Poster

1. Design of Persistence Probability in the M2M Random Access
Network 1
Design of Persistence Probability
in the M2M Random Access Network 何浩平 B97901049
陳姵伶 B97901075
Introduction
Figure 1 M2M network [1]
• For example: weather prediction
- Sensors send data every second.
- Delay needs to be minimized.
- Power of sensors is limited.
• Random access: machines compete for limited
channels.
• Persistence probability pm : a base station will
broadcast pm to decide how many machines can start
random access.
• pm plays an important role in performance of random
access.
[1] TelecomTV: http://www.telecomtv.com
System Model
We use the random access channel and the random-access
procedure in UMTS-LTE. Since we consider a scenario under
M2M network, there are some assumptions as follows.
1. Bursting arrival of all machines happens at a time and
each machine has only a set of data to send.
2. Before they doing random access, they should randomly
pick up a q=[0, 1], if q is smaller than the pm, then a
machine can start the random access. Otherwise, it’ll
retry in the next slot until it successfully transmits.
3. When only one machine chooses a specific preamble, the
machine is considered to be successful, and can start to
transmit.
4. Backoff system is not considered since its effect is
somewhat the same as persistence probability.
Theorem
A. Compete for preambles
Except for the process of comparing to pm, at the procedure of
random access, we define ! k | n,P( ) as a probability that k
among v machines can start to transmit their packets under a total
of P preambles
! k | n,P( )=
1
Pv
Ck
P
Ck
v
k! "1( )m
Cm
P"k
Cm
v"k
m! P " k " m( )v"k"m
m=0
min v"k, P"k( )
#
where min v " k, P " k( )$ 0
(1)
Using the principle of inclusion and exclusion can derive this
equation. Since there’re only k preambles being uniquely chosen,
each of last preambles should contain more than 2 machines.
With the above equation, we can derived the expected
successful number:
E[ k | n,P( )] = v 1!
1
P
"
#$
%
&'
v!1
(2)
To find the maximal v given P, we have:
d
dv
v 1!
1
P
"
#$
%
&'
v!1
= 0
(3)
voptimal =
!1
ln(1! 1
P)
(4)
Later, our analysis will use equation (4) again.
B. Markov Chain Analysis
Based on the assumptions mentioned in the section of System
Model, it can be seen that the number of contending machines

2. Design of Persistence Probability in the M2M Random Access
Network 2
forms a finite discrete Markov chain. Here we use the same
concept as [2] to solve the problem.
The probability of transition from state u to v is:
tuv =
B i,u, pm( )! u " v | i,P( )i=u"v
u
# v $ u, u % 0, pm & 0,1( )
! u " v | u,P( ) v $ u, u % 0, pm = 1
0 v > u or pm = 0
1 u, v = 0
'
(
)
))
*
)
)
)
(5)
Clearly, there is one absorbing state (0). Given the current
state M (M machines come in the first slot), the mean delay of the
system aM is:
aM =
1
1! tMM
1+ tMkak
k=1
M !1
"
#
$%
&
'(
(6)
With this equation, we can implement dynamic programming
to find an optimal set of pm to let aM minimize.
[2] M. Lotfinezhad, B. Liang and E. S. Sousa, “Adaptive Cluster-Based Data
Collection in Sensor Networks with Direct Sink Access” IEEE
Transactions on Mobile Computing, 7 (7) (2008), pp. 884–897
Design
Method A:
Using equation (6), we can implement dynamic algorithm to
find an optimal set of pm to let aM minimize.
Method B: (UMTS with pm, and consider the backoff system [3])
Based on equation (6), for a specific machine number M, we
find a best pm to let aM minimize.
Method C:
Combine equation (4) and equation (6), we can find a set of
pm to let aM close to the result of Method A.
[3] 3GPPTS25.321V5.14.0,Third-GenerationPartnershipProject;Medium Access
Control (MAC) Protocol Specification, Sophia-Antipolis, France, Sep. 2008.
Estimation of the Machine Number
Since the Method A, B and C need some feedback of
estimation of contending machine number, here we provide a
method to solve this problem.
A base station will accurately know that the number of empty
preamble which no one chooses (Pempty), the number of successful
preamble which is only chosen by one machine (x) and the total
number of preambles (P). With this information, assume the
arriving machine number is v, we can derive the equation:
! x | v,P'( )=
CPempty
Ptotal
Pv
P'
P'" x
#
$%
&
'(
v
P'" x
#
$%
&
'( P'" x( )! ("1)n
Cn
x
Cn
v"(P'"x)
n!( ) "1( )m
Cm
x"n
x " n " m( )v"(P'"x)"n
m=0
x"n
)
#
$%
&
'(
n=0
x
)
*
+
,
-
.
/
(7)
Where v ! P'! x( )" 2x, v ! P' " x, and P' = Ptotal ! Pempty.
This equation uses the same concept as (1). With a specific
Pempty, x and P, we can find a v* make (7) maximal, and this way
is highly accurate.
Protocol
Figure 2 Flow Chart of Protocol Design
Analysis
Figure 3 Comparison among different settings with M=300
and P=54
• Method C is as good as Method A.
• For Method B, under M=300, choosing pm=0.4~0.5 will
have the lowest delay. Comparing to pm=1, pm=1 needs
another 31 slots to deal the traffic. However, this method
is still worse than the others.

3. Design of Persistence Probability in the M2M Random Access
Network 3
M 20 50 70 100 130 200 250 300
Pm, opt
1.0 1.0 0.8 0.53 0.41 0.28 0.22 0.2
M x Pm, opt
20 50 56 53 53.3 56 55 60
Table 1 a set of optimal pm by Method A
• Method A tends to filter all machines such that the
expected machine number allowed to start random
access matches the best machine number that maximizes
success probability.
Figure 4 Comparison among different settings 2
• This again shows that Method C is as good as Method A.
Besides, Method C and A show much more efficient
than Method B especially when M grows.
Figure 5 Differences between Method A and C
• Method A and C is not the same, but when preamble
number is large enough, their performance is almost the
same.
Figure 6 Difference of complexity of 2 Methods
• This shows that the complexity of Method C is much
simpler than Method A. It significantly reduces the
complexity of programming.
Figure 7 The impact of an inaccurate feedback
• This shows that if there’s an inaccurate feedback that
provides an inaccurate estimation of contending machine
number, the impact on Method C seems slight.
• The error caused by an inaccurate feedback can also be
seen as the frequency of updating the pm is low. Thus, if
a base station extends the period to broadcast a pm, the
efficiency will be still good enough.
Conclusion
• By the above analysis, we can see that Method C is a
flexible method since it doesn’t need a complex
programming, and with a large tolerance for an error in
the estimation of the coming machine number,
• Although it may increase power consumption since a
base station needs to continuously update the pm, the
period of update pm is available to extend without losing
much efficiency.
Ø Overall, under these kind of scenerios, our work of
designing persistence probability provides a general
solution: Method C. With slightly increasing the system
complexity, Method C truely gives a lot of efficiency.

4. Design of Persistence Probability in the M2M Random Access
Network 1