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is analytical in its two variables (the fact that the support of functions does not contain 0 is used here) Similarly, the standardization function v is analytical and does not cancel itself on ]0, 1[ It follows that, if we truncate the series (647) by considering only a nite number of dyadics , then the random function which results from it has the same regular multifractional function h In addition, the irregularity of the trajectories of the MBM is a consequence of high frequency phenomena (ie, dependent on (t, h(t)) for | | + ) We can nd in [BEN 97b] the high frequency estimates for the MBM, which are generalizations of (616) For every K N: | t, h(t) | C(K) 2 h(t)j 1 1+ |2j x k|K + 1 1 + |k|K (649)

AODV [48] is a reactive routing protocol that has been developed speci cally for MANET In AODV, whenever a node needs to send data to another node that it does not have a route to, it tries to discover a new route Route discovery is accomplished using a route request (RREQ) message Thus, a node that needs to discover a route to another node sends out a RREQ message The RREQ contains the IP address of the node originating the request and the IP address of the destination node, that is, the node the originator is trying to reach The RREQ message is broadcast through the network until a node that has a fresh route to the destination or the destination itself responds to the request with a route reply (RREP) message The RREP message is sent back towards the originator and as the message traverses towards the originator it helps establish the end-to-end path between the originating and destination node RREP messages contain a lifetime eld that de nes how long the route will be valid This ensures that nodes do not send packets through stale paths To minimize overhead, the originator may limit how far the RREQ may be distributed via the time-to-live (TTL) value in the RREQ message The RREQ message will be propagated in the network until the number of hops that the message has traversed is less than the TTL value We now describe the protocol in more detail As mentioned earlier, whenever a node needs to discover a path to another node, it sends out a RREQ message One of the elds contained in the RREQ message is the hop-count eld, which indicates the number of hops traversed by the RREQ message Whenever a node receives an RREQ message, it checks the hop-count eld contained in the RREQ message indicating the number of hops the RREQ message had to travel to get to this node from the originator of the RREQ message The node then creates a new route towards the originator of the RREQ (unless it has a shorter route to it already), which will be used for routing the RREP messages The route to the originator from this node goes through the immediate node from which the RREQ message was received The length of the route is equal to the hop-count eld contained in the received RREQ message The node then checks if it has a route to the destination of the RREQ message If the node that receives the RREQ message does not know a route to the destination, it increments the value of the hop-count eld and then forwards the RREQ message to its neighbors If the RREQ message is received by a node that knows of a fresh route to the destination or if the RREQ is received by the destination itself, then the node responds to the originator of the RREQ request with a RREP message The RREP is unicast towards the originator of the RREQ request via the path that was created during the propagation of the RREQ message The RREP message also includes the hop count from the node that generates the RREP message to the destination (0 if the RREP is generated by the destination itself) The hop count in the RREP message is incremented by each node that forwards the RREP message towards the originator of the RREQ request Since any node that knows of a fresh route to the destination may generate a RREP message, multiple RREP messages for the same destination might reach the source of the RREQ message When the originator of the RREQ message receives multiple RREP messages it can compare them and select the route with the smallest hop count Optionally the originator of the RREQ may also send a route reply acknowledgment (RREP-ACK) once it receives the RREP message We illustrate the operation of the AODV protocol in Figure 42 In this gure we show node A as the source which desires to determine a route to node B, which is the destination Node A creates and propagates the RREQ messages Node B replies with a RREP message on receiving such a RREQ query.

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