# B3 Routing Policies — Pseudocode

Reference: `scripts/cache_aware_proxy.py`. All five policies share the
same per-worker state machine; only the per-request `pick_instance_*`
function differs.

## Shared per-instance state

```text
inst.url
inst.ongoing_tokens        # sum of input_length across in-flight reqs
inst.pending_prefill_tokens
inst.ongoing_decode_tokens
inst.num_requests          # waiting + running
inst.cached_blocks         # LRU set of 512-token block hashes
inst.estimate_cache_hit(tokens) -> int
                           # longest prefix of `tokens` (in BLOCK_SIZE
                           # chunks) currently in cached_blocks
```

Each pick is one round-trip on every routing decision; counters are
mutated when a request starts/finishes, not inside the picker.

## 1. `lmetric` — main baseline

Pure per-request LMetric scoring. No session affinity, no
overload-break logic.

```text
def pick_lmetric(instances, token_ids, input_length):
    best, best_score = None, +inf
    for inst in instances:
        cache_hit   = inst.estimate_cache_hit(token_ids)
        new_prefill = max(0, input_length - cache_hit)
        p_tokens    = inst.pending_prefill_tokens + new_prefill
        bs          = inst.num_requests
        score       = p_tokens * bs
        if score < best_score:
            best, best_score = inst, score
    return best
```

Intuition: prefer the instance where the expected new prefill cost
times the running batch size is smallest. Cache hit reduces
`new_prefill`, so cache-warm workers win at equal load.

## 2. `load_only` — B3 control (no cache, no affinity)

```text
def pick_load_only(instances):
    return min(instances, key=lambda inst: inst.num_requests)
```

Ties: Python `min` returns the first-seen, so when `num_requests` is
equal across all instances (e.g. fresh start), pick always lands on
`instances[0]`. This produces unintentional stickiness at low
concurrency — the B3 lmetric/load_only comparison reads APC=54.1%
for load_only partly because of that.

## 3. `sticky` — B3 control (hard affinity)

Once a session is bound, never break the binding under any load.

```text
def pick_sticky(instances, session_id, affinity):
    if session_id in affinity:
        return instances[affinity[session_id]]  # unconditional
    chosen = min(instances, key=lambda i: i.num_requests)
    affinity[session_id] = index_of(chosen)
    return chosen
```

This is the upper bound on locality and the worst case on hot-spot
behavior — a single heavy session pins one worker forever.

## 4. `unified` — hybrid affinity + LMetric fallback

Sticks to the affinity worker only when the cache is genuinely warm
and the affinity worker is not overloaded; otherwise falls back to
LMetric with a 4-key tie-breaker.

```text
def pick_unified(instances, token_ids, input_length, session_id, affinity):
    avg_reqs = max(mean(inst.num_requests for inst in instances), 1.0)

    # Affinity gate (both must hold)
    if session_id in affinity:
        a = instances[affinity[session_id]]
        a_hit_ratio = a.estimate_cache_hit(token_ids) / max(input_length, 1)
        if a_hit_ratio > 0.5 \
                and a.num_requests <= avg_reqs * OVERLOAD_FACTOR:
            return a   # stick

    # LMetric fallback with multi-key tie-break
    keys = []
    for inst in instances:
        cache_hit   = inst.estimate_cache_hit(token_ids)
        new_prefill = max(0, input_length - cache_hit)
        p_tokens    = inst.pending_prefill_tokens + new_prefill
        bs          = inst.num_requests
        score       = p_tokens * bs
        keys.append((score, new_prefill, bs, idx_of(inst)))

    best_3tuple = min(k[:3] for k in keys)
    tied = [k for k in keys if k[:3] == best_3tuple]
    if len(tied) > 1:
        # Round-robin among ties so brand-new traffic doesn't pin
        # instance 0 when BS=0 across the board.
        winner = tied[_rr_counter % len(tied)]
        _rr_counter += 1
    else:
        winner = tied[0]
    return instances[winner.idx]
```

Tie-break ordering: `score` (LMetric primary), then `new_prefill`
(prefer the most cache-warm at equal score), then `num_requests`
(prefer least-loaded), then a global round-robin counter.

`OVERLOAD_FACTOR` defaults to 2.0; when the affinity worker is
above 2× average load, the picker treats it as overloaded and steers
away.

## 5. `capped` — `lmetric` on a session-mass-capped trace

Not a new picker. The picker is the same `pick_lmetric` from §1; the
input trace is preprocessed.

```text
def build_capped_trace(input_path, output_path, MAX_TURNS=8):
    by_session = group_by_session_id(load(input_path))
    capped = []
    for sid, turns in by_session.items():
        turns.sort_by(lambda t: (t.turn_id, t.timestamp))
        capped.extend(turns[:MAX_TURNS])
    capped.sort_by(timestamp)        # restore wall-clock order
    write_jsonl(capped, output_path)

# At run time:
trace      = build_capped_trace("w600_r0.0015_st30.jsonl")
picker     = pick_lmetric
```

For this trace `MAX_TURNS=8` truncates the heavy-tail sessions (full
trace turns/session p90=1, p99=18, max=3091). The intent is to
isolate "what does LMetric look like when no session is heavy
enough to hot-spot a worker?" — comparing capped vs lmetric is the
session-mass ablation.

## Decision matrix

|  | session affinity | cache aware | load aware | overload break |
|---|---|---|---|---|
| `lmetric` | ✗ | ✓ (via `cache_hit` → `new_prefill`) | ✓ (`num_requests` BS factor) | n/a |
| `load_only` | ✗ | ✗ | ✓ (`num_requests` only) | n/a |
| `sticky` | ✓ (hard) | ✗ (relies on physical hits, not scoring) | only on first turn | **never** |
| `unified` | ✓ (gated) | ✓ | ✓ | gate: `cache_ratio>0.5` AND `num_req ≤ 2× avg` |
| `capped` | same as `lmetric`; the trace itself is truncated | | | |

## What each control isolates

- `lmetric` vs `load_only` → contribution of cache awareness alone.
- `lmetric` vs `sticky` → contribution of session affinity vs
  per-request LMetric scoring at the cost of hot-spot.
- `lmetric` vs `unified` → did adding gated session affinity help?
- `lmetric` vs `capped` → how much of the residual hot-spot in
  `lmetric` is driven by heavy-tail sessions specifically?