On the other hand, in lower data traffic in which ACK and NACKs just encounter for example one backoff time, the inequality (5) can be estimated as following:
Since in our protocols, each node which sends main packet will send ACK and each node which sends duplicate packet will send NACK, second sigma can calculate sum of sizes of all packets and corresponding ACKs or NACKs sent in each suppression phase and [n/m] shows number of suppression phases (we call forwarding steps from sending duplicate packet until its suppression as a suppression phase).
In the last suppression phase, all branches usually will be suppressed by NACKs but main branch will be stopped at the destination of the packet which can be nearer to the beginning of the last suppression phase.
The reason why overhead of CBF with ACK increases dramatically in network with averagely 15 neighbors for nodes, is the traffic of data transmissions and consequently increasing in waited and delayed ACKs and NACKs that causes more duplications and also more overhead of ACKs' and NACKs' transmissions, themselves.
In addition, some part of overhead of CBF with ACK is for ACKs and NACKs especially in that network density that delayed ACKs and NACKs themselves cause more overhead, but in reuleaux area-based there is no such messages and overhead is only for duplicate data packets.
In the first one that we call it "CBF with ACK", we use ACK and NACK messages to reduce duplications.
Meanwhile, each neighbor which has sent that packet (except the confirmed neighbor by the ACK) sends a NACK to announce to its neighbors that packet has been sent by it, is duplicate.
Thus, by sending little ACK and NACK messages in CBF with ACK, overhead of duplicate packets can be controlled.
Figure 3 indicates a sample scenario which shows the reason of high probability of successful NACK sending in the first try.
Therefore, with considerable probability ACK/NACK messages can stop duplications of each forwarding step of transmission in first try especially in non-dense traffic and because of ACK and NACK are sent by only those nodes that have forwarded the packet (main or duplicate) and these kinds of message have little sizes in comparison with data packets, this mechanism can reduce the overhead of routing.
With this mechanism in network with heavy data traffic, we can be sure that duplicate packets which have propagated because of delayed ACK and delayed NACK will be stopped in utmost nth hop ahead.
Bud Nack still lives on the ranch where he was born in Escondido, Calif.
Bud has very vivid memories of the Einer's Mead Mighty Mouse, particularly during its operation on the Nack ranch while San Diego County's waterline was being installed across their land.
There are many other projects at the Nack ranch, but the Mighty Mouse restoration was perhaps the most important because it reconnected Bud and his family with several generations of relatives and friends.