Fork-join and split-merge queueing systems are mathematical abstractions of parallel task processing systems in which entering tasks are split into N subtasks which are served by a set of heterogeneous servers. The original task is considered completed once all the subtasks associated with it have been serviced. Performance of split-merge and fork-join systems are often quantified with respect to two metrics: task response time and subtask dispersion. Recent research effort has been focused on ways to reduce subtask dispersion, or the product of task response time and subtask dispersion, by applying delays to selected subtasks. Such delays may be pre-computed statically, or varied dynamically. Dynamic in our context refers to the ability to vary the delay applied to a subtask according to the state of the system, at any time before the service of that subtask has begun. We assume that subtasks in service cannot be preempted. A key dynamic optimisation that benefits both metrics of interest is to remove delays on any subtask with a sibling that has already completed service. This paper incorporates such a policy into existing methods for computing optimal subtask delays in split-merge and fork-join systems. In the context of two case studies, we show that doing so affects the optimal delays computed, and leads to improved subtask dispersion values when compared with existing techniques. Indeed, in some cases, it turns out to be beneficial to initially postpone the processing of non-bottleneck subtasks until the bottleneck subtask has completed service

This paper introduces a technique for minimising subtask dispersion in hidden stochastic PERT networks. The technique improves on existing research in two ways. Firstly, it enables subtask dispersion reduction in DAG structures, whereas previous techniques have only been applicable to single-layer split-merge or fork-join systems. Secondly, the exact distributions of subtask processing times do not need to be known, so long as there is some means of generating samples. The technique is further extended to use a metric which trades off subtask dispersion and task response time.

Abstract. Bennett has shown how to simulate arbitrary forwards-only computations by fully reversible computation. In particular he has given a space-efficient linear time simulation. After describing a different lineartime reversible simulation with improved space efficiency, we initiate the study of real-time simulations. In addition to being linear-time, these must offer continuous progress, meaning that the delay between successive forward events must be bounded by a constant.

This paper investigates various ways in which the triple trade-off metrics between task response time, subtask dispersion and energy can be improved in split-merge queueing systems. Four ideas, namely dynamic subtask dispersion reduction, state-dependent service times, multiple redundant subtask service servers and restarting subtask service, are examined in the paper. It transpires that all four techniques can be used to improve the triple trade-off, while combinations of the techniques are not necessarily beneficial.

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