Advanced Mathematics and Numerical Modeling of IoT

Receiver

Sender

PFS

Data pending

Neighbor(1)

PFS

Neighbor(2)

PFS

TFS

Data

ACK

Listen

Standby active

PFS

Back-off

···

···

···

m∗TDP

Figure 5: SpeckMAC-D.

Receiver

Sender

Data pending

Beacon

Data pending

Neighbor(1)

Neighbor(2)

PBS

PBS

···

···

TDPT

TBS

TDT

Data

Standby active Back-off

Figure 6: RI-MAC.

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

푇SPECK-MAC-D(푅)=푇req+푛∗푇resp

=(푛+1)∗푇req=(푛+1)∗(푇퐵+푇DP∗푚).

(20)

4.6. RI-MAC.RI-MAC is a representative receiver-initiated
LPL protocol. Each RI-MAC device basically performs
periodic beacon sending (PBS). A sender first switches to
reception (RX) mode and waits to receive the beacon of a
corresponding receiver. As soon as a corresponding beacon is
received, the sender transmits data and then goes back to PBS.
The receiver of the data acknowledges a beacon, as shown in
Figure 6.

4.6.1. Periodic Report.The report time of an RI-MAC device

is as follows:

푇resp=푇DT+2∗푇BS. (21)

Therefore, the total report time of푛nodes is

푇RI-MAC(푃)=푛∗푇resp=푛∗(푇DT+2∗푇BS). (22)

4.6.2. Request-Oriented.The required time for a concentrator

to transmit its request to devices is

푇req=푇DT+2∗푇BS. (23)