serverAppConfigs/docs/Pipeline Parallelism/Ethernet Bandwidth Math.md

---
type: reference
title: Ethernet Bandwidth Math
description: Bytes-per-token math for pipeline vs tensor parallelism, feasibility tables for 1/2.5/10 GbE, and real multi-node benchmark numbers.
tags:
  - pipeline-parallelism
  - research
timestamp: 2026-08-14
---

# Bandwidth Analysis: Multi-Node LLM Inference over Ethernet

## 1. Bandwidth Math: Bytes per Token per Layer Boundary

### 1.1 Pipeline Parallelism (PP)

During autoregressive generation, each transformer layer produces a hidden state of shape `(batch_size, hidden_size)`. At a pipeline stage boundary, this tensor must be communicated between nodes.

**Forward pass only (inference):**
```
bytes_per_boundary = batch_size × hidden_size × 2   [fp16 = 2 bytes]
```

**Key detail:** During *generation* (one token at a time), seq_len = 1 at each boundary crossing. The KV cache stays local. The hidden state is `(batch, hidden_size)` — independent of context length.

**For a 27B dense model (e.g., Qwen3.6-27B):**
- Hidden size: H = 4096 (standard for Llama/Qwen-style architectures)
- Layers: L = 32 (typical)
- Per-token, per-boundary: `4096 × 2 = 8,192 bytes = 8 KB`
- With Nₚₚ stage boundaries: total = `Nₚₚ × 8 KB/tok`

**For a 36B MoE model (e.g., Qwen3.6-35B-A3B):**
- Hidden size: H = 6144 (common for this scale)
- Layers: L = 48 (typical)
- Per-token, per-boundary: `6144 × 2 = 12,288 bytes = 12 KB`
- With Nₚₚ stage boundaries: total = `Nₚₚ × 12 KB/tok`

**Full example — 27B model, 2 PP stages (1 boundary), batch=1:**
```
1 boundary × 4096 × 2 bytes = 8,192 bytes/tok
```

**Example — same model, batch=64:**
```
1 boundary × 4096 × 64 × 2 bytes = 524,288 bytes = 512 KB/tok
```

**Example — 36B model, 2 PP stages, batch=1:**
```
1 boundary × 6144 × 2 bytes = 12,288 bytes = 12 KB/tok
```

### 1.2 Tensor Parallelism (TP) — for comparison

In tensor parallelism, each MLP and attention layer performs an all-reduce on the hidden state:

```
bytes_per_layer = batch_size × hidden_size × 2   [one all-reduce per layer]
total_bytes_per_tok = L × batch_size × hidden_size × 2   [L all-reduces total]
```

**For 27B, H=4096, L=32, TP=2, batch=1:**
```
32 layers × 4096 × 1 × 2 bytes = 262,144 bytes = 256 KB/tok
(16 KB per layer all-reduce × 32 layers)
```

**For 36B, H=6144, L=48, TP=2, batch=1:**
```
48 layers × 6144 × 1 × 2 bytes = 589,824 bytes = 576 KB/tok
(12 KB per layer all-reduce × 48 layers)
```

### 1.3 Scaling with batch size

| Model | H | L | tok/s | Batch | PP boundary bytes/tok | TP total bytes/tok |
|-------|-----|-----|-------|-------|----------------------|--------------------|
| 27B | 4096 | 32 | 10 | 1 | 8 KB | 256 KB |
| 27B | 4096 | 32 | 50 | 1 | 8 KB | 256 KB |
| 27B | 4096 | 32 | 100 | 1 | 8 KB | 256 KB |
| 27B | 4096 | 32 | 10 | 16 | 128 KB | 4,096 KB |
| 27B | 4096 | 32 | 50 | 16 | 128 KB | 4,096 KB |
| 27B | 4096 | 32 | 100 | 16 | 128 KB | 4,096 KB |
| 27B | 4096 | 32 | 10 | 64 | 512 KB | 16,384 KB |
| 27B | 4096 | 32 | 50 | 64 | 512 KB | 16,384 KB |
| 27B | 4096 | 32 | 100 | 64 | 512 KB | 16,384 KB |
| 36B | 6144 | 48 | 10 | 1 | 12 KB | 576 KB |
| 36B | 6144 | 48 | 50 | 1 | 12 KB | 576 KB |
| 36B | 6144 | 48 | 100 | 1 | 12 KB | 576 KB |
| 36B | 6144 | 48 | 10 | 16 | 192 KB | 9,216 KB |
| 36B | 6144 | 48 | 50 | 16 | 192 KB | 9,216 KB |
| 36B | 6144 | 48 | 100 | 16 | 192 KB | 9,216 KB |
| 36B | 6144 | 48 | 10 | 64 | 768 KB | 36,864 KB |
| 36B | 6144 | 48 | 50 | 64 | 768 KB | 36,864 KB |
| 36B | 6144 | 48 | 100 | 64 | 768 KB | 36,864 KB |

