Subject: Hidden Terminals: Independence Assumption

From: "Y. C. Tay" <[email-masked]>
Date: Sun, 14 Nov 1999 02:37:04 +0800 (SST)

My problem is with the assumption that p_ij's are independent.

Consider i and i', both the same distance from j,
think about i and i' beside each other, 
or i and i' on opposite sides of j.

> Date: Sat, 13 Nov 1999 17:20:09 +0100
> To: "Y. C. Tay" <[email-masked]>, [email-masked]
> Subject: Re: Hidden Terminals
> Cc: [email-masked]
> 
> I think your model is related to the random graph model. Models are never
> realistic, However it seems to make sense if p_ij depends on the distance
> between node i and j. If p_ij is a constant, therefore this would be
> exactly the random graph model which is relevant for short range network
> where propagation attenuation comes more from obstacles than from distances. 
> 
> We are currently working on the random graph model applied to some Manet
> protocols.
> 
> Philippe

---

From: [email-masked]
Date: Sat, 13 Nov 1999 15:17:19 -0600 (CST)

> or i and i' on opposite sides of j.

  As described in detail in:

@article{ChlamtacF99,
  author      = "Chlamtac, I. and Farag\'o, A.",
  title       = "A New Approach to the Design and Analysis of
                 Peer-to-Peer Mobile Networks",
  journal     = "Wireless Networks",
  volume      = 5,
  number      = 3,
  pages       = "149--156",
  month       = "May",
  year        = "1999"
}

it is difficult to consider an ad hoc (or peer-to-peer) network as a
random graph. In that paper, the authors enrich the standard RG setting
with rather sophisticated techniques that consider the dependencies
among the links of the nets but still the p_ij does not consider the
distance among nodes i and j, and this is another issue that does not
allow us to use RG as a reasonable model. That is too bad becasue the RG
model has three great things (among others): 1) The bigger is the
network the better (more accurate) are the results (scalability), 2)
many problems that in a common network setting would be computationally
hard are easily computable (e.g., independent sets, i.e, clustering) and
3) several great results are already available.

> > We are currently working on the random graph model applied to some Manet

  When time allows, in cooperation with Ivan Stojmenovich (U Ottawa), we
are looking at a model that consider both distance and dependencies.
But we have no results yet ...

  St.

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From: [email-masked]
Date: Mon, 15 Nov 1999 16:05:58 +0100

Dear Tay,

On limit of radio range (where p_ij and p_i'j are not trivially close to
1), multipath, obstacles and other sources of fadding can make dramatical
changes in quality signal on short distance. I would tend to say that
independence assumption is a kind of natural and worth to be studied and,
most certainly, it has very convenient features. Definitely a good starting
point and can probably give interesting results.

Philippe