)β€…β€Š=β€…β€ŠO(log⁑n/n),T_{\text{D2D}}(n, M) \;=\; \Theta(M/N), \qquad T_{\text{infra}}(n, M) \;=\; O(\log n / n),

where TinfraT_{\text{infra}} is the per-user throughput of an infrastructure-based network serving all nn users through a single base station. D2D dominates infrastructure as nn grows.

Infrastructure: all nn users share a single downlink of bounded capacity; each gets Θ(1/n)\Theta(1/n). With MAN caching, the shared capacity grows as log⁑(1+nM/N)\log(1 + nM/N) at best β€” still β†’0\to 0 per user for fixed M/NM/N.

D2D: local communication bypasses the shared bottleneck; per-user throughput is constant in nn. The advantage of D2D is Ξ©(n)\Omega(n).

Proof
Infrastructure bound

With single BS serving nn users, total downlink capacity is O(log⁑n)O(\log n) (classical capacity bound for interference-limited cellular). Per-user: O(log⁑n/n)β†’0O(\log n / n) \to 0.

D2D bound

From Theorem 10.1: per-user throughput Θ(M/N)\Theta(M/N), constant in nn.

Ratio

TD2D/Tinfra=Θ(nM/(Nlog⁑n))=Θ(n/log⁑n)T_{\text{D2D}}/T_{\text{infra}} = \Theta(nM/(N \log n)) = \Theta(n/\log n) for fixed ΞΌ\mu. D2D is asymptotically much better per user. β– \blacksquare

Caveat

The bound is asymptotic. For small nn, infrastructure can outperform D2D due to neighbor-sparsity. The crossover is around n∼10n \sim 10-100100 depending on density and cell size.

D2D vs Infrastructure Throughput

Compare per-user throughput of three schemes: (blue) D2D + caching = M/NM/N; (red) infrastructure + MAN = log⁑2(1+nM/N)/n\log_2(1+nM/N)/n; (green) infrastructure no cache = 1/n1/n. D2D's advantage grows with cache ratio and network size.

Parameters
100

Example: Small vs Dense D2D Network

(a) A small office network: n=10n = 10 users, M=100M = 100 files, N=1000N = 1000 files (ΞΌ=0.1\mu = 0.1). Compare D2D and cellular per-user throughput. (b) A dense stadium: n=10,000n = 10{,}000 users, same per-user cache.

Solution
(a) Office

D2D: Θ(0.1)\Theta(0.1) β€” constant. But with only 10 users, the "Θ\Theta" constant may be small due to few neighbors. Cellular: O(log⁑10/10)β‰ˆ0.33O(\log 10 / 10) \approx 0.33. Cellular may actually win at this nn because D2D's constant factor is small.

(b) Stadium

D2D: Θ(0.1)\Theta(0.1), same. With 10,000 users, the constant factor reaches its full asymptotic value. Cellular: log⁑104/104β‰ˆ0.001\log 10^4 / 10^4 \approx 0.001. Cellular collapses.

Crossover

The crossover between "cellular better" and "D2D better" is around n∼50n \sim 50-200200 for typical densities. Below that, cellular wins; above, D2D wins.

Hybrid design

Deploy both: D2D for popular/local content; cellular (with MAN) for unpopular/wide-area content. Mixed-architecture designs beat either alone; see Ji-Caire-Molisch 2018 hybrid-scheme extension.

Local Reuse Rate Under Zipf Popularity

For Zipf popularity, the fraction of requests servable by local D2D caches is a non-linear function of M/NM/N. High-popularity files benefit disproportionately from small caches; diminishing returns at higher M/NM/N.

Parameters
0.8
100
1000

Key Takeaway

D2D + caching dominates infrastructure at scale (nn large). Per-user throughput: Θ(M/N)\Theta(M/N) for D2D, O(log⁑n/n)O(\log n/n) for infrastructure. The crossover occurs around n∼100n \sim 100. At stadium / urban densities, D2D is the only option for maintaining per-user rate.

⚠️Engineering Note

Hybrid D2D + Infrastructure Networks

Real deployments will combine D2D and infrastructure:

  1. Tiered offloading. Base station handles wide-area, high- capacity, low-latency content. D2D offloads local, popular, latency-tolerant content.
  2. Cache pre-population. BS pre-places content in D2D-reachable areas (stadiums, malls, residential blocks). D2D then serves the cached content locally.
  3. Signaling. BS provides device discovery and pairing information. D2D does the delivery.
  4. Charging. Users pay for D2D contribution (or ISP pays users who participate). Business model is key.

6G vision (3GPP Rel-19+ study items): cache-aided D2D for XR and video. Analysis of this hybrid architecture is a major CommIT research topic.

Practical Constraints
  • β€’

    3GPP LTE Rel-12 ProSe: direct discovery and communication

  • β€’

    5G NR Sidelink Rel-16+: V2X and basic D2D

  • β€’

    6G study items (Rel-19/20): cache-aided D2D, MBSFN extensions

  • β€’

    Energy cost: D2D transmitter ~100 mW vs cellular ~500 mW

Common Mistake: Density Assumption Matters

Mistake:

Quoting D2D Θ(M/N)\Theta(M/N) throughput for networks that are too sparse (neighbors too few).

Correction:

The Θ(M/N)\Theta(M/N) scaling assumes a dense network where each user has Θ(log⁑n)\Theta(\log n) neighbors within D2D range. In sparse deployments (e.g., rural, low-density), this assumption fails: neighbors are few, local hit probability is low, effective throughput is reduced.

For sparse networks, infrastructure dominates. The correct interpretation of Ji-Caire-Molisch is: D2D is a dense-network regime result. At sparse deployment density, Gupta-Kumar-style 1/n1/\sqrt{n} scaling is the regime.

Historical Note: From Gupta-Kumar to D2D Caching

2000–2016

The story of wireless ad-hoc scaling started pessimistically:

  • 2000: Gupta and Kumar established the celebrated Θ(1/n)\Theta(1/\sqrt{n}) scaling for ad-hoc throughput. Per-user rate β†’0\to 0. Widely interpreted as "ad-hoc doesn't scale."
  • 2002-2010: Franceschetti-Migliore-Minero variations; Franceschetti-Dousse-Tse on percolation. Constants improved, but the 1/n1/\sqrt{n} scaling persisted.
  • 2016: Ji, Caire, Molisch broke the barrier: with caching, per-user throughput is constant, Θ(M/N)\Theta(M/N). This is the first throughput result in ad-hoc wireless that does not decay with nn.

The result is not just an asymptotic curiosity: it justifies the architectural paradigm of user-driven content delivery, which underpins many 6G / cell-free / MEC designs.

The Θ(M/N)\Theta(M/N) Scaling Law (Ji-Caire-Molisch)Design Principles for Practical D2D Caching