A Unified Framework for Theoretical and Experimental Evaluation of Classical and Modern Sorting Algorithms in Real-Time Systems

This paper presents a theoretical and experimental evaluation of eight popular sorting algorithms HeapSort, QuickSort, MergeSort, Parallel MergeSort, TimSort, IntroSort, Bitonic Sort, and MSD Radix Sort—assessing their suitability for real-time computing environments. The study combines algorithmic analysis with large-scale benchmarks across various input distributions (random, almost sorted, reverse-sorted) and data scales, focusing on execution time and memory usage. Results show that hybrid and adaptive algorithms outperform classical ones. TimSort had the shortest execution times (as low as 1.0 ms on sorted data), and IntroSort showed consistent performance across data types (11-13 ms on random inputs) with minimal memory (<7.90 MB). HeapSort maintained predictable O (n log n) behavior, suitable for hard real-time constraints, while QuickSort and MergeSort had lower latency but higher memory usage. These findings are significant for latency-sensitive applications like high-frequency trading and sensor data processing. The study recommends using hybrid algorithms like TimSort and IntroSort for general-purpose workloads, providing evidence-based guidance for real-time system design.