Subject: [manet] Ad hoc networks capacity: again...

From: Pietro Michiardi <[email-masked]>
Date: Fri, 17 Feb 2006 16:56:54 +0100

Dear List,

I'd be glad to have your adivce on the following.

While reading the paper "the capacity of wireless networks" (Gupta,
Kumar) I understand the following:
- given:
    * an optimal placement of the nodes (there are n nodes)
    * an optimal (and fair) scheduling to access the medium
    * an optimal routing
=> the BEST we can obtain for the throughput capacity of a multihop
network is:
lambda(n) goes as OMEGA( W / sqrt( n log n) )

where W bit/sec is the "initial" capacity available at each node with
identical and fixed radio range.

This asymptotically tight bound basically says that, if my W = 54Mbps,
and n = [10:100], then the throughput behavior I will obtain given all
the hypotesis aforementioned is:

So, for example, if I have 20 nodes I should expect the throughput to
be, AT BEST, of 7Mbps.

Am I right so far?

Now, suppose I build an application for this ad hoc network.
The scalability properties of the application, in terms of the behavior
of the *application* throughput I will obtain at best, are limited by
this graph. There is no guarantee though that the slope will go as
OMEGA( 1 / sqrt( n log n) ). Right?

Well, that's it for now. Thanks for your reply.

Pietro

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From: Philippe Jacquet <[email-masked]>
Date: Fri, 17 Feb 2006 17:25:27 +0100

Dear Pietro,

GK result must be understood the following way: if source and 
destination are choosen randomly and uniformly then
1. the PER NODE capacity is OMEGA( W / sqrt( n log n) )
2. if optimal node placement, then the per node capacity rise to OMEGA( 
W / sqrt( n ) )

In all cases the total capacity is O(sqrt(n)) since you multiply by n 
and the capacity augments with the network size.

This needs some assumption on signal attenuation and SNR, and of course 
an optimal scheduling of packet transmission.

Bad news: IEEE 802.11 does not seem to meet the requirement as shown by 
GK in further publications.

Best regards,
Philippe

Pietro Michiardi wrote:

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