Subject: Zone Radius = 0

From: Marc Pearlman <[email-masked]>
Date: Fri, 21 Jul 2000 07:30:13 -0400

Hi Laurent,

> Something I do not understand is why your curve does not have a
> discontinuity at ZR=0.
>
> total traffic
>	^
>	|
>	| *                     *
>	|  *                 *
>	|   *              *
>	|   *            *
>	|*   *         *
>	|.    *      *
>	|.     *   *
>	|.      ***
>	|.
>	-.-------|--------------> Zone Radius
>        .  the optimal ZR
>         .
>         .<--- hello packets ---->
>         .
>         .
>   no hello
> (pure reactive)

You are right.. There is a "discontinuity" at ZR=0.

In general, when the zone radius (ZR) increases, more proactive routing 
traffic is generated, but reactive route discovery traffic is reduced 
through zone-based bordercasting.  The exception to this rule is the zone 
radius increase from ZR = 0 to ZR = 1 hops.  In this case, we incur the 
proactive overhead of neighbor discovery traffic (ie. HELLOs), but we get 
*no* savings in reactive route discovery (bordercasting defaults to "flood 
searching" for both ZR=0 and ZR=1).  As a result, ZR=0 (purely reactive 
routing) outperforms ZR=1, as illustrated by your figure above.

For ZR >=1 hop, the control traffic is convex ("U-shaped") with respect to 
the zone radius.  Therefore, there is only one local minimum in this 
"U-shaped" region.   We can call the corresponding zone radius ZR_Lmin.

The behavior of ZR_Lmin is well understood.  In particular, this *locally* 
minimum zone radius steadily increases with the call-to-mobility ratio 
(CMR).  In order for ZR_Lmin to be the *globally* optimal zone radius, the 
control traffic produced at ZR_Lmin must be less than the control traffic 
produced by ZR=0.

Consider a broadcast channel ad-hoc network exhibiting very low CMR (ie. 
low traffic load and/or high node mobility).  The optimal zone radius will 
be ZR = 0 (purely reactive routing).  As we increase the CMR (ie. increase 
data traffic / slow down mobility)  ZR_Lmin will gradually increase from 1 
hop, but the optimal zone radius will still remain at 0 hops.  At some 
critical CMR level, the optimal zone radius will jump from 0 hops to 
ZR_Lmin, skipping over the zone radii in between.  For even higher CMR, the 
optimal zone radius will follow ZR_Lmin.

The option of a purely reactive ZR=0 configuration adds an interesting 
threshold behavior to the ZRP.  However, this does not change the simple 
premise on which ZRP is based:   For every network there is an optimal zone 
radius.  For some networks, the optimal radius is 0 (purely reactive).  For 
other networks, the optimal radius is \inf (purely proactive).  For the 
rest of the networks, a zone radius somewhere between the two extremes is 
best.

regards,

Marc