Queueing Theory

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TODO: 2018.07.20 - The Essential Guide to Queueing Theory.pdf in Learning.

Overview

Queueing in Pipelines

This section discusses queueing for pipelines.

A pipeline consists in a series of stages, which process a stream of data fed into the pipeline. If there are no buffers (queues) between stages, a slow stage will block the upstream stages from working. This is because a slow stage will be unable to process, thus accept a new stream element from the upstream stage, making the upstream stage unable to hand over the stream element, thus blocking it. The delay will propagate upstream in the pipeline, possibly all the way to the pipeline input, preventing new stream elements to be processed altogether. Introducing queues seems like an obvious optimization, but in most situation, this is actually not the case.

Queueing is the technique of storing stream elements in a temporary location in memory, after they have been processed by a stage, so that other stage can retrieve it later. The producing stage does not hold a reference to the processed stream elements.

Decoupling

Introducing queues between stages makes possible to hold data stream elements processed by an upstream stage, while the downstream stage is still busy, thus freeing up the upstream stage to continue doing work. Queues decouple stages. However, if the difference in processing speed remains constant, the queue will fill up after a while, so introducing the queue will only delay blocking the upstream stage, not eliminate it.

Queueing and Overall Pipeline Performance

Adding queueing between the pipeline stages will almost never speed up the pipeline. It will only allow it to behave differently. The effect of introducing queues is that the time spent in a blocking state of the stage upstream of the queue is reduced.

Queueing and Synchronization Issues

Adding queueing prematurely can hide synchronization issues such as deadlocks and livelocks. As the program converges towards correctness, you may find that you need more or less queueing.

Queue Tuning

Pipeline Throughput