chore: Implement singleton pattern for enginestatscraper, requeststatsmonitor, and router

[gaocegege]

Currently, we depend on a global variable to manage instances of EngineStatsScraper, RequestStatsMonitor, and Router. We should initialize this variable within the vllm_router.router.InitializeAll function.

https://github.com/vllm-project/production-stack/blob/c8cdf9de34b21532089146148efafefbec84d46e/src/vllm_router/router.py#L423:#L431

To enhance our design, we could implement a singleton pattern for these components. By doing so, we would ensure that only one instance of each class exists throughout the application lifecycle. This approach can help prevent potential issues related to state management and resource usage.

For more information on various methods to implement singletons in Python, you can refer to this Stack Overflow discussion.

[sitloboi2012]

@gaocegege could you assign this to me as well so I can do it next because it's gonna link with what I'm currently doing with the Router Observability (need to modify the EngineStat, RequestStat, etc.) 😄 Seems like we will need some sort of dashboard to keep up who is doing what lol 😆