[cadynce] Model CPU Utlizations Predict End-to-End Times

[Gautam Thaker]

Raj Rajkumar wrote:
> Hi Alan, Patrick and Gautam:
> 
> Can we have a short discussion about computing e2e times in general?  I 
> apologize if this was discussed in some recent meetings and/or telecons; 
> I may not have been present when these discussions occurred.
> 
> Clearly, e2e delay is a sum of delay components along the entire path 
> (processors and links) of an application string.  There are worst-case 
> and average-case considerations.
> 
> Beyond the above, real-time scheduling theory holds that when individual 
> components have different arrival rates (e.g. periods), execution times 
> and a scheduling policy (preemptive or not, fixed priority or not), the 
> response time for a task on a processor (or a communication link) is a 
> function of not just utilizations but also the individual parameters 
> (C's and T's of the task at hand + all its higher priority tasks, not 
> just the total utilization).   Just having e2e times be a function of 
> utilizations runs counter to scheduling theory (+ real measurements, one 
> would argue).
> 
> Thoughts?  Thanks,

Hi Raj:

I think Alan was probably not suggesting that traditional scheduling 
theory be dropped in any way but just seeking to understand the current 
data better. Thus, i see his use of 6 CPU utils as just something he is 
looking at for the time being. I am not surprised if good model fit can 
be found for *average* end to end time and CPU loads.

I believe we do have enough time in CADYNCE the seedling to talk of all 
these things. we can do more teleconferences or propose a 1 day meeting, 
no one has yet responded to my proposal for June 5th (though may be best 
to wait till Todd's May 24th meeting to see what is best.)

Gautam

> 
> ---
> Raj
> 
> Alan F. Karr wrote:
>> Patrick,
>>
>> This is an investigation the extent to which the CPU utilizations 
>> given the the models predict the measured end-to-end times (averaged 
>> over messages--we will do the worst case times today). Everything is 
>> restricted to the critical path. The model is in R-like notation: the 
>> six CPU utilizations are the predictor (independent) variables. The 
>> six coefficients are implied. I've revised the PPT to try to make this 
>> a bit clearer, and will put it on the wiki. It's also attached, since 
>> it's so small.
>>
>> --- Alan
>>
>> Patrick Lardieri wrote:
>>> Hi Alan,
>>>
>>> Interesting thoughts that I am not sure I understand fully.
>>>
>>> At the 100,000 ft level it seems you are offering an alternative to 
>>> scheduling theory to predict the response time.  Specifically, you 
>>> seem to be suggesting that a linear regression model could be used to 
>>> predict the mean end-to-end response time of an appstring by 
>>> considering the  CPU utilizations  of the critical path components  
>>> as the independent variables.  Is this correct?
>>>
>>> A couple of questions:
>>>
>>> 1) It is not clear in the slide what the independent variables really 
>>> are. Are the the software components specified worst case execution 
>>> time? The software component's measured mean execution time? The 
>>> utilization on the CPU that the application runs on?
>>>
>>> 2) The equation on slide 2 has one coefficient but slide 3 implies 
>>> there is a coefficient per CPU term. Which is correct?
>>>
>>> 3) You are estimating mean e2e times. Correct? Typically we are also 
>>> interested in worst case end to end times. Do you intend to consider 
>>> that problem as well?
>>>
>>> Thanks,
>>>
>>> Patrick
>>>
>>>
>>>
>>> Alan F. Karr wrote:
>>>> Colleagues,
>>>>
>>>> Here is some interesting evidence that the pieces of our tool chain 
>>>> are actually links.
>>>>
>>>> We took all configurations tested to date with 42, 43 or 44 
>>>> processors (As discussed yesterday, this is in some sense "where the 
>>>> action is") and asked whether the /*model-derived*/ CPU utilizations 
>>>> along the critical path predict the /*measured*/ end-to-end times, 
>>>> also along the critical path. So far, the only models are considered 
>>>> are linear regressions. The fits are quite remarkably good.
>>>>
>>>> A PowerPoint file summarizing the results is attached. Comments and 
>>>> reactions are welcome. I will attempt to put this on the wiki.
>>>>
>>>> --- Alan
>>>>
>>>> -- 
>>>> ******************************************************************
>>>> * Alan F. Karr, Director                     * Tel: 919.685.9300 *
>>>> * National Institute of Statistical Sciences * FAX: 919.685.9310 *
>>>> * 19 T. W. Alexander Drive (FedEx/UPS)       * karr at niss.org     *
>>>> * P.O. Box 14006 (USPS)                      * www.niss.org      *
>>>> * Research Triangle Park, NC 27709-4006      *                   *
>>>> ******************************************************************
>>>>   
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