Conference Paper

5.1
OpenFlow Switch Performance
The flow entry matching for all packets are assumed to be independent and the packet
processing time can be supposed to follow an exponential distribution. With the assump‐
tions above the performance of OpenFlow switches can be modeled as a M/H2/1 queue,
Fig. 9.
State transition diagram of an M/H2/1 queue
Analysis and Performance Evaluation of SDN Queue Model
33

---

which means packets arrive at the ith switch at rate λi and the service time is represented
by a two-phase hyperexponential distribution. The state transition diagram of this queue
is shown in Fig. 
9
. With probability ρ, a packet receives service at rate μ1, while with
probability 1 − ρ it receives service at rate μ2.
A state is represented by a pair (a, b), where a is the total number of packets in the
switch and b is the current service phase. In our case b can be only 1 or 2. The stationary
distribution of this queue in the ith switch can be obtained by applying the Matrix-
Geometric Method. We denote the stationary probability vector π(i) as
π
(
i
)
= (π
(
i
)
0
,
π
(
i
)
1
,
π
(
i
)
2
,
…
,
π
(
i
)
k
,
…)
(1)
𝜌
=
𝜆
μ
<
1
(2)
𝜋
0
=
1
−
𝜌
(3)
𝜋
k
= (
1
−
𝜌
)
𝜌
k
(4)
Where πk(i) is the probability of k packets in the ith switch.
Then the mean number of packets in the queueing system can be computed as:
N
i
=
∑
∞
k
=
0
k
𝜋
(
i
)
k
(5)
N
i
=
∑
∞
k
=
0
(
1
−
𝜌
)
𝜌
k
(6)
For k = 0, the product is zero then we can start the sum from k = 1
N
i
= (
1
−
𝜌
)
∑
∞
k
=
1
k
𝜌
k
= (
1
−
𝜌
)
𝜌
∑
∞
k
=
1
k
𝜌
k
−
1
(7)
Since 
k
𝜌
k
−
1
can be written as 
k
𝜌
k
−
1
=
d
𝜌
k
d
𝜌
Respectively
N
i
= (
1
−
𝜌
)
𝜌
∑
∞
k
=
1
d
d
𝜌
𝜌
k
= (
1
−
𝜌
)
𝜌
d
d
𝜌
(∑
∞
k
=
1
𝜌
k
)
(8)
Since 
∑
∞
k
=
1
𝜌
k
=
∑
∞
k
=
0
𝜌
k
−
1
=
1
1
−
𝜌
−
1
=
𝜌
1
−
𝜌
We c
a
n wr
i
te
N
i
= (
1
−
𝜌
)
𝜌
d
d
𝜌
(
𝜌
1
−
𝜌
)
(9)
34
S. Muhizi et al.

---

N
i
=
𝜌
1
−
𝜌
,
(10)
where (ρ < 1) and 
ρ =
𝜆
μ
N
i
=
𝜆
μ −
𝜆
(11)
According to Little’s law, the average packet processing time in the ith switch can
be given by
W
si
=
1
𝜆
N
i
=
1
μ −
𝜆
(12)
The mean packet processing time of switches can be given by
W
s
=
∑
n
i
=
1
𝜆
i
∑
n
i
=
1
𝜆
i
W
si
(13)
5.2
Numerical Evaluation and Results
With the mentioned analytical framework and presented outcomes, we can evaluate the
proposed queuing model with different parameters and report the upper bound of packet
processing delay in the SDN switch. The switch average packet processing time is shown
2.20E-05
4.40E-05
8.80E-05
1.76E-04
3.52E-04
7.04E-04
1.41E-03
2.82E-03
5.63E-03
1.13E-02
1%
6%
11
%
16
%
21
%
26
%
31
%
36
%
41
%
46
%
51
%
56
%
61
%
66
%
71
%
76
%
81
%
86
%
91
%
96
%
10
0%
Ws
ρ
μ
=40000
Fig. 10.
Average packet processing time of switch
Analysis and Performance Evaluation of SDN Queue Model
35

---

in Fig. 
10
. As packets arrival rate at the switch increases, the average packet processing
time constantly increases. It sharply increases to the maximum when packet arrival rate
is closer to the switch processing service rate. That matches the time when the switch
runs out of resources and can’t perform packet processing service.
6
Conclusion
Understanding the performances and limitations of OpenFlow-based SDN is a prereq‐
uisite of its deployment. In this work we have proposed a model for an OpenFlow SDN
based on queueing theory, and resolves its average packet processing time. We reviewed
the optimal parameter combinations of Openflow switch and controller to allow future
network architects and administrators to be able to compute an upper bound estimation
of packet delay and buffer requirement of SDN switches and controller for a given packet
arrival rate.
Furthermore, we will extend the analysis to the possibility of SDN network from a
single controller to the case of controller clusters to evaluate how much switches a given
controller can handle in a network without much performance loss.
Acknowledgment. 
The publication was financially supported by the Ministry of Education and
Science of the Russian Federation (the Agreement number 02.a03.21.0008), RFBR according to
the research project No. 17-57-80102 “Small Medium-sized Enterprise Data Analytics in Real
Time for Smart Cities Applications”.
References
1. Kreutz, D., Ramos, F., Verissimo, P., Rothenberg, C., Azodolmolky, S., Uhlig, S.: Software-
defined networking: a comprehensive survey. Proc. IEEE