This document discusses modelling machine type communication in IEEE 802.11ah networks. It presents a model to calculate the probability that a marked station successfully transmits its frame and the probability that all stations successfully transmit their frames within a restricted access window (RAW) slot. The model uses a Markov chain approach with states for empty slots, collisions, and successful transmissions. It finds that for 1000 stations each with a 30% chance of a packet, splitting stations into 50 groups and using a RAW slot duration of around 20ms minimizes channel time while providing a 90% delivery probability. The paper presents this as an example of how the model can evaluate new .11ah mechanisms and help determine optimal parameter settings.

1. Alexander KrotovEvgeny Khorov Andrey Lyakhov
IEEE International Conference on Communications -Workshop on 5G & Beyond - EnablingTechnologies and Applications. London, UK, June, 2015

2. Swarm of sensor STAs
High collision rate
State-of-the-art wireless networks (e.g. Wi-Fi)
do not support swarms of sensors involved into
Internet of things interaction
Evgeny Khorov, Alexander Krotov, Andrey Lyakhov. Modelling MachineType Communication in IEEE 802.11ah Networks 2
802.11ah Restricted access window
Key Idea:
to divide STAs into small groups and spread their access
attempts over a long period of time
To support IoT scenarios, IEEE 802 is developing a novel
amendment to theWi-Fi standard: IEEE 802.11ah.
Among other modifications, it describes RAW, new channel
access method, which allows the AP to allocate some time
interval called RAW slot to a group of STAs.
Inside each RAW slot, the STAs use legacy EDCA channel
access
𝐶𝑊𝑖
i
15 31 63
127
511
255
1023
0 1 2 3 4 5 6 7
54 213
σ Data
ACK
SIFS
AIFS
Backoff
Empty slot
Successful slot
Select
backoff
[0, 𝐶𝑊0]
RAW start
Data
AckTimeout
Collision slot
Select new
backoff
[0, 𝐶𝑊𝑖]
Collision
EDCA

3. 𝑁
𝑀
RAW
Scenario
Let the AP select a group of M sensor STAs and estimate that N of M STAs have data.
More precisely, let each of N STAs have one data frame at the beginning of the RAW slot.
What length of the RAW slot is enough?
Task
For a given duration of the RAW slot find the probability that:
A. Marked STA successfully transmits its frame;
B. All N STAs successfully transmit their frames.
How to choose values of RAW parameters?
General Problem
• No hidden stations
• Frames are not corrupted due to noise
• Lengths of all frames are equal
Stations are working
synchronously
Assumptions

4. 𝑷𝒓 𝑻𝑿, 𝒕, 𝒓 =
1
CW0
, 𝑟 = 0, 𝑡 < 𝐶𝑊0
0, 𝑟 = 0, 𝑡 ≥ 𝐶𝑊0
1
CWr 𝑖=𝑡−𝑊𝑟
𝑡−1
𝑃𝑟(𝐶, 𝑖, 𝑟 − 1) r > 0
1
𝐶𝑊𝑟
…
𝐶𝑊𝑟
𝑟 > 0
1
𝐶𝑊0
…
𝐶𝑊0
𝑟 = 0
Probability of transmission in slot 𝒕 after 𝑟 retries:
𝑷𝒓 𝒕, 𝒓 =
1 −
𝑖=0
𝑡−1
Pr 𝑇𝑋, 𝑖, 𝑟 , 𝑟 = 0
𝑖=0
𝑡−1
Pr 𝐶, 𝑖, 𝑟 − 1 −
𝑖=0
𝑡−1
Pr 𝑇𝑋, 𝑖, 𝑟 , 𝑟 > 0
Attempt 𝑟 − 1 failed Attempt 𝑟 has not occurred
Probability of reaching slot 𝒕 with retry counter 𝒓:
For 𝑵 → ∞ each transmission attempt leads to a collision: 𝑷𝒓 𝑪, 𝒕, 𝒓 = 𝑷𝒓(𝑻𝑿, 𝒕, 𝒓)
Trick: Since 𝑷𝒓(𝑻𝑿|𝒕, 𝒓) almost does not depend on 𝑵, use 𝑷𝒓 𝑪, 𝒕, 𝒓 = 𝑷𝒓(𝑻𝑿, 𝒕, 𝒓) for any value of 𝑵
Evgeny Khorov, Alexander Krotov, Andrey Lyakhov. Modelling MachineType Communication in IEEE 802.11ah Networks 4
Let us number EDCA virtual slots inside RAW: t.
Probability of transmitting in slot 𝒕 if STA reached it with retry counter 𝒓: 𝐏𝐫 𝑻𝑿|𝒕, 𝒓 =
𝑷𝒓(𝑻𝑿, 𝒕, 𝒓)
𝑷𝒓(𝒕, 𝒓)

