Subject: [Ans-research] Recent discussions on the Notes on Scalability draft

From: "[email-masked]" <[email-masked]>
Date: Mon, 20 Oct 2003 08:21:09 -0400 (EDT)

Dear All,

Please see appended below a summary of recent discussions on the
Notes on Scalability draft and some suggested changes to the draft.

As always, comments are welcome.

We will modify the draft and submit shortly.

Zygmunt.
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Prof. Zygmunt J. Haas                    http://people.ece.cornell.edu/haas 
Wireless Networks Laboratory		 http://wnl.ece.cornell.edu
School of Electrical Engineering         
Cornell University			 tel: +1-607-255-3454
323 Frank Rhodes Hall			 fax: +1-607-255-9072
Ithaca, NY 14853			 e-mail: [email-masked]
U.S.A                             
	WNL web page: http://wnl.ece.cornell.edu
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Summary of comments and proposed changes to the Notes on Scalability draft
==========================================================================
Thank you to everyone who submitted comments on the scalability draft. We summarize them 
and provide our comments on them below.

We've discussed the fact that 'absolute scalability' discussed in the draft may not be 
possible in a given environment, and in such a situation, one may be more interested in 
the best achievable scaling properties w.r.t. a given (environment, independent parameter, 
primary metric(s)). In the revised version of the draft, we intend to classify methods 
that have this property under the suggested 'optimal scalability' definition. It will be 
defined as follows:

	A method is termed optimally scalable w.r.t. a given (environment, independent 
	parameter, primary metric(s)) triple, if it is more scalable than any other method 
	with respect to the same triple.

We agree that the definition could provide more insight for the development of new methods 
or protocols, since this knowledge can help us not to waste time and effort to search for 
methods that are better than the optimal.

We also want to emphasize that all of the definitions, including optimal scalability, 
requires the precise statement of the (environment, independent parameter, primary metric(s)) 
triple, since different selections of the components of this triple can lead to different 
conclusions. For example, a routing protocol can be optimally scalable w.r.t. the bandwidth 
consumption metric, but it may not be optimally scalable w.r.t. to another metric such as 
memory consumption.

The term 'maximal scalability' has also been suggested; it was suggested that a method is 
termed 'maximally scalable' if there does not exist another method that is 'more scalable' 
w.r.t. at least one primary metric, without being less scalable w.r.t. another metric. 
However, it was noted that with this definition, many maximally scalable methods that have 
different scaling properties (in terms of the metrics) can exist at the same time. Therefore, 
we feel that the information this definition provides may not be very useful.

The term 'sufficiently scalable' (w.r.t. a certain triple), which requires defining a "genie"
method, has also been suggested. It was suggested that a method is termed 'sufficiently 
scalable' w.r.t. an (environment, independent parameter, primary metric) triple(s), if the 
method is not less scalable than a genie method w.r.t. the same triple. An equivalent 
definition in terms of 'equal scalability' definition present in the draft was also noted. 
It was also suggested that a sufficiently scalable method is not necesarily 'optimally 
scalable' through the following example:

	  >Consider a networking scenario where the bandwidth consumption of
	  >the genie-approach is O(N^1.5) where N is the network size.
	  >Suppose there exist an optmally scalable
	  >protocol Opt that induces an extra bandwidth  consumption (total
	  >overhead) that is O(N^1.25). There is also a protocol P whose total
	  >overhead is O(N^1.4). Both protocols (Opt and P) are suffiently
	  >scalable, since in both cases the total bandwidth consumption is O(N^1.5)
	  >For Opt:  Bandwidth consumption = O(N^1.5) + O(N^1.25) = O(N^1.5)
	  >For P:    Bandwidth consumption = O(N^1.5) + O(N^1.4)  = O(N^1.5)
	  >So, P is NOT optimally scalable but it is sufficently scalable.
	  
However, we think that 'sufficient scalability' implies 'optimal scalability' if they are both 
defined w.r.t. the same metric. The reason this does not appear so in the above example is that 
there are two different metrics above. One is the bandwidth consumption(m1), and the other is 
the overhead(m2). Both Opt and P are *sufficiently scalable w.r.t. m1*, and they must also be 
optimally scalable w.r.t. m1, since, w.r.t. m1, they perform in the best way they can; that is,
as good as the genie method.  On the other hand, P is not optimally scalable w.r.t. m2, since 
Opt is more scalable than P w.r.t. m2. It is obviously possible that a method can be sufficiently 
scalable w.r.t. a metric, but not optimally scalable w.r.t. another metric. However, for a given 
metric, sufficient scalability w.r.t. the metric implies optimal scalability w.r.t. the metric, 
since no method can be more scalable than the genie method w.r.t the metric. So, sufficient 
scalability is just a degree of optimal scalability, where the optimally scalable method is 
equally scalable with the genie method that is associated with the metric.

We feel that, at this stage, there are not well enough established rules to determine the genie 
method for any possible metric. Since this can cause different interpretations of the genie method 
and lead to opposing views on the sufficient scalability of a method, we prefer not to introduce 
the new term 'sufficient scalability' into the draft at this stage.

As suggested by William Su, we will also add "Amount of available spectrum" to the environmental 
parameters of the draft.  Another suggestion regarding network lifetime was adding the condition 
that the network dies when it becomes fragmented. We found that this condition is already present 
in the draft, since it corresponds to the dying of the network when the the maximum number of 
possible connections decreases below N(N-1), i.e., the fraction of possible connections gets below 
the threshold 100%.
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