Warmup and Benchmark User ID Overlap Causes Prefix Cache Hits

Nobody has claimed this yet.

**File:** `synthetic-multi-round-qa/long_input_short_output_run.sh`

## Summary

The warmup and benchmark phases use the same `--init-user-id`, causing user ID overlap. When vLLM's prefix caching is enabled, the first benchmark request gets a cache hit from warmup, showing ~60ms TTFT instead of the expected ~4-16 seconds for 21,000-token prompts.

## Bug Location

```bash
# Lines 48 and 69 both use the same INIT_USER_ID
warmup() {
python3 ... --init-user-id "$INIT_USER_ID" ... # Line 48
}

run_benchmark() {
warmup
python3 ... --init-user-id "$INIT_USER_ID" ... # Line 69 - same value
INIT_USER_ID=$(( INIT_USER_ID + NUM_USERS_WARMUP )) # Incremented after, not between
}
```

## Why User 97?

With `INIT_USER_ID=81`:
- **Warmup** (10s, `gap_between_users=0.5s`): spawns users 83, 84, ... ~102
- **Benchmark** `_ramp_up()`: creates users 82-96 with virtual history
- Users 83-96 are mid-conversation (no cache hit possible)
- User 82 has largest offset → `question_id=20=num_rounds` → already "done" at t=0
- **Benchmark** replaces "done" user 82 with fresh spawn: user 97

User 97 exists in both warmup and benchmark with identical 21k-token prompts → vLLM prefix cache hit.

## Evidence

Every benchmark run has exactly one request with impossible ~60ms TTFT for 21,000 tokens:

| QPS | 1st Request TTFT | 2nd Request TTFT | Prompt Tokens |
|-----|------------------|------------------|---------------|
| 0.25 | 0.061s | 4.84s | 21,045 |
| 0.5 | 0.058s | 11.24s | 21,045 |
| 1.0 | 0.060s | 14.60s | 21,045 |
| 2.0 | 0.058s | 16.12s | 21,046 |

60ms for 21,000 tokens = 350,000 tokens/sec prefill

## Reproduction

1. Start vLLM:
```bash
vllm serve --port 8000 --gpu-memory-utilization 0.80 --max-model-len 32000 Qwen/Qwen3-8B
```
2. Run:
```bash
./long_input_short_output_run.sh Qwen/Qwen3-8B http://localhost:8000 ./test_output 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0
```
3. Check each `test_output_output_*.csv`: first request has ~60ms TTFT, second has ~4000ms+

## Potential Fix

Add increment between warmup and benchmark:

```bash
run_benchmark() {
warmup
INIT_USER_ID=$(( INIT_USER_ID + NUM_USERS_WARMUP )) # ADD: skip past warmup users
python3 ... --init-user-id "$INIT_USER_ID" ...
sleep 10
INIT_USER_ID=$(( INIT_USER_ID + NUM_USERS_WARMUP )) # KEEP: skip past benchmark users
}
```

warmup.csv (User 97)
```python
prompt_tokens,generation_tokens,ttft,generation_time,user_id,question_id,launch_time,finish_time
21045.0,100.0,66.03855228424072,26.03457522392273,97,1,1768228281.4217596,1768228373.4948874
```
output.csv (User 97)
```python
prompt_tokens,generation_tokens,ttft,generation_time,user_id,question_id,launch_time,finish_time
21045.0,100.0,0.06429886817932129,29.62334132194519,97,1,1768228377.583655,1768228407.2712955
```

Full Warmup
```python
prompt_tokens,generation_tokens,ttft,generation_time,user_id,question_id,launch_time,finish_time
21045.0,100.0,4.0325767993927,30.620036840438843,83,1,1768228274.410371,1768228309.062985
21045.0,100.0,7.745214462280273,31.387547969818115,84,1,1768228274.9116695,1768228314.0444322
21045.0,100.0,11.579217433929443,32.04589629173279,85,1,1768228275.4124584,1768228319.0375724
21045.0,100.0,15.546088457107544,32.542940616607666,86,1,1768228275.9133482,1768228324.0023775
21045.0,100.0,19.24747633934021,32.79804229736328,87,1,1768228276.4143176,1768228328.4598362
21045.0,100.0,23.450685024261475,33.05583620071411,88,1,1768228276.9149776,1768228333.4214993
21045.0,100.0,27.83380889892578,33.13601541519165,89,1,1768228277.415833,1768228338.3856573
21045.0,100.0,33.816718101501465,33.097196102142334,90,1,1768228277.9167144,1768228344.8306289
21045.0,100.0,38.28431248664856,33.11025857925415,91,1,1768228278.4174414,1768228349.812013
21045.0,100.0,42.73971652984619,32.667768478393555,92,1,1768228278.9180489,1768228354.325534
21045.0,100.0,46.781073331832886,32.58684802055359,93,1,1768228279.418835,1768228358.7867563
21045.0,100.0,51.220503091812134,32.61380910873413,94,1,1768228279.9195848,1768228363.7538974
21045.0,100.0,55.66105651855469,32.631749391555786,95,1,1768228280.4203286,1768228368.7131348
21045.0,100.0,60.10296177864075,30.73545265197754,96,1,1768228280.9210896,1768228371.7595043
21045.0,100.0,66.03855228424072,26.03457522392273,97,1,1768228281.4217596,1768228373.4948874
21045.0,100.0,70.10655903816223,21.79459857940674,98,1,1768228281.9224482,1768228373.8236058
21045.0,100.0,74.58828473091125,17.163147926330566,99,1,1768228282.4232018,1768228374.1746347
21046.0,100.0,79.03585720062256,12.499950408935547,100,1,1768228282.923967,1768228374.4597747
21046.0,100.0,83.47929239273071,7.807913780212402,101,1,1768228283.424782,1768228374.7119882
21046.0,100.0,87.65989756584167,3.3384878635406494,102,1,1768228283.9255624,1768228374.9239478
```

