Design an hourly call-agent scheduler

Problem Statement

You are building a scheduler for a call-agent platform. You are given a list of tasks (calls), where each task has a start_time and a duration (in hours). You also have a set of agents available to handle these calls.

Constraints:

1. Each agent can handle at most one call at any given time.
2. Each task must be assigned to an agent who is available for the entire duration of the task.
3. A single customer (identified by customer_id) can have multiple calls, but they cannot have more than max_concurrency calls occurring simultaneously.

Implement a function schedule_tasks(tasks, max_concurrency) that returns a dictionary mapping task_id to agent_id. If it is impossible to schedule all tasks, return an empty dictionary.

Input Format

• tasks: A list of dictionaries: [{'task_id': int, 'customer_id': int, 'start_time': int, 'duration': int}, ...]
• max_concurrency: An integer representing the limit of simultaneous calls per customer.

Example

tasks = [
    {'task_id': 1, 'customer_id': 101, 'start_time': 0, 'duration': 2},
    {'task_id': 2, 'customer_id': 101, 'start_time': 1, 'duration': 2}
]
# If max_concurrency = 1, these cannot be scheduled together.

Constraints

• 0 <= start_time < 24
• 1 <= duration <= 24
• 1 <= len(tasks) <= 1000
• Time is measured in integer hourly blocks.