Dynamic mapping (matching and scheduling) heuristics for a class of independent tasks using heterogeneous distributed computing systems are studied. Two types of mapping heuristics are considered, immediate mode and batch mode heuristics. Three new heuristics, one for batch mode and two for immediate mode, are introduced as part of this research. Simulation studies are performed to compare these heuristics with some existing ones. In total five immediate mode heuristics and three batch mode heuristics are examined. The immediate mode dynamic heuristics consider, to varying degrees and in different ways, task affinity for different machines and machine ready times. The batch mode dynamic heuristics consider these factors, as well as aging of tasks waiting to execute. The simulation results reveal that the choice of which dynamic mapping heuristic to use in a given heterogeneous environment depends on parameters such as (a) the structure of the heterogeneity among tasks and machines and (b) the arrival rate of the tasks. © 1999 Academic Press.