Dynamic Tuning Retransmission Limit of IEEE 802.11 MAC Protocol for Networked
Control Systems
Jia Bai, Emeka P. Eyisi, Yuan Xue, Xenofon D. Koutsoukos
Department of Electrical Engineering and Computer Science
Vanderbilt University
Nashville, TN, USA
{jia.bai, emeka.p.eyisi, yuan.xue, xenofon.koutsoukos}@vanderbilt.edu
Abstract—Building networked control systems over wireless
networks is an extremely challenging task, as the wireless
communication characteristics such as random packet losses
and delay, significantly affect the stability and the performance
of the control systems. We present a novel approach to the
design of wireless networked control system. This approach
decomposes the design concerns into two factors and ad-
dresses them separately in two design spaces – stability of
the system is ensured using a passivity-based architecture
at the control layer, while the performance of the system
is optimized at the communication layer by adjusting the
network operation parameters. This paper focuses on the
design of IEEE 802.11-based wireless network. In particular,
we present a MAC controller that dynamically adjusts the
retransmission limit to track the optimal trade-off between
packet losses and transmission delays and thus optimizes the
overall control system performance. Simulation results show
that our approach significantly improves the performance of
the networked control systems.
I. INTRODUCTION
The integration of physical systems through computing
and networking has become a trend now known as Cyber-
Physical Systems (CPS). Many CPS such as automotive
vehicles and distributed robotics, are monitored and con-
trolled by Networked Control Systems (NCS) which ex-
change information among sensors, controllers and actuators
over a communication network. Wireless network is gaining
increasing popularity with NCS, as it provides great con-
venience in terms of deployment and mobility support. Yet
building NCS over wireless networks is an extremely chal-
lenging task. The wireless communication characteristics,
such as random packet loss, time-varying delay and limited
channel capacity, significantly affect the stability and the
performance of the control systems.
This research was sponsored by the U.S. Army Research Office and
Lockheed Martin and was accomplished under Cooperative Agreement
W911NF-10-1-0005. The views and conclusions contained in this document
are those of the authors and should not be interpreted as representing
the official policies, either expressed or implied, of the Army Research
Laboratory or the U.S. Government. The U.S. Government is authorized to
reproduce and distribute reprints for Government purposes notwithstanding
any copyright notation hereon. This work is also supported in part by the
National Science Foundation under Grant CNS-1035655 and CCF-0820088.
Two major approaches have been investigated in the exist-
ing literature to address the challenges in building wireless
networked control systems. One approach, independently
of the network protocol design, investigates the design of
the control layer (e.g., controller). The goal is to achieve a
desired control system performance despite of the underlying
network difficulties. For example, several works [1], [2]
have been done to ensure the stability of the NCS in
presence of packet losses and time-varying delay. Other
works have focused on improving the performance of the
NCS [3], [4], [5], [6], [7]. Yet without any support from
the network, it is quite hard for the control layer to achieve
stability and optimal performance simultaneously. For the
works that ensure the NCS stability [1], [2], the issue of
performance degradation is not addressed. For the works
that improve the NCS performance [3], [4], [5], [6], [7], it
is not clear whether they can achieve stability in wireless
environment. The other approach is to perform a co-design
of the control layer and the communication layer (e.g.,
network protocols) [8], [9], [10], [11], [12]. While this
approach can achieve both stability and optimal performance
of NCS, its design inevitably involves too many interactions
between the control and the communication layers, which
prevents efficient layer abstraction and encapsulation and
also hinders broader adoption.
To address the above open issues, we present a novel
approach to the design of wireless networked control system.
This approach decomposes the design concerns into two
factors and addresses them separately in two design spaces
– stability of the system is ensured through controller
design at the control layer; performance of the system is
optimized through adjusting network protocol parameters at
the communication layer. At the control layer, we leverage
our previous work on using a passivity-based architecture in
designing NCS that is robust to network delay and packet
loss [2], [13]. In this paper, we focus on studying the impact
of MAC layer packet retransmission on the performance of
the passive controller and investigating the optimal design
of retransmission strategies.
