Subject: [manet] A Measure of Throughput

From: "Mullen, John P. (Contractor)" <[email-masked]>
Date: Mon, 8 Jul 2002 09:21:52 -0600

Hello,

I notice in this working group's statement of scope that statistical
measures of end-to-end data throughput and delay are included in measures of
MANET routing protocols.  I have done some work in this area and would like
to see if exploration of this topic is within the scope of this working
group.  This following is a sketch of my approach.

In measuring throughput, I took the approach that one should consider the
impact of delay on the value of throughput.  In addition, I tried to look at
the anticipated impact of this delayed throughput on the MANET's eventual
users in a way that is independent of the manner in which the MANET is
implemented.  In this way, one gets a measure of effectiveness that 1)
combines the consideration of throughput and delay into a single measure, 2)
compares different options on an equal footing and 3) is meaningful to the
eventual users (who will pay for the system and want to have some idea
whether or not they will be getting their money's worth).

A message has two sorts of value.  The first is Importance (I), which is a
quantifiable estimate of the impact the message would have on the simulated
evolution.  The second is Timeliness (T), which describes how that impact is
degraded by delay in the delivery of that message.  Timeliness is a
non-increasing function of the delay time (t) and differs from message to
message.  If a message is urgent, its T(t) decreases very quickly to zero,
while less urgent messages decay more gradually.  There is no necessary
linkage between Timeliness and Importance.  A message may be extremely
urgent, but not very important.  Finally, a message that is never delivered
would have a timeliness of zero.  

Throughput can be thought of as a situation in which all messages are of
equal importance and T(t) is a binary function equal to 1.0 for all finite
values of t, but equal to zero at infinity.  Alternatively, one can look at
this weighted, time-degraded value as a refinement of throughput.

The value of a delivered message is the product V(t) = IT(t).  A figure of a
protocol's merit would be the relative value of delivered messages, the
weighted sum of actual time-affected message values divided by the same,
assuming all delays were zero.  Of course, this would have to be estimated
over a set of standard scenarios, but that would have to be true for any
measure of performance or effectiveness to have any relevancy.

Although the determination of I and T(t) would be a matter for MANET users,
it would be best if the models of  I and T(t) were compatible with the
design and evaluation carried out by MANET designers.  There are also some
mathematical properties one can exploit.  For example, one can adopt the
convention that T(0) = 1.0 and the limit as t approaches infinity of T(t) is
zero.  It is also reasonable to assume that dT(t)/dt <= 0 for all
non-negative values of t.   Models that are both determinable by MANET users
and tractable by MANET designers can serve as a means of communication
between the two communities.  MANET users can use them to effectively
communicate to designers important performance needs while MANET designers
can use the same functions to communicate to users reasonable expectations
of their system's performance.

In my own work, I found that such functions enable designers to make
intermediate design choices on the basis of user's input.  Also, one can
estimate the uncertainty due to the problem statement by looking at the
tolerance in model parameters to determine if further analysis will be
productive or not.  That is, there is little value in calculating a
performance measure to three decimal places when the tolerance in model
parameters implies no greater precision than two.

Anyhow, if there is some interest, please let me know.

Thanks,

John P. Mullen, 
Contractor

Mail to:
    Director
    USATRAC-WSMR
    Attn: ATRC-WBC (John Mullen)
    White Sands Missile Range, NM  88002-5502

Phone:  
    (505) 678-5275
    DSN 258-5275

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