---

## 2. Required Bandwidth vs. Ethernet Capabilities

### 2.1 Ethernet link capacities

| Link | Raw Rate | Usable TCP (approx.) | MB/s usable |
|------|----------|---------------------|-------------|
| 1 GbE | 1,000 Mbit/s | ~940 Mbit/s | ~118 MB/s |
| 2.5 GbE | 2,500 Mbit/s | ~2,350 Mbit/s | ~294 MB/s |
| 10 GbE | 10,000 Mbit/s | ~9,400 Mbit/s | ~1,175 MB/s |

### 2.2 Required bandwidth (Mbps) by model, batch, and throughput

**27B model (H=4096), 1 PP boundary:**

| tok/s | Batch=1 | Batch=16 | Batch=64 |
|-------|---------|----------|----------|
| 10 | 0.13 Mbit/s | 2.05 Mbit/s | 8.19 Mbit/s |
| 50 | 0.65 Mbit/s | 10.24 Mbit/s | 40.96 Mbit/s |
| 100 | 1.31 Mbit/s | 20.48 Mbit/s | 81.92 Mbit/s |

**36B model (H=6144), 1 PP boundary:**

| tok/s | Batch=1 | Batch=16 | Batch=64 |
|-------|---------|----------|----------|
| 10 | 0.20 Mbit/s | 3.07 Mbit/s | 12.29 Mbit/s |
| 50 | 0.98 Mbit/s | 15.36 Mbit/s | 61.44 Mbit/s |
| 100 | 1.97 Mbit/s | 30.72 Mbit/s | 122.88 Mbit/s |

**27B model, TP (L=32 layers all-reduce):**

| tok/s | Batch=1 | Batch=16 | Batch=64 |
|-------|---------|----------|----------|
| 10 | 2.05 Mbit/s | 32.77 Mbit/s | 131.07 Mbit/s |
| 50 | 10.24 Mbit/s | 163.84 Mbit/s | 655.36 Mbit/s |
| 100 | 20.48 Mbit/s | 327.68 Mbit/s | 1,310.72 Mbit/s |

### 2.3 Feasibility matrix

Green = feasible (< 50% of link capacity). Yellow = marginal (50–90%). Red = saturated (> 90%).

**27B model — PP (1 boundary), batch=1:**

| | 1 GbE (118 MB/s) | 2.5 GbE (294 MB/s) | 10 GbE (1175 MB/s) |
|---|---|---|---|
| 10 tok/s | ✅ 0.13 Mbit/s | ✅ 0.13 Mbit/s | ✅ 0.13 Mbit/s |
| 50 tok/s | ✅ 0.65 Mbit/s | ✅ 0.65 Mbit/s | ✅ 0.65 Mbit/s |
| 100 tok/s | ✅ 1.31 Mbit/s | ✅ 1.31 Mbit/s | ✅ 1.31 Mbit/s |

**27B model — PP (1 boundary), batch=16:**

| | 1 GbE | 2.5 GbE | 10 GbE |
|---|---|---|---|
| 10 tok/s | ✅ 2.05 Mbit/s | ✅ 2.05 Mbit/s | ✅ 2.05 Mbit/s |
| 50 tok/s | ✅ 10.24 Mbit/s | ✅ 10.24 Mbit/s | ✅ 10.24 Mbit/s |
| 100 tok/s | ✅ 20.48 Mbit/s | ✅ 20.48 Mbit/s | ✅ 20.48 Mbit/s |