In IEEE 802.11 MAC protocol, a frame will get retrans-
mitted up to a certain limit, if it is lost due to random channel
errors. It is obvious that allowing a higher retransmission
limit increases the chance of successful packet transmissions
at the cost of longer packet transmission delays; while a
lower limit will result in a larger packet loss probability
with smaller delays for delivered packets. Since both packet
loss and transmission delay have negative impact on the
performance of the controller, the key questions we would
like to answer are, what is the packet retransmission limit
that optimizes the controller performance and how to achieve
it. We consider a passive controller which produces a tra-
jectory for the plant (a robotic arm in our system) to track
and define the performance of this NCS as its absolute
tracking error. We observe that the relationship between
the NCS performance and the MAC retransmission limit
can be characterized by convex functions depending on
the channel error probability. Using this convex property,
we design a heuristic control algorithm that dynamically
adjusts the MAC retransmission limit to track the optimal
retransmission limit under time-varying channel errors. Sim-
ulation results show that the MAC controller can converge
quickly to a proper retransmission limit which optimizes the
performance of the control system.
The main contributions of this paper are as follows. First,
we present a novel approach to NCS design. By ensuring
the stability of NCS at the controller layer and optimizing
its performance at the communication layer, this approach is
able to achieve both design goals of NCS while maintaining
a clean cross-layer interaction. Second, we present a control
algorithm that dynamically adjusts the MAC retransmission
limit to track the best trade-off between packet loss and delay
that optimizes NCS performance.
The rest of the paper is organized as follows. The system
models are described in Section II. Section III shows the ob-
servation of the effect of loss and delay to the performance of
the NCS. The MAC controller is designed in Section IV. The
experiment evaluation results are presented in Section V.
Finally, Section VI summarizes this paper.
II. SYSTEM MODELS
We consider a networked control system consisting of
a controller and a plant communicating through a UDP
connection over an IEEE 802.11-based wireless network.
The controller controls the plant, which is a robotic arm, to
follow.
A. Control Layer
Fig. 1 shows the structure of the system in the control
layer. The figure depicts a passive control architecture for
the digital control of a continuous plant, over a wireless
Local Area Network (LAN). In [2], the architecture is shown
to be passive by design, which means it ensures stability
of the NCS in the presence of network uncertainties such
as time varying delays and packet losses. A control system
is considered stable if its output will stay bounded for any
Figure 1: Passivity Based Control Architecture Over Wireless Networks
bounded input, and the system performance is considered as
how fast and accurate the plant can track the control signal
within the bound. Using this passive architecture allows us
to focus solely on system performance. We provide a brief
description of this architecture, and refer the reader to [2] for
a detailed description and proofs pertaining to the passive
control architecture.
In Fig. 1, G
p
(τ
u
) is the plant system to be controlled. The
plant is a continuous linear time-invariant system and the
composite dynamics of the plant is by design, strictly output
passive. The plant system takes the torque control command
τ
u
(t) as input, and outputs velocity
˙
Θ(t). G
c
( ˙e[i]) denotes
the digital controller which controls the plant to behave
in a desired manner. The digital controller is a discrete-
time linear time-invariant system and is also designed to be
strictly output passive. The controller takes as input, the error
velocity ˙e[i] between the reference and the plant output, and
outputs torque command τ
uc
[i].
The block b transforms the power variables (i.e., the direct
input and output of plant and controller) into wave variables
for communication over a wireless network. These wave
variables preserve the passivity of the system. On the plant
side, the wave variable v
ucd
(t) and the velocity measurement
˙
θ(t) are considered inputs to the wave transform block
and the wave variable u
p
(t) and delayed torque command
τ
ucd
(t) are considered outputs of the wave transform block.
On the controller side, the wave variable u
pd
[i] and the
control torque τ
uc
[i] are considered inputs to the wave
transform block and the wave variable v
uc
[i] and delayed
velocity measurement,
˙
θ
d
[i] are considered outputs of the
wave transform block.
The [P S, T
s
] and [P H, T
s
] blocks represent the passive
sampler and passive hold respectively. The passive sampler,
at a sampling time T
s
, interconnects the plant to the digital
controller. It converts the continuous wave variable u
p
(t)
to an appropriately scaled discrete wave variable u
p
[i].
The passive hold, on the other hand, converts the discrete
time wave variable v
ucd
[i] to an appropriately scaled wave
variable v
ucd
(t) which is held for T
s
seconds.
B. Communication Layer
The controller and the plant are implemented on two sepa-
rated nodes which send their commands and measurements
(precisely wave variables) using UDP protocol. The UDP
packet rate naturally corresponds to the sampling rate of the
controller.
