RE: Queing theory

["Jonathan Siegel" <jmsiegel.info.research@worldnet.att.net>]

It might be worth taking a step back for a moment and looking at the
issue conceptually before delving in to the statistical theory. 

Goldratt pays quite a bit of attention to capacity planning. I'd suggest
a look at "Theory of Constraints" and "The Haystack Syndrome" before
delving into queueing mathematics. Goldratt advocates multiple queues,
and his reasons why are worth a look. Although most of his examples are
in terms of things like batching in a manufacturing setting, the issues
involved are similar. 

Statistical control implies that the behavior of what we're measuring is
essentially random and observation of how it varies gives us no other
knowledge of its future behavior. The goal of classical statistical
process control is produce consistently uniform output. 

The goal of capacity planning is a bit different: it's to avoid
bottlenecks -- to prevent the high end of variation in load from
exceeding capacity (as cheaply as possible), not to ensure that load
stays at a target. We have no reason to expect or want the different
jobs in a computer system to use uniform amounts of resources, and
experience shows that they vary widely.  Different goals require
different behavior. 

Although the jobs that run in a computer system may be quite varied, the
system itself will often be consistent in its inconsistency. Traffic can
be very heavy at certain times of day (e.g. during business hours) and
very light at other times. Certain jobs will consistently use more
resources than others or occur in predictable patterns. A few jobs may
use orders of magnitude more resources than any of the others, and we're
often in a position to know which ones. We can use this knowledge to
predict.

When we have a credible theory about how a system will behave that
predicts its future behavior, I believe Deming says that we have every
right -- indeed, a responsibility -- to use that theory to manage the
system. When we do this, we are not tampering. The reason why is that if
our theory is useful, we will address behavior that is systematic, not
random, in character. 

Tampering refers to reacting to random system behavior. Theory helps us
address the system and prevents us from tampering.

After applying whatever theory we have, there will still be variation.
If our intervention isn't based on theory or our theory turns out to be
wrong, we are tampering and we can make things worse.

Goldratt advocates, among other things, separate queues at bottlenecks. 

I've done a bit of computer capacity planning myself in the past and
have often worked with capacity planners. It makes all the sense in the
world to do things like schedule large, potential bottleneck jobs for
times when the system is likely to be less busy. Although it can be
overdone, having different queues for jobs with different
characteristics is one way of achieving this. 

But if supervisors are not basing their queues on theory, are not
coordinating their efforts, and are not identifying and focusing on the
overall system bottleneck as Goldratt suggests, they probably are
tampering. 

Jonathan Siegel 

-----Original Message-----
From: Roy Greenhalgh [mailto:rgreenh@attglobal.net] 
Sent: Saturday, April 06, 2002 3:08 AM
To: DENlist
Subject: Queing theory

Denizens

A slightly off-ball request.

I am working with a client who has recently installed a new Document
Image Processing system for a very large volume of local government
forms.

Very simply, the forms are scanned, checked for readability, indexed,
given a processing category and then placed on one of a growing number
of queues awaiting processing on a PC by one of up to 50 processing
staff.  A common system these days.

What is growing out of control is the setting up of more and more queues

by supervisors in an attempt to speed up certain categories of document
at the expense of others. This is the most rampant form of tampering I
have seen for some time, encouraged as it is by the suppliers of such
software.

It is 20 years since I undertook serious queuing theory work (for large
IBM CPU's, disk controllers and the then large disc data storage
systems).

Can anyone point me to a current book describing queuing theory as I
think it is time I looked at the detrimental effects of random queue
installation with this client.

Many thanks

Roy Greenhalgh