Advanced Mathematics and Numerical Modeling of IoT

Receiver

Sender

PPS

Data pending Data pending

Schedule Schedule

Unicast

packet

Wa i t i n g

Neighbor(1)

PPS

Neighbor(2)

PPS

···

···

TDC

TP

TMP

Back-off

Preamble

Data

Listen

Standby active

PPS

Preamble detected

ACK

Figure 2: WISE-MAC.

Receiver

Sender

PPS

Data pending

PPS

Neighbor(1)

Neighbor(2)

PPS

PPS

Back-off

Preamble

Data

Listen

Standby active

PPS

Preamble detected

ACK

TAW T

MP

···

···

···

Figure 3: X-MAC.

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

푇req=푇퐵+푚∗(푇MP+푇AW)+푇DT+푇ACK. (11)

And, unlike B-MAC and WISE-MAC, X-MAC cannot trigger
all devices with a single preamble transmission. Therefore,

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

푇X-MAC(푅)=푛∗(푇req+푇resp)=2∗푛∗푇req

=2∗푛∗(푇퐵+푚∗(푇MP+푇AW)+푇DT+푇ACK).

(12)