A recent paper by Gaver et al. 6 argued the importance of studying service control problems in which the usual assumptions (i) that tasks will wait indefinitely for service and (ii) that successful service completions can be observed instantaneously are relaxed. Military and other applications were cited. They proposed a model in which arriving tasks are available for service for a period whose duration is unknown to the system's controller. The allocation of a large amount of processing to a task may make more likely its own successful completion but may also result in the loss of many unserved tasks from the system. Gaver et al. 6 called for the design of dynamic policies for the allocation of service which maximizes the rate of successful task completions achieved, or which come close to doing so. This is the theme of the paper. We utilize dynamic programming policy improvement approaches to design heuristic dynamic policies for service allocation which may be easily computed. In all cases studied, these policies achieve throughputs close to optimal. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008