The two nodes communicate with each other directly over
wireless channel using the IEEE 802.11 MAC protocol. Here
we consider a wireless channel with random errors. In IEEE
802.11, if a frame is corrupted due to channel errors, it
will be retransmitted. When the number of retransmission
reaches a certain limit, the frame will be dropped. Accord-
ing to [14], the value of retransmission limit depends on
the size of the frame. For frames with sizes larger than
RTSThreshold, LongRetryLimit of 4 times will be used; for
frames smaller than RTSThreshold, ShortRetryLimit of 7
times will be used. To simplify the system model, we disable
the RTS/CTS mechanism by setting RTSThreshold to a very
large value in the IEEE 802.11 MAC protocol.
It is obvious that the MAC retransmission strategy may
affect the NCS performance. Given a packet loss probability,
allowing a larger retransmission limit increases the chance
of successful transmission of a particular packet. However, it
can also result in a longer delay in the packet transmission,
which can be harmful especially if the system is delay-
sensitive. On the other hand, if a small retransmission limit
is used, the packets may experience a higher drop rate,
which can also degrade the system performance especially
if the system is loss-sensitive. Yet, to identify the optimal
MAC retransmission strategy, we need to investigate how
much the delay and the loss will be factored into the NCS
performance.
III. OBSERVATIONS
To understand how the network loss and delay may affect
the performance of the NCS and how retransmission strategy
should be designed to minimize such effect, we perform a
set of experiments using ns-2 simulator.
A. Methodology
We implement the passive control architecture on top of
IEEE 802.11 wireless network in ns-2 simulator. In our
experiment, the sampling rates of the plant and the controller
are both 20 samples/sec, which is also the UDP packet rate.
The packet size is 210 bytes. The wireless network has a
capacity of 1Mbps. Each simulation runs for 100 seconds.
The velocity of the plant system G
p
(τ
u
) tracks a sinu-
soidal reference input
˙
θ
r
[i] = sin(ωi) with ω =
2π
10
. The
performance of the system is evaluated using the instanta-
neous tracking error J [i] = |
˙
θ[i] −
˙
θ
r
[i]|, where
˙
θ[i] is the
plant’s output and
˙
θ
r
[i] is the reference input the plant is
supposed to track. J [i] demonstrates the tracking ability of
the system.
In what follows, we first inspect how the network loss
affects the plant output when network delay is negligible,
then test the effect of network delay to the NCS in a loss
free condition. We finally investigate the effect of the MAC
retransmission limit on the NCS, which will establish the
basis of our control algorithm for retransmission limit.
B. Effect of Packet Loss
In this experiment, we disable the retransmission mech-
anism of IEEE 802.11 MAC so that each packet will only
be transmitted once. In this case, the packet error directly
translates to a packet loss.
0
0.05
0.1
0.15
0.2
0.25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Average Tracking Error
Packet Error Probability (%)
(a)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Maximum Tracking Error
Packet Error Probability (%)
(b)
Figure 2: Impact Of Loss Rate On System Performance
Fig. 2 demonstrates the system performance with differ-
ent packet error probabilities. Fig. 2(a) shows the average
tracking error
¯
J over all sampling points with standard
deviation J
d
. Fig. 2(b) shows the maximum tracking er-
ror J
m
experienced out of all samples corresponding to
different error probabilities. With the increase of the error
probabilities,
¯
J, J
d
and J
m
all increase. When the error
probability is small, only a few packets are dropped. If the
samples are exchanged frequently enough, the plant and
the controller can still keep track of each other’s status.
However, when too many packets are dropped, the plant
cannot interpret the control command correctly, while the
controller no longer has the right velocity information of the
plant. For example, when the packet error probability is 70%,
the errors suddenly become very large. Further experiments
using different passive controllers on different signals and
with different sampling rates all show the same trend. Yet the
exact mathematical relation between error probability and
tracking error varies depending on these system parameters
(e.g., signal, sampling rate).
C. Effect of Network Delay
In this experiment, the controller and the plant work
in a loss free network. A varying amount of delay D is
introduced before the packet transmission at the MAC layer.
The value of D can be regarded as the time a packet spends
in channel contention. Thus it is an indicator of the intensity
of background traffic in the wireless network. Fig. 3 shows
the NCS performance in terms of average and maximum
tracking error under different values of D.
