Calculating CDN Caching Efficiency with AV1

Large-scale Content Delivery Networks (CDNs) quantify the caching benefits of the AV1 video codec by analyzing how its superior compression ratio—typically yielding 30% to 50% smaller file sizes than H.264—alters data footprint dynamics at the edge. By evaluating metrics such as the Byte Hit Ratio (BHR), the Working Set Size (WSS), Mean Time to Eviction (MTTE), and origin offload percentages, CDNs mathematically determine how smaller payload sizes expand effective cache capacity, reduce origin egress, and lower operational overhead.

1. Working Set Size Compression

The foundational variable in caching efficiency is the Working Set Size (WSS)—the total volume of unique data requested by users within a designated observation window. When a library is encoded in AV1 rather than legacy codecs like H.264 (AVC) or H.265 (HEVC), the aggregate bytes needed to represent the video streams decrease.

CDNs model the AV1 working set size reduction as:

\[WSS_{\text{AV1}} = WSS_{\text{legacy}} \times (1 - \delta)\]

Where \(\delta\) represents the bitrate savings percentage (typically \(0.20 \le \delta \le 0.40\) against HEVC, and up to \(0.50\) against AVC).

Because edge storage (RAM and NVMe drives) is finite, shrinking the physical footprint of each video segment directly reduces the overall footprint of the active catalogue.

2. Cache Retention and Mean Time to Eviction (MTTE)

Cache eviction policies (typically variations of Least Recently Used [LRU] or Segmented LRU [SLRU]) drop segments when cache capacity is exceeded. CDNs calculate the lifespan of an asset in cache using the Mean Time to Eviction (MTTE).

Because edge nodes operate on fixed-capacity boundaries:

\[\text{Cache Shelf-Life} \approx \frac{\text{Edge Storage Capacity (Bytes)}}{\text{Unique Byte Ingress Rate (Bytes/Second)}}\]

Because AV1 reduces the byte ingress rate of unique video chunks, content remains in the cache longer without requiring hardware expansion. CDNs calculate the retention gain by observing the displacement velocity of objects. A 30% reduction in file footprint results in an effective capacity increase of approximately 43%, allowing more distinct catalog titles (particularly the "long-tail" content) to persist at edge tiers instead of midgress or origin tiers.

3. Shift from Request Hit Ratio to Byte Hit Ratio (BHR)

While Request Hit Ratio (RHR) measures whether an asset was served from cache, large-scale networks prioritize Byte Hit Ratio (BHR) when calculating infrastructure economics. BHR directly maps to bandwidth utilization and egress transit billing.

\[\text{BHR} = \frac{\sum \text{Bytes Served from Cache}}{\sum \text{Total Bytes Requested}}\]

When migrating to AV1, CDNs separate their telemetry into request cohorts. Even if RHR remains constant across codecs, BHR shifts because cache misses on AV1 files incur smaller penalty payloads from the origin.

To determine the net efficiency gain (\(G_{\text{BHR}}\)), CDNs measure the difference in bytes backhauled to the origin tier (\(B_{\text{origin}}\)) per million video requests:

\[G_{\text{BHR}} = 1 - \frac{B_{\text{origin, AV1}}}{B_{\text{origin, Legacy}}}\]

4. Mathematical Modeling Using Che’s Approximation

For predictive capacity planning, CDNs apply Che's approximation under Zipf-distributed video popularity. In a Zipfian distribution, a small fraction of files represents the majority of requests, while the long tail represents lower individual request frequencies.

Che's approximation calculates the hit probability \(P_i\) of an object \(i\) with size \(s_i\) and request rate \(\lambda_i\) in an LRU cache of size \(C\):

\[P_i = 1 - e^{-\lambda_i t_C}\]

Where \(t_C\) is the characteristic time it takes for \(C\) bytes of unique data to enter the cache:

\[\sum_{j} s_j (1 - e^{-\lambda_j t_C}) = C\]

When AV1 reduces every individual segment size \(s_j\), the characteristic time \(t_C\) increases significantly. CDNs measure this extended time parameter to predict how deeply into the long-tail catalog the edge cache can serve requests before a miss occurs.

5. Multi-Codec Fragmentation Overhead Analysis

To calculate the net efficiency gain, CDNs subtract the performance penalty caused by storage fragmentation. Serving AV1 concurrently with H.264 and HEVC temporarily splits the cache into separate asset variants for the same media title.

Engineers model this using an asset replication penalty:

\[\text{Net Efficiency} = \text{Footprint Savings} - \text{Variant Duplication Factor}\]

The CDN tracks the percentage of AV1-capable client traffic. The financial and cache-efficiency tipping point occurs when AV1 client density exceeds the ratio needed to offset the storage of coexisting legacy variants, after which the net reduction in global ingress immediately yields higher origin offload efficiency.