The Tiered Algorithm is presented for time-efficient and message-efficient detection of process termination. It employs a global invariant of equality between process production and consumption at each level of process nesting to detect termination, regardless of execution interleaving order and network transit time. Correctness is validated for arbitrary process launching hierarchies, including launch-in-transit hazards, where processes are created dynamically based on runtime conditions for remote execution. The performance of the Tiered Algorithm is compared to three existing schemes with comparable capabilities, namely, the Chandrasekaran and Venkatesan (CV), Lai, Tseng, and Dong (LTD), and Credit termination detection algorithms. For synchronization of X tasks terminating in E epochs of idle processing, the tiered algorithm is shown to incur O(E) message count complexity and O(T lg T) message bit complexity while incurring detection latency corresponding to only integer addition and comparison. The synchronization performance in terms of message overhead, detection operations, and storage requirements are evaluated and compared across numerous task creation and termination hierarchies.

Efficient determination of processing termination at barrier synchronization points can occupy an important role in the overall throughput of parallel and distributed computing systems. Even though relatively efficient termination detection techniques have been proposed for certain environments, no effective performance analysis methodology has been introduced to determine application attributes that favor the use of a particular termination detection technique. This fact has hindered the adoption and development of termination detection schemes. This paper addresses this problem by developing a communication pattern based methodology to improve the precision of the theoretical performance of termination detection techniques in lieu of laborious experiments or potentially subjective benchmarking studies. By measuring message complexity from the idle period respect, it provides a simple and effective way to evaluate existing termination detection techniques or design new termination detection algorithms.