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From: Darren on 30 Nov 2009 00:45
I have seen the formula R = S/(1-U) where R is response time, S is
service time, and U is resource utilization.

One thing troubles me, and that is how resource utilization is
defined?

Let's say that I have a server request exactly every 1/10th of a
second. Let's further suppose that S is 1/10th of a second also. Then
it is natural to say that U=1 since the server is constantly busy.

Alternatively you could argue that U=0, since at the point when the
message comes in, the last message has been processed and the CPU is
effectively idle at that exact point.

Any thoughts on this?

From: Tim Little on 30 Nov 2009 04:56
On 2009-11-30, Darren <anon5874(a)yahoo.com> wrote:
> One thing troubles me, and that is how resource utilization is
> defined?
>
> Let's say that I have a server request exactly every 1/10th of a
> second.

The formula above is typically based on conditions of a specific type
of *random* arrival distribution. If you violate the conditions, the
formula does not apply.


- Tim
From: Patricia Shanahan on 30 Nov 2009 09:31
Darren wrote:
> I have seen the formula R = S/(1-U) where R is response time, S is
> service time, and U is resource utilization.
>
> One thing troubles me, and that is how resource utilization is
> defined?
>
> Let's say that I have a server request exactly every 1/10th of a
> second. Let's further suppose that S is 1/10th of a second also. Then
> it is natural to say that U=1 since the server is constantly busy.
>
> Alternatively you could argue that U=0, since at the point when the
> message comes in, the last message has been processed and the CPU is
> effectively idle at that exact point.
>
> Any thoughts on this?
>

If the server is always busy, its utilization is 1.

I agree with Tim Little's comment on the inapplicability of the formula.

Patricia
From: Darren on 30 Nov 2009 10:18
On Nov 30, 1:56 am, Tim Little <t...(a)little-possums.net> wrote:
> On 2009-11-30, Darren <anon5...(a)yahoo.com> wrote:
>
> > One thing troubles me, and that is how resource utilization is
> > defined?
>
> > Let's say that I have a server request exactly every 1/10th of a
> > second.
>
> The formula above is typically based on conditions of a specific type
> of *random* arrival distribution.  If you violate the conditions, the
> formula does not apply.
>
> - Tim

Perhaps you can elaborate on the exact conditions when this formula
applies? Does it need to be a Markov process?

Also, I am still troubled by resource utilization. I have seen
implementations where the server busy loops waiting for messages to be
processed. It would seem that taking the resource utilization as
reported by the OS would be misleading in this scenario, since at the
point the message comes in (which could be random), the message might
be processed immediately.
From: Barb Knox on 1 Dec 2009 02:16
In article
<ac070d06-00ef-4e21-b259-ea335b31ccd8(a)f20g2000prn.googlegroups.com>,
Darren <anon5874(a)yahoo.com> wrote:

> On Nov 30, 1:56�am, Tim Little <t...(a)little-possums.net> wrote:
> > On 2009-11-30, Darren <anon5...(a)yahoo.com> wrote:
> >
> > > One thing troubles me, and that is how resource utilization is
> > > defined?
> >
> > > Let's say that I have a server request exactly every 1/10th of a
> > > second.
> >
> > The formula above is typically based on conditions of a specific type
> > of *random* arrival distribution. �If you violate the conditions, the
> > formula does not apply.
> >
> > - Tim
>
> Perhaps you can elaborate on the exact conditions when this formula
> applies? Does it need to be a Markov process?

As Tim says, the formula applies to purely RANDOM arrivals. Having
random arrivals averaging 10 per second is emphatically not the same as
having regular arrivals every 1/10th second.


> Also, I am still troubled by resource utilization. I have seen
> implementations where the server busy loops waiting for messages to be
> processed. It would seem that taking the resource utilization as
> reported by the OS would be misleading in this scenario, since at the
> point the message comes in (which could be random), the message might
> be processed immediately.

In the abstract world of queuing theory, utilisation is the fraction of
the time that the server is busy actually servicing arrived requests.
If it's not servicing a request then it's not considered busy
(regardless of whatever else a real server computer might be doing then).


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