test: benchmark scripts (#3160)

# What does this PR do?
1. Add our own benchmark script instead of locust (doesn't support
measuring streaming latency well)
2. Simplify k8s deployment
3. Add a simple profile script for locally running server

## Test Plan
❮ ./run-benchmark.sh --target stack --duration 180 --concurrent 10

============================================================
BENCHMARK RESULTS
============================================================
Total time: 180.00s
Concurrent users: 10
Total requests: 1636
Successful requests: 1636
Failed requests: 0
Success rate: 100.0%
Requests per second: 9.09

Response Time Statistics:
  Mean: 1.095s
  Median: 1.721s
  Min: 0.136s
  Max: 3.218s
  Std Dev: 0.762s

Percentiles:
  P50: 1.721s
  P90: 1.751s
  P95: 1.756s
  P99: 1.796s

Time to First Token (TTFT) Statistics:
  Mean: 0.037s
  Median: 0.037s
  Min: 0.023s
  Max: 0.211s
  Std Dev: 0.011s

TTFT Percentiles:
  P50: 0.037s
  P90: 0.040s
  P95: 0.044s
  P99: 0.055s

Streaming Statistics:
  Mean chunks per response: 64.0
  Total chunks received: 104775

docs/source/distributions/k8s-benchmark/README.md

@@ -0,0 +1,156 @@
+# Llama Stack Benchmark Suite on Kubernetes
+
+## Motivation
+
+Performance benchmarking is critical for understanding the overhead and characteristics of the Llama Stack abstraction layer compared to direct inference engines like vLLM.
+
+### Why This Benchmark Suite Exists
+
+**Performance Validation**: The Llama Stack provides a unified API layer across multiple inference providers, but this abstraction introduces potential overhead. This benchmark suite quantifies the performance impact by comparing:
+- Llama Stack inference (with vLLM backend)
+- Direct vLLM inference calls
+- Both under identical Kubernetes deployment conditions
+
+**Production Readiness Assessment**: Real-world deployments require understanding performance characteristics under load. This suite simulates concurrent user scenarios with configurable parameters (duration, concurrency, request patterns) to validate production readiness.
+
+**Regression Detection (TODO)**: As the Llama Stack evolves, this benchmark provides automated regression detection for performance changes. CI/CD pipelines can leverage these benchmarks to catch performance degradations before production deployments.
+
+**Resource Planning**: By measuring throughput, latency percentiles, and resource utilization patterns, teams can make informed decisions about:
+- Kubernetes resource allocation (CPU, memory, GPU)
+- Auto-scaling configurations
+- Cost optimization strategies
+
+### Key Metrics Captured
+
+The benchmark suite measures critical performance indicators:
+- **Throughput**: Requests per second under sustained load
+- **Latency Distribution**: P50, P95, P99 response times
+- **Time to First Token (TTFT)**: Critical for streaming applications
+- **Error Rates**: Request failures and timeout analysis
+
+This data enables data-driven architectural decisions and performance optimization efforts.
+
+## Setup
+
+**1. Deploy base k8s infrastructure:**
+```bash
+cd ../k8s
+./apply.sh
+```
+
+**2. Deploy benchmark components:**
+```bash
+cd ../k8s-benchmark
+./apply.sh
+```
+
+**3. Verify deployment:**
+```bash
+kubectl get pods
+# Should see: llama-stack-benchmark-server, vllm-server, etc.
+```
+
+## Quick Start
+
+### Basic Benchmarks
+
+**Benchmark Llama Stack (default):**
+```bash
+cd docs/source/distributions/k8s-benchmark/
+./run-benchmark.sh
+```
+
+**Benchmark vLLM direct:**
+```bash
+./run-benchmark.sh --target vllm
+```
+
+### Custom Configuration
+
+**Extended benchmark with high concurrency:**
+```bash
+./run-benchmark.sh --target vllm --duration 120 --concurrent 20
+```
+
+**Short test run:**
+```bash
+./run-benchmark.sh --target stack --duration 30 --concurrent 5
+```
+
+## Command Reference
+
+### run-benchmark.sh Options
+
+```bash
+./run-benchmark.sh [options]
+
+Options:
+  -t, --target <stack|vllm>     Target to benchmark (default: stack)
+  -d, --duration <seconds>      Duration in seconds (default: 60)
+  -c, --concurrent <users>      Number of concurrent users (default: 10)
+  -h, --help                    Show help message
+
+Examples:
+  ./run-benchmark.sh --target vllm              # Benchmark vLLM direct
+  ./run-benchmark.sh --target stack             # Benchmark Llama Stack
+  ./run-benchmark.sh -t vllm -d 120 -c 20       # vLLM with 120s, 20 users
+```
+
+## Local Testing
+
+### Running Benchmark Locally
+
+For local development without Kubernetes:
+
+**1. Start OpenAI mock server:**
+```bash
+uv run python openai-mock-server.py --port 8080
+```
+
+**2. Run benchmark against mock server:**
+```bash
+uv run python benchmark.py \
+  --base-url http://localhost:8080/v1 \
+  --model mock-inference \
+  --duration 30 \
+  --concurrent 5
+```
+
+**3. Test against local vLLM server:**
+```bash
+# If you have vLLM running locally on port 8000
+uv run python benchmark.py \
+  --base-url http://localhost:8000/v1 \
+  --model meta-llama/Llama-3.2-3B-Instruct \
+  --duration 30 \
+  --concurrent 5
+```
+
+**4. Profile the running server:**
+```bash
+./profile_running_server.sh
+```
+
+
+
+### OpenAI Mock Server
+
+The `openai-mock-server.py` provides:
+- **OpenAI-compatible API** for testing without real models
+- **Configurable streaming delay** via `STREAM_DELAY_SECONDS` env var
+- **Consistent responses** for reproducible benchmarks
+- **Lightweight testing** without GPU requirements
+
+**Mock server usage:**
+```bash
+uv run python openai-mock-server.py --port 8080
+```
+
+The mock server is also deployed in k8s as `openai-mock-service:8080` and can be used by changing the Llama Stack configuration to use the `mock-vllm-inference` provider.
+
+## Files in this Directory
+
+- `benchmark.py` - Core benchmark script with async streaming support
+- `run-benchmark.sh` - Main script with target selection and configuration
+- `openai-mock-server.py` - Mock OpenAI API server for local testing
+- `README.md` - This documentation file