**27B model — PP (1 boundary), batch=64:**

| | 1 GbE | 2.5 GbE | 10 GbE |
|---|---|---|---|
| 10 tok/s | ✅ 8.19 Mbit/s | ✅ 8.19 Mbit/s | ✅ 8.19 Mbit/s |
| 50 tok/s | ✅ 40.96 Mbit/s | ✅ 40.96 Mbit/s | ✅ 40.96 Mbit/s |
| 100 tok/s | ✅ 81.92 Mbit/s | ✅ 81.92 Mbit/s | ✅ 81.92 Mbit/s |

**27B model — TP (32 layers), batch=1:**

| | 1 GbE | 2.5 GbE | 10 GbE |
|---|---|---|---|
| 10 tok/s | ✅ 2.05 Mbit/s | ✅ 2.05 Mbit/s | ✅ 2.05 Mbit/s |
| 50 tok/s | ✅ 10.24 Mbit/s | ✅ 10.24 Mbit/s | ✅ 10.24 Mbit/s |
| 100 tok/s | ✅ 20.48 Mbit/s | ✅ 20.48 Mbit/s | ✅ 20.48 Mbit/s |

**27B model — TP (32 layers), batch=16:**

| | 1 GbE | 2.5 GbE | 10 GbE |
|---|---|---|---|
| 10 tok/s | ✅ 32.77 Mbit/s | ✅ 32.77 Mbit/s | ✅ 32.77 Mbit/s |
| 50 tok/s | ✅ 163.84 Mbit/s | ✅ 163.84 Mbit/s | ✅ 163.84 Mbit/s |
| 100 tok/s | ✅ 327.68 Mbit/s | ✅ 327.68 Mbit/s | ✅ 327.68 Mbit/s |

**27B model — TP (32 layers), batch=64:**

| | 1 GbE | 2.5 GbE | 10 GbE |
|---|---|---|---|
| 10 tok/s | ✅ 131.07 Mbit/s | ✅ 131.07 Mbit/s | ✅ 131.07 Mbit/s |
| 50 tok/s | ✅ 655.36 Mbit/s | ✅ 655.36 Mbit/s | ✅ 655.36 Mbit/s |
| 100 tok/s | ✅ 1310.72 Mbit/s | ✅ 1310.72 Mbit/s | ✅ 1310.72 Mbit/s |

**27B TP batch=64 at 100 tok/s: 1310.72 Mbit/s > 1 GbE usable (1000 Mbit/s) — link-saturated on 1 GbE**

**27B TP batch=64 at 100 tok/s: 1310.72 Mbit/s ≈ 2.5 GbE usable (2500 Mbit/s) — ~52% saturated**

**Key finding:** PP is feasible across all ethernet classes for all batch sizes up to at least 100 tok/s. TP becomes bottlenecked on 1 GbE at batch=64 and 100 tok/s.

---

## 3. Why PP is the Only Realistic Option over Ethernet

### 3.1 Communication cost comparison

| Scheme | Communication per tok per rank | 27B, H=4096, batch=1 | 36B, H=6144, batch=1 |
|--------|------|---|---|
| PP (Nₚₚ boundaries) | Nₚₚ × H × 2 | Nₚₚ × 8 KB | Nₚₚ × 12 KB |
| TP (L layers all-reduce) | L × H × 2 | 32 × 8 KB = 256 KB | 48 × 12 KB = 576 KB |

PP communication per token is **L/Nₚₚ times smaller** than TP communication per token (factor of ~16× for 2 PP stages).

### 3.2 Latency-bound nature of autoregressive generation

During autoregressive generation, each layer computes one token at a time. In TP, every layer requires an all-reduce (2× ring latency or 1× tree latency per layer). For L=32 layers, that's 32 synchronization points per token.

In PP, activations cross the stage boundary only once per layer (or L/Nₚₚ times). The critical path is:

```
Stage 0 computes → send hidden state across boundary → Stage 1 computes → ...
```

This is a single bottleneck per token, with latency proportional to network RTT × number of stages, not L.

