We consider the problem of scheduling dependent real-time tasks for overloads on a multiprocessor system, yielding best-effort timing assurance. The application/scheduling model includes tasks with time/utility function time constraints, mutual exclusion constraints, and arbitrary arrival, execution-time and resource access behaviors, with the timeliness optimization objective of maximizing the total accrued utility while ensuring mutual exclusion constraints and deadlock-freedom. Since this problem is NP-hard, we develop a class of polynomial-time heuristic algorithms, called the Global Utility Accrual (GUA) class of algorithms, and present two algorithm instances, namely, Non-Greedy Global Utility Accrual (NG-GUA) and Greedy Global Utility Accrual (G-GUA). We establish several properties of the algorithms including conditions under which optimal total utility is accrued, mutual exclusion constraints are satisfied, and deadlock-freedom is achieved. We develop a Linux-based real-time k...