[Bugfix] Fix multi-turn benchmark's sleep to match the configured request rate

[nikonyrh-siloai]

Purpose

The average sleep at benchmarks/multi_turn/benchmark_serving_multi_turn.py is always 1 / request_rate, but this doesn't take into account the time that was spent on waiting for server's response. E.g. at request rate of 10 / minute, if server's response takes two seconds, then we should sleep for four seconds. Then we are sending a request on average every six seconds.

Test Plan

Run the script before and after the patch, and compare the reported requests / second to the configured one.

# The target is 2 requests / second:
python benchmark_serving_multi_turn.py \
  --model deepseek-ai/DeepSeek-V3 \
  --input-file config.json \
  --num-clients 20 \
  --request-rate 0.1 \
  --max-active-conversations 200 \
  --max-num-requests 360

Test Result

This fixes the discrepancy. The issue is worse on bigger loads, but already seen at 2 requests / second.

Before fix: Estimated req/sec 1.790
After fix: Estimated req/sec 2.015

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• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model.

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[gemini-code-assist]

Code Review

This pull request refactors the request timing logic in the multi-turn benchmark to implement a compensating delay, ensuring the target request rate is maintained by accounting for request duration. The poisson_sleep function was updated to accept a mean interval, and the client logic now calculates the remaining sleep time after each request. Feedback suggests that when the calculated interval is non-positive, the function should yield control to the event loop using await asyncio.sleep(0) to prevent a single client from monopolizing the loop and starving others.

[gemini-code-assist]

Code Review

This pull request refactors the poisson_sleep function and its usage in the multi-turn benchmark to more accurately maintain request rates by accounting for the duration of the requests themselves. It also updates the logging to support custom headers and color-coded output. A review comment identifies a technical inaccuracy in the documentation of poisson_sleep, noting that the inter-arrival times follow an exponential distribution rather than a Poisson distribution, and provides a suggestion to correct the comment.

[gemini-code-assist]

The comment incorrectly states that the interval is generated from a Poisson distribution. In a Poisson process, the number of events in a fixed interval follows a Poisson distribution, while the time between events follows an Exponential distribution. Since np.random.exponential is used, the comment should be updated for accuracy.

Suggested change

	async def poisson_sleep(mean_interval: float, verbose_header: str = None) -> None:
	# Generate a random time interval from the Poisson distribution
	async def poisson_sleep(mean_interval: float, verbose_header: str = None) -> None:
	# Generate a random time interval from the exponential distribution