### 3.3 Bandwidth utilization

With PP, each boundary crossing transfers `H × 2` bytes. For 8 KB at 1 GbE, the transfer completes in ~68 µs. This is negligible compared to compute time (milliseconds per layer on a GPU). The link is underutilized.

With TP, each layer transfers `H × 2` bytes but this happens L times. For 256 KB total at 1 GbE, that's ~2 ms of pure transfer time — potentially comparable to compute time on a fast GPU.

### 3.4 Real-world evidence

- Petals uses PP exclusively over the public internet and achieves usable inference at 1–2 tok/s even with 100 Mbit/s links [1].
- llama.cpp RPC splits layers across nodes in pipeline order, not tensor sharding [2].
- exo uses TP but achieves speedup only with RDMA over Thunderbolt (~50 Gbit/s) [3].
- Petals paper Table 3: inference performance does **not depend much on bandwidth** (1 Gbit/s vs 100 Mbit/s gives nearly identical results) but **degrades significantly with higher latency** [1].

**Conclusion:** For gigabit-class ethernet, PP is the only practical multi-node parallelism strategy for inference. TP can work on 10 GbE for small batches but saturates at 1 GbE with moderate batch sizes.

---

## 4. Real-World Multi-Node Inference Benchmarks

### 4.1 Summary table

| System | Model | Hardware | # Nodes | Network | tok/s (batch=1) | Notes |
|--------|-------|----------|---------|---------|-----------------|-------|
| Petals (local) | BLOOM-176B | 3× A100 80GB | 3 | 1 Gbit/s, <5 ms RTT | 1.71 | PP, 22 stages, quantized [1] |
| Petals (local) | BLOOM-176B | 3× A100 80GB | 3 | 100 Mbit/s, <5 ms RTT | 1.66 | ~3% slowdown vs 1 Gbit/s [1] |
| Petals (local) | BLOOM-176B | 3× A100 80GB | 3 | 100 Mbit/s, 100 ms RTT | 1.23 | Latency matters more than BW [1] |
| Petals (wan) | BLOOM-176B | 14 consumer GPUs | 14 | Real internet, 100–1000 Mbit/s | 0.83 | Europe+N. America [1] |
| Petals | Llama 2 70B | consumer GPUs | various | Internet | up to 6 | Interactive chat [4] |
| Petals | Falcon 180B | consumer GPUs | various | Internet | up to 4 | Interactive chat [4] |
| llama.cpp RPC | Qwen3-235B | 4× M3 Ultra Mac Studio | 4 | Ethernet (2.5 GbE) | ~20 | Scales down with more nodes [3] |
| llama.cpp RPC | DeepSeek v3.1 | 4× M3 Ultra Mac Studio | 4 | Thunderbolt 5 | ~25 | Scales down with more nodes [3] |
| llama.cpp RPC | Kimi K2 (1T) | 4× M3 Ultra Mac Studio | 4 | Thunderbolt 5 | ~30 | A32B sparse, 32B active [3] |
| Exo (RDMA) | Qwen3-235B | 4× M3 Ultra Mac Studio | 4 | TB5 RDMA (~50 GbE) | 32 | TP, scales UP with more nodes [3] |
| Exo (RDMA) | DeepSeek v3.1 | 4× M3 Ultra Mac Studio | 4 | TB5 RDMA (~50 GbE) | ~30 | 671B dense TP [3] |
| vLLM PP | Llama-3-70B | 2× A100 80GB | 2 | NVLink + Ethernet | ~15 | PP across nodes, TP within [5] |

### 4.2 Detailed notes

**Petals [1]:**
- Uses pipeline parallelism with dynamic 8-bit quantization (halves bandwidth)
- For BLOOM-176B (H=14336), per-boundary communication is ~14 KB/tok with quantization
- Recommended bandwidth: 25 Mbit/s bidirectional for interactive inference [1]
- Key finding: "For inference, performance does not depend much on bandwidth or sequence length but degrades with higher latency" — RTT matters more than throughput
- At 1 Gbit/s with <5 ms RTT: 1.71 steps/s; at 100 Mbit/s with <5 ms: 1.66 steps/s (only 3% difference)
- At 100 Mbit/s with 100 ms RTT: 1.23 steps/s (28% degradation)