Full Benchmark
```python
prompt_tokens,generation_tokens,ttft,generation_time,user_id,question_id,launch_time,finish_time
21046.0,100.0,15.451107740402222,32.98561429977417,83,1,1768228380.7874646,1768228429.224187
21173.0,100.0,59.79264044761658,33.4884295463562,83,2,1768228429.2511828,1768228522.532253
21046.0,100.0,32.88628697395325,33.44575047492981,84,1,1768228383.9910362,1768228450.3230739
21173.0,100.0,63.26081323623657,33.09952783584595,84,2,1768228450.3874269,1768228546.747768
21046.0,100.0,49.24628400802612,32.93089699745178,85,1,1768228387.1946235,1768228469.3718047
21173.0,100.0,75.51643824577332,8.048285722732544,85,2,1768228469.423379,1768228552.9881034
21046.0,100.0,4.300148248672485,31.531845569610596,86,1,1768228378.3848696,1768228414.216864
21172.0,100.0,53.35515594482422,33.377912521362305,86,2,1768228414.2351642,1768228500.9682329
21046.0,100.0,19.02207589149475,33.119444847106934,87,1,1768228381.5882692,1768228433.72979
21172.0,100.0,60.35233736038208,33.05792427062988,87,2,1768228433.7558215,1768228527.1660833
21046.0,100.0,37.06291079521179,33.533162355422974,88,1,1768228384.7920196,1768228455.388093
21173.0,100.0,69.83038926124573,26.496456146240234,88,2,1768228455.3932168,1768228551.7200623
21046.0,100.0,53.433995723724365,32.9296555519104,89,1,1768228387.9958158,1768228474.359467
21172.0,100.0,75.38190579414368,3.390859842300415,89,2,1768228474.4290762,1768228553.201842
21046.0,100.0,7.909069776535034,32.09600353240967,90,1,1768228379.1858044,1768228419.190878
21173.0,100.0,53.3221390247345,33.405515909194946,90,2,1768228419.2401805,1768228505.9678357
21045.0,100.0,23.115331172943115,33.24005389213562,91,1,1768228382.3890383,1768228438.7444239
21171.0,100.0,64.90626335144043,33.02594494819641,91,2,1768228438.772832,1768228536.7050407
21045.0,100.0,41.262274980545044,33.08293962478638,92,1,1768228385.592925,1768228459.93814
21170.0,100.0,70.32939887046814,21.833589553833008,92,2,1768228459.998516,1768228552.1615045
21045.0,100.0,57.610445976257324,32.932292222976685,93,1,1768228388.7965636,1768228479.3393018
21045.0,100.0,11.610830545425415,32.60366344451904,94,1,1768228379.9866097,1768228424.201104
21171.0,100.0,58.282360553741455,33.435781955718994,94,2,1768228424.245589,1768228515.9637315
21045.0,100.0,27.26021122932434,33.28636121749878,95,1,1768228383.1898859,1768228443.7364585
21171.0,100.0,64.88479328155518,33.054969787597656,95,2,1768228443.7790673,1768228541.7188306
21045.0,100.0,45.05794095993042,32.94720673561096,96,1,1768228386.3938456,1768228464.3989935
21170.0,100.0,70.52046370506287,17.526437044143677,96,2,1768228464.4031951,1768228552.4500961
21045.0,100.0,0.06429886817932129,29.62334132194519,97,1,1768228377.583655,1768228407.2712955
21170.0,100.0,50.73230814933777,32.89437675476074,97,2,1768228407.317312,1768228490.9439971
21045.0,100.0,60.204896211624146,33.36027669906616,98,1,1768228392.8007195,1768228486.3658926
21045.0,100.0,54.6002357006073,33.348283529281616,99,1,1768228408.0283864,1768228495.9769058
21046.0,100.0,54.27728247642517,33.447853088378906,100,1,1768228423.2444117,1768228510.9695475
21046.0,100.0,60.22674560546875,32.98647689819336,101,1,1768228438.4724448,1768228531.6856675
21046.0,100.0,64.96357321739197,31.338298559188843,102,1,1768228453.6917243,1768228549.9935963
21046.0,100.0,71.00475406646729,12.809065818786621,103,1,1768228468.922831,1768228552.7366512
```

Start in synthetic-multi-round-qa/long_input_short_output_run.sh, especially run_benchmark() and its INIT_USER_ID updates around the warmup call. Reproduce with the provided vLLM command and benchmark invocation, then verify that warmup and benchmark users do not overlap and that the first benchmark request no longer gets an unexpected prefix-cache TTFT.

Written by the indexing model from the issue text.