Evaluating the Average-case Performance Penalty of Bandwidth-like Interfaces

Many solutions for composability and compositionality rely on specifying the interface for a component using bandwidth. Some previous works specify period (P) and budget (Q) as an interface for a component. Q/P provides us with a bandwidth (the share of a processor that this component may request); P specifies the time-granularity of the allocation of this processing capacity. Other works add another parameter deadline which can help to provide tighter bounds on how this processing capacity is distributed. Yet other works use the parameters a and D where a is the bandwidth and D specifies how smoothly this bandwidth is distributed. It is known [4] that such bandwidth-like interfaces carry a cost: there are tasksets that could be guaranteed to be schedulable if tasks were scheduled directly on the processor, but with bandwidth-like interfaces, it is impossible to guarantee the taskset to be schedulable. And it is also known that this penalty can be infinite, i.e., the use of bandwidth-like interfaces may require the use of a processor that has a speed that is k times faster, and one can show this for any k. This brings the question: "What is the average-case performance penalty of bandwidth-like interfaces?" This paper addresses this question. We answer the question by randomly generating tasksets and then for each of these tasksets, compute a lower bound on how much faster a processor needs to be when a bandwidth-like scheme is used. We do not consider any specific bandwidth-like scheme; instead, we derive an expression that states a lower bound on how much faster a processor needs to be when a bandwidth-like scheme is used. For the distributions considered in this paper, we find that (i) the experimental results depend on the experimental setup, (ii) this lower bound on the penalty was never larger than 4.0, (iii) for one experimental setup, for each taskset, it was greater than 2.4, (iv) the histogram of this penalty appears to be unimodal, and (v) for implicit-deadline sporadic tasks, this lower bound on the penalty was exactly 1.