Task Scheduling Critical Path

You are given a collection of tasks, where each task is represented as an object with the following properties:

• id: A unique identifier for the task (string or integer).
• duration: A non-negative integer representing the time required to complete the task.
• prerequisites: An array of task identifiers which must be completed before this task can start.

Assume that the collection of tasks forms a Directed Acyclic Graph (DAG), meaning there are no circular dependencies.

Your task is to write a function that computes the minimum total time required to complete all tasks, given that multiple tasks can be executed concurrently as long as all of their prerequisites have been met.

For example, consider designing the function interface as follows:

# Example in Python

def minimum_completion_time(tasks: List[Dict]) -> int:
    # Your implementation here
    pass

Please implement your solution in a programming language of your choice. The function should take in the list of tasks and return the minimum total time required to complete all the tasks. Ensure that your solution correctly handles concurrency given the dependency constraints.

Good luck!