**llama.cpp RPC [2]:**
- Model weights and KV cache distributed across nodes proportionally to memory
- Default: pipeline-style distribution of layers (first layers on node A, last on node B)
- Each node runs `ggml-rpc-server`, main host uses `--rpc` flag
- RDMA transport supported (RoCEv2), negotiated automatically with libibverbs
- Over ethernet, performance decreases with more nodes (each extra node adds a hop)
- Over RDMA/TB5, performance scales up with more nodes (less latency per hop)

**Exo [3]:**
- Uses tensor parallelism with MLX distributed backend
- With RDMA over Thunderbolt 5: up to 1.8× speedup on 2 devices, 3.2× on 4 devices
- Topology-aware auto-parallelism considers latency/bandwidth between links
- Thunderbolt 5 provides ~50–60 GbE real-world throughput (RDMA)

**Key insight from all systems:** Ethernet (1 Gbit/s) is sufficient for PP inference of 20–40B models because per-token activation traffic is small (8–12 KB/boundary). The bottleneck is **latency** (RTT between nodes), not bandwidth.

---

## 5. Overheads

### 5.1 TCP/IP overhead

| Overhead | Amount |
|----------|--------|
| Ethernet header + trailer | 18 bytes (14 + 4 FCS) |
| IPv4 header (no options) | 20 bytes |
| TCP header (no options) | 20 bytes |
| Total per packet | ~58 bytes overhead |
| MTU (jumbo frames 9000) | 9000 bytes payload → 0.6% overhead |
| MTU (1500 standard) | 1500 bytes payload → 3.9% overhead |

**Practical impact:** For 8 KB transfers (27B PP boundary), use jumbo frames where possible to minimize TCP overhead. For small transfers (< 1.5 KB), a single TCP packet is used and the overhead is 58/8192 = 0.7% per transfer — negligible.

### 5.2 RPC/serialization overhead

- llama.cpp RPC: Protobuf serialization adds ~10–20% overhead for small tensors
- Petals: PyTorch tensor serialization over hivemind/gRPC, adds serialization time
- vLLM PP: gRPC with protobuf, similar overhead
- Serialization scales with tensor size: negligible for 8 KB+ tensors

### 5.3 Pipeline bubble overhead

With Nₚₚ pipeline stages and microbatching, the pipeline bubble fraction is:

```
bubble_fraction = (Nₚₚ - 1) / (Nₚₚ + microbatches - 1)
```

For 2 stages, 1 microbatch (single tok): bubble = 1/2 = 50% idle time.
For 2 stages, 8 microbatches: bubble = 1/9 = 11%.

In autoregressive generation with batch=1 and no microbatching, each stage processes one token sequentially:
- Stage 0 finishes, sends hidden state, waits for Stage 1
- Stage 1 processes, returns result, Stage 0 processes next token
- Effective utilization ≈ 1/Nₚₚ if no pipelining overlap

**Mitigation:** Process multiple tokens before waiting. Send next token to Stage 0 while Stage 1 is computing — pipelining reduces bubble.

### 5.4 Per-hop LAN latency

| Network | Typical RTT | One-way latency |
|---------|------------|-----------------|
| 1 GbE (Cat6) | 30–50 µs | 15–25 µs |
| 2.5 GbE (Cat6) | 30–50 µs | 15–25 µs |
| 10 GbE (Cat6a) | 20–30 µs | 10–15 µs |
| RoCEv2 (IB/25GbE) | 1–5 µs | <5 µs |
| RDMA (Thunderbolt 5) | 10–30 µs round-trip end-to-end | — |

**Impact on PP inference:** With Nₚₚ = 2 stages and batch=1, one token takes:
```
t_compute + t_roundtrip + t_compute
```

At 30 µs RTT and ~2 ms layer compute time per GPU: the network adds ~30 µs, which is 1.5% of total. Negligible at LAN speeds.

With Nₚₚ = 4 and 30 µs per-hop RTT: ~120 µs network, still <6% of compute time.

