Web task manager?

Question

Task Management

In addition to the standard ones, I really want to have the following feature:
A task is assigned a priority, an estimated duration, and an executor.
Tasks, for each performer, are automatically lined up according to priority. Accordingly, the system itself
is able to answer / show when a particular task is expected in accordance with its priority, complexity and workload of the performer with other tasks. The system must be installed on its own server and work on the web (not microsoft). If not free, at least not very expensive.

Answer 1

Redmine

Answer 2

+1 for Jira, it's pretty flexible.

Answer 3

Yes, on the same little-known resource habr: D Jira is spinning in advertising banners. It is not a problem to create a list of assigned tasks on the dashboard sorted by time and priority.