We observe that when D is small, the system performance
does not change much. When exceeding certain value,
the performance degrades significantly. Consider that the
controller is a discrete time system, when the delay is
smaller than one discrete time step, the controller can still
receive the signals for the next sampling period in time,
so the performance does not deteriorate. However, when a
larger delay is experienced, signals cannot reach the other
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.005 0.01 0.015 0.02 0.025
Average Tracking Error
D (sec)
(a)
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0 0.005 0.01 0.015 0.02 0.025
Maximum Tracking Error
D (sec)
(b)
Figure 3: Impact Of Transmission Delay On System Performance
end within one sampling period. In this case, When the
controller receives a signal from the plant, the state of the
continuous plant may have already changed considerably.
But the controller will still produce a control signal for
the plant using the received plant state information. This
control signal will also experience transmission delay before
it arrives at the plant. When these two delays are combined,
the plant will deviate more from the expected trajectory.
It is important to note that increasing D also reduces the
departure rate of the packets and may cause queueing delay
(e.g., when D = 0.023s
1
), so the actual delay experienced
by the system is much larger. Due to this reason, this delay
threshold (0.02 in this experiment) highly depends on the
sampling rate, the signal of the system and the channel
capacity. Further experiments on different signals and with
different sampling rates validate the same observation.
D. Effect of MAC retransmission
In IEEE 802.11-based wireless networks, packet loss will
be recovered through retransmission up to a limit. As a
result, a packet may experience higher delay before getting
successfully transmitted. In the first two experiments, we
have demonstrated that increasing either the network loss or
delay will harm the performance of the control system. To
achieve the optimal NCS performance, the retransmission
strategy needs to be carefully designed to provide the best
trade-off between the packet delay and the loss. Here,
we exam the impact of MAC retransmission strategy by
varying the retransmission limit and measure the system
performance.
Fig. 4 shows the average and maximum tracking errors
of the system under different retransmission limits, with
varied packet error probabilities and delay parameters D.
We observe that the relationship between the tracking error
and the retransmission limit follows a convex curve in all
experiments. When the retransmission limit is small, high
packet loss rate leads to relatively large tracking errors.
When the limit is too high (e.g., 7 defined as Short-
RetryLimit in IEEE 802.11), the tracking error raises due to
large delay. Experiments with different signals and sampling
1
To have a controlled environment, where only the impact of delay is
assessed, the queue length and the value of D are carefully chosen in this
experiment, making sure no queuing loss is incurred.
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
0 2 4 6 8 10 12
Average Tracking Error
Retransmission Limit
(a) D = 0
error prob: 50%
60%
70%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12
Maximum Tracking Error
Retransmission Limit
(b) D = 0
error prob: 50%
60%
70%
0.04
0.05
0.06
0 1 2 3 4 5
Average Tracking Error
Retransmission Limit
(c) error prob: 50%
D = 0.005s
D = 0.01s
2.50
1.00
2.77
1.16
0.1
0.2
0.3
6.0
7.0
0 1 2 3 4 5
Maximum Tracking Error
Retransmission Limit
(d) error prob: 50%
D = 0.005s
D = 0.01s
6.30
7.42
Figure 4: Impact Of Retransmission Limit On System Performance
rates confirm the convex relation between the retransmission
limit and the tracking error. This observation implies that
there exists a unique optimal value for retransmission limit.
Yet this optimal value varies depending on the channel
error probability, background traffic, signal property, etc. We
summarize our observations below:
• The NCS performance based on passive controller is
negatively affected by network factors, including packet
losses and transmission delays.
• The MAC-layer packet retransmission limit and the
NCS performance follows a convex relation, which
shows the existence of a unique value for retrans-
mission limit that optimizes the NCS performance.
This optimal value depends on many control system
properties, such as sampling rate, signal type, as well
as network factors, such as channel error probability,
background traffic, etc.
• The fixed retransmission limit (4 as LongRetryLimit,
7 as ShortRetryLimit) used in IEEE 802.11 is not
optimal for the NCS performance, considering the
dynamics in wireless network with bursty traffic and
fluctuating channel conditions. To achieve the optimal
NCS performance, the retransmission limit needs to be
dynamically adjusted based on the system property.