5. A. the marked STA successfully transmits its frame
Transition Processes
𝑡
𝑡 + 1
c s r
c+1
c+1
r+1
s+1
c s r
absorbing states
𝜋 𝑒
𝜋 𝑐
+
𝜋 𝑐
−
𝜋 𝑠
−𝜋 𝑠
+
Empty slot
Collision without marked STA
Collision with marked STA
Successful transmission
of another STA
Markov chain A Markov chain B
…
absorbing
states
c
s
c
s
c+1
s
c
s+1
c=1
N
𝜋 𝑒
𝜋 𝑐
𝜋 𝑠
c=0
N
…
𝜋 𝑒 𝑡, 𝑐, 𝑠 = (1 − 𝑝) 𝑁−𝑠
𝜋 𝑠 𝑡, 𝑐, 𝑠 = 𝑁 − 𝑠 𝑝(1 − 𝑝) 𝑁−𝑠−1
𝜋 𝑐 𝑡, 𝑐, 𝑠 = 1 − 𝜋 𝑒 − 𝜋 𝑠
𝜋 𝑒
− 𝑡, 𝑐, 𝑠, 𝑟 = 𝜋 𝑒
′ 𝑡, 𝑐, 𝑠 1 − Pr 𝑇𝑋 𝑡, 𝑟
𝜋 𝑠
− 𝑡, 𝑐, 𝑠, 𝑟 = 𝜋 𝑠
′(𝑡, 𝑐, 𝑠)(1 − Pr 𝑇𝑋 𝑡, 𝑟 )
𝜋 𝑐
− 𝑡, 𝑐, 𝑠, 𝑟 = 𝜋 𝑐
′ 𝑡, 𝑐, 𝑠 1 − Pr 𝑇𝑋 𝑡, 𝑟
𝜋 𝑠
+
𝑡, 𝑐, 𝑠, 𝑟 = Pr 𝑇𝑋 𝑡, 𝑟 𝜋 𝑒
′
𝑡, 𝑐, 𝑠
𝜋 𝑐
+ 𝑡, 𝑐, 𝑠, 𝑟 = Pr 𝑇𝑋 𝑡, 𝑟 (1 − 𝜋 𝑒
′ 𝑡, 𝑐, 𝑠
Let
𝜋 𝑒
′
= (1 − 𝑝) 𝑁−𝑠−1
𝜋 𝑠
′ = 𝑁 − 𝑠 − 1 𝑝(1 − 𝑝) 𝑁−𝑠−2
𝜋 𝑐
′
= 1 − 𝜋 𝑒
′
𝑡, 𝑐, 𝑠 − 𝜋 𝑠
′
(𝑡, 𝑐, 𝑠)
𝑝 = Pr 𝑇𝑋 𝑡, 𝑐, 𝑠 =
𝑟=0
𝑐
Pr 𝑇𝑋 𝑡, 𝑟 Pr(𝑡, 𝑐, 𝑠, 𝑟)
𝑟=0
𝑐
Pr(𝑡, 𝑐, 𝑠, 𝑟)
Transmission attempt probability for non-marked STA:
Evgeny Khorov, Alexander Krotov, Andrey Lyakhov. Modelling MachineType Communication in IEEE 802.11ah Networks
Tasks: For :a given RAW slot duration find the probability that
B. all N STAs successfully transmit their frames
+: marked STA transmits
-: marked STA does not transmit
𝑐: number of collisions
𝑠: number of successful slots
𝑟: retry counter
𝑡
𝑡 + 1
6

6. PDF
CDF
Evgeny Khorov, Alexander Krotov, Andrey Lyakhov. Modelling MachineType Communication in IEEE 802.11ah Networks 6
Numerical Results
Probability that the marked STA successfully transmits its frame Probability that all N STAs successfully transmit their frames.

7. By the beginning of the RAW slot
each of 1000 STAs has
a packet with probability 0.3
Evgeny Khorov, Alexander Krotov, Andrey Lyakhov. Modelling MachineType Communication in IEEE 802.11ah Networks 7
For N stations
Solution:
Split stations into several groups
Splitting into 50 groups minimizes channel time
in this scenario
Slot duration ~20 ms
Required RAW slot duration
Required delivery probability: 0.9
For N=Bin(M=1000, p=0.3) stations
More than 1 second
(exceeds protocol limit)

8. This paper
An example of usage of this model
The model can be also applied to study and manage many new mechanisms developed in .11ah and described in
8