Advanced Mathematics and Numerical Modeling of IoT

Receiver

Sender

PWS

Data pending

Neighbor(1)

PWS

Neighbor(2)

PWS

···

···

···

Data

Wake-up packet

Wake-up detected

ACK

Listen

Back-off

PWS

Standby active

m∗TWP TAW

Figure 7: BoX-MAC-1.

And푇reqis equal to푇resp. So the total aggregation time of푛
nodes per request is

푇RI-MAC(푅)=푛∗(푇req+푇resp)=2∗푛∗푇req

=2∗푛∗(푇DT+2∗푇BS).

(24)

4.7. BoX-MAC-1.As shown inFigure 7, BoX-MAC-1 is one
of the packet-based LPL protocols, and푇AW(to wait for ACK
of the receiver) is followed by consecutive wake-up packets.
Then, on reception of the ACK, the data are transmitted.

4.7.1. Periodic Report.The report time of a BoX-MAC-1
device is as follows:

푇resp=푇퐵+푚∗푇WP+푇ACK+푇DT, (25)

where푚is a maximum time to trigger the receiver and푚≤
푇DC.
Therefore, the total report time of푛nodes is

푇BOX-MAC-1(푃)=푛∗푇resp=푛∗(푇퐵+푚∗푇WP+푇ACK+푇DT).

(26)

4.7.2. Request-Oriented.The required time for a concentrator
to transmit its request to devices is

푇req=푇퐵+푚∗푇WP+푇ACK+푇DT. (27)

And since data transmission is started only when an ACK is
received, the request of the concentrator must be transmitted

as many times as the number of devices. So the total

aggregation time of푛nodes per request is as follows:

푇BOX-MAC-1(푅)=푛∗(푇req+푇resp)

=2∗푛∗푇req

=2∗푛∗(푇퐵+푚∗푇WP+푇ACK+푇DT).

(28)

4.8. BoX-MAC-2.BoX-MAC-2 is one of the wake-up,

packet-based LPL protocols. However, unlike BoX-MAC-1

or SpeckMAC-B utilizing consecutive wake-packet transmis-

sions, a sender waits for ACK from the receiver for푇AW,

per wake-up transmission, as shown inFigure 8. Therefore, a

sender repeats wake-up packet transmission and RX for ACK

until receiving the ACK.

4.8.1. Periodic Report.The report time of a BoX-MAC-2

device is as follows:

푇resp=푇퐵+푚∗(푇WP+푇AW)+푇DT+2∗푇ACK, (29)

where푚is a maximum time to trigger the receiver and푚≤

푇DC.

Therefore, the total report time of푛nodes is

푇BOX-MAC-2(푃)

=푛∗푇resp

=푛∗(푇퐵+푚∗(푇WP+푇AW)+푇DT+2∗푇ACK).

(30)