Issues with _pid and router._producers causing worker idling and errors

**Description:**
I have encountered a couple of issues in the current codebase that are impacting the proper functioning of the application. I am planning to create a Pull Request to address these concerns, and I wanted to document them here for better visibility and discussion.

1. The `_pid`s of workers are currently `undefined`, preventing the proper distribution of routers across different workers. As a result, all workers except one are idled. This is a critical issue as it significantly impacts the efficiency of the system.

2. After adding `_pid`s to workers, when piping producers to routers, the expression `router._producers.has(producerId)` is throwing errors. This error disrupts the expected flow of data distribution and must be addressed to ensure the smooth operation of the application.

**Expected Behavior:**
1. Workers should have valid `_pid`s to enable proper distribution of routers.
2. Piping producers to routers should not result in errors related to `router._producers.has(producerId)`.

I will be working on creating a Pull Request to fix these issues.

**Note to Reviewers:**
I am in the process of creating a Pull Request to address these issues. Your insights and guidance during the review process will be invaluable.

Thank you!

Start by tracing the worker setup and router producer-piping path described in the issue, then reproduce the undefined worker IDs and the router._producers.has(producerId) error. Done means workers have valid IDs for router distribution and producer piping completes without that error; no file or test paths are named in the issue.

Written by the indexing model from the issue text.