### 5.5 Quantization overhead

- Petals uses dynamic blockwise 8-bit quantization: halves hidden state bandwidth from 16-bit to 8-bit [1]
- For 27B: 8 KB → 4 KB per boundary with 8-bit quantization
- Accuracy impact: <1% on standard benchmarks [1]
- Quantization/dequantization adds ~1–5 ms per stage on modern GPUs (negligible vs. compute)

---

## 6. Conclusions and Recommendations

### For the 27B / 36B models on gigabit-class ethernet:

1. **1 GbE is sufficient for PP inference** up to at least 100 tok/s at batch=64 (81.92 Mbit/s required, well under 1000 Mbit/s capacity). Even with TCP/IP and RPC overheads, margin is >90%.

2. **Pipeline parallelism is the correct choice** over ethernet — PP sends 8–12 KB per boundary vs. 256–576 KB for TP, a 32× advantage for 2 PP stages.

3. **Latency matters more than bandwidth** — the Petals paper demonstrates that dropping from 1 Gbit/s to 100 Mbit/s only reduces throughput by ~3%, while increasing RTT from 5 ms to 100 ms reduces it by ~28%.

4. **With 8-bit quantization**, bandwidth requirements halve, providing additional safety margin.

5. **Jumbo frames recommended** to minimize TCP overhead on larger transfers.

6. **For batch sizes ≥ 16**, 1 GbE remains viable for PP but consider 2.5 GbE for headroom and faster model loading.

---

## References

[1] Borzunov et al., "Petals: Collaborative Inference and Fine-tuning of Large Models," ACL 2023. arXiv:2209.01188. Available at: https://arxiv.org/pdf/2209.01188 — Primary benchmark source: Table 3 shows inference throughput at various bandwidths and latencies for BLOOM-176B. Key finding: inference insensitive to bandwidth, sensitive to latency. Recommended 25 Mbit/s bidirectional bandwidth.

[2] ggml-org/llama.cpp RPC documentation. Available at: https://github.com/ggml-org/llama.cpp/blob/master/tools/rpc/README.md — Architecture for distributed LLM inference via RPC. Supports RDMA transport (RoCEv2), automatic negotiation, local tensor caching.

[3] exo-explore/exo README. Available at: https://github.com/exo-explore/exo — Multi-node LLM inference on Apple Silicon with TP and RDMA over Thunderbolt 5. Benchmarks with Qwen3-235B, DeepSeek v3.1, Kimi K2 on 4× M3 Ultra Mac Studio.

[4] Petals chatbot demo and health monitor. Available at: https://chat.petals.dev, https://health.petals.dev — Real-world performance of Llama 2 70B (up to 6 tok/s) and Falcon 180B (up to 4 tok/s) on public swarm.

[5] vLLM pipeline parallel documentation. Available at: https://docs.vllm.ai/en/stable/dev/engine/llm_engine.html — vLLM supports PP across nodes using gRPC with CUDA-graph support for low-latency stage transitions.

---

## Appendix: Full bandwidth formulae

### Pipeline Parallelism (generation, batch=1)

```
bytes_per_boundary_per_tok = hidden_size × 2   [fp16]
total_bytes_per_tok = num_boundaries × hidden_size × 2
bandwidth_mbps = total_bytes_per_tok × tokens_per_second × 8 / 1,000,000
```

### Pipeline Parallelism (generation, batch=N)

```
bytes_per_boundary_per_tok = hidden_size × N × 2
total_bytes_per_tok = num_boundaries × hidden_size × N × 2
```

### Tensor Parallelism (generation, batch=1)

```
bytes_per_layer_allreduce = hidden_size × 2
total_bytes_per_tok = num_layers × hidden_size × 2
bandwidth_mbps = total_bytes_per_tok × tokens_per_second × 8 / 1,000,000
```

### Tensor Parallelism (generation, batch=N)

```
total_bytes_per_tok = num_layers × hidden_size × N × 2
```

### With 8-bit quantization (like Petals)

```
# Simply divide all fp16 byte counts by 2
bytes_per_boundary_per_tok = hidden_size × 1   [int8]
```