IV. MAC CONTROL DESIGN
In this section, we present a MAC-layer controller that
dynamically adjusts the retransmission limit under different
network conditions. Most NCS systems define a maximum
performance error they can tolerate. We use
˜
J to represent
this threshold. Our MAC controller can achieve the follow-
ing two goals: (1) keep the NCS performance within this
error threshold; (2) minimized the NCS performance error
(when the error threshold is not achievable, or set to a very
small value).
Figure 5: MAC Controller Architecture
Fig. 5 is an overview of the MAC controller architecture,
which consists of a monitor, a controller and an actuator. The
monitor resides on the same node as the NCS controller. It
interfaces with the NCS and measures the average track error
¯
J[k] of the last m samples in the current MAC sampling
period k
2
. The monitor will then derive the difference e[k]
between
¯
J[k] and
˜
J as e[k] =
¯
J[k] −
˜
J and pass it to the
controller. Let r[k + 1] be the retransmission limit that will
be used in the MAC layer at time k + 1 and ∆r[k + 1]
be the adjustment of r[k + 1]. The controller will compute
∆r[k + 1] based on e[k], and send it to the actuator. The
actuator interfaces with the wireless network and tunes the
retransmission limit to r[k + 1] = r[k] + ∆r[k + 1]. For the
node on which the NCS controller resides, the actuator will
directly pass the new retransmission limit to the MAC layer.
For the node on which the plant resides, the MAC actuator
sends the new retransmission limit information on a separate
packet or piggyback on a data packet.
The MAC controller at the communication layer and the
“main” NCS controller at the control layer form a time-
scale-decomposed system, where the MAC controller is
the slow system that evolves with a larger time scale and
operates with a lower sampling rate. This allows the NCS
performance to converge with the new retransmission limit.
Figure 6: MAC Controller Design
To indicate whether the NCS system is within its error
threshold, the MAC controller maintains two states, IDLE
and BUSY, as in Fig. 6. Initially the controller is at the
IDLE state. If the measured error is within the threshold (i.e.,
e[k] < 0), the controller will remain at the IDLE state with
2
As explained below, the sampling period of the MAC controller is larger
than the sampling period of the NCS controller.
∆r[k+1] set to 0, meaning no changes to the retransmission
limit. When the measured error is greater than the threshold
(i.e., e[k] > 0), the controller will transit from the IDLE
state to the BUSY state and set ∆r[k + 1] to 1.
At the BUSY state, the MAC controller will determine
the change of retransmission limit for time slot k + 1 based
on the change of the tracking error from time k − 1 to k
∆e[k] = ˜e[k]−˜e[k−1]. If the tracking error becomes smaller
(i.e., ∆e[k] < 0), which means the previous change of the
retransmission limit ∆r[k] decreases the tracking error of
the NCS, the controller will keep the same change to the
limit:
∆r[k + 1] = ∆r[k] (1)
If ∆e[k] > 0, which means ∆r[k] increases the tracking
error, the controller will then change the retransmission limit
towards the opposite direction:
∆r[k + 1] = −∆r[k] (2)
Whenever the tracking error falls below
˜
J, the controller
will transit the state back to IDLE.
Discussion. We make the following important notes about
the MAC controller design:
• This MAC controller will adjust the retransmission
limit so that the NCS performance error is within a
predefined threshold. When there are multiple values of
the retransmission limit that can enable the system to
perform within the error threshold, the MAC controller
may bring the limit to any of these values.
• If the threshold is too small that no feasible retran-
simission limit value can bring the NCS system within
this threshold, the MAC controller will bring the re-
transmission limit close to the optimal value where the
NCS performance error is minimized. This is ensured
by the convexity property in the relationship between
retransmission limit and the NCS performance as we
have demonstrated in Section III. We can exploit this
feature to achieve the goal of optimal NCS performance
by manually setting the threshold to a very small value.
• In its current design, though the MAC controller can
bring the retransmission limit to the optimal value, it
can not stay at this point. Rather it will oscillate around
it. To ensure the controller stabilizes at the optimal
value, we improve its design in two ways. First, a
counter is used to count the number of times the con-
troller oscillates around one retransmission limit. If the
counter exceeds a certain value, we consider the limit
as the optimal value and fix the retransmission limit to
it. After some time, the MAC controller will resume
to the BUSY state in case the optimal retransmission
limit has changed.
