Towards the Performance Analysis of IEEE 802.11 in Multi-hop Ad-Hoc Networks

Towards the Performance Analysis of IEEE 802.11
in Multi-hop Ad-Hoc Networks
Yawen Barowski and Saˆ d Biaz
a Prathima Agrawal
Computer Science and Software Eng. Dept. Wireless Engineering Research and Education Center
Samuel Ginn College of Engineering Samuel Ginn College of Engineering
Auburn University Auburn University
Auburn, AL 36849-5347, USA Auburn, AL 36849-5347, USA
Email: {dyeaiya,biazsaa}@eng.auburn.edu Email: agrawpr@eng.auburn.edu

Abstract— The performance of IEEE 802.11 in multi-hop In all previous work, one or more performance aspects were
wireless networks depends on the characteristics of the protocol reported for single hop IEEE 802.11 networks under saturated
itself, and on those of the upper layer routing protocol. Extensive traffic conditions. Inspired by Bianchi’s saturated throughput
work has been done to analyze and evaluate the performance of
single hop networks under saturated traffic conditions, either model, we propose a model to describe the behavior of IEEE
through simulations or mathematical modeling. Little work 802.11 under different offered traffic loads. This model shows
has been done on the analysis of the performance of IEEE the effect of the offered load on the transmission probability.
802.11 protocol under unsaturated traffic conditions that arise in We also propose a three dimensional model to attempt to
multi-hop networks. This paper proposes analytical models and describe the behavior of multi-hop 802.11 networks. The 3D
scenarios to analyze the IEEE 802.11 protocol under unsaturated
traffic conditions for multi-hop networks. ns-2 simulations with model allows the modeling of not only data sources (as in
different network configurations validate the proposed models for Bianchi’s model) but also relay stations that forward traffic.
performance metrics such as throughput, message delay, average Section II of this paper briefly describes the IEEE 802.11
queue length, and energy consumption. Simulation results show DCF scheme, stressing key elements related to this paper. In
that the proposed models work well. Key to the modeling of the Section III-A, work related to this paper [3] and our model
multi-hop networks is a treatment of the upper layer routing
protocols that can affect the network performance through the for analyzing the protocol under unsaturated traffic loads is
way they forward packets and the impact of that on the traffic discussed. This model is extended in Section IV into a three
load. The model proposed takes into account the impact of the dimensional model that could be used to model IEEE 802.11
upper layer routing protocol by introducing a packet acceptance in multi-hop networks.
factor with which each relay station accepts packets from the
wireless medium before forwarding the same. II. IEEE 802.11 DCF S CHEME
IEEE 802.11 is a contention-based MAC protocol. It has
I. I NTRODUCTION
two working modes. The point coordination function (PCF)
IEEE 802.11 [11] medium access control (M AC) protocol mode is a centralized scheme designed for an infrastructure
is currently the most popular random access M AC layer network. This mode uses a point coordinator that operates at
protocol used in wireless ad-hoc networks. It uses a distributed the base station to select the next wireless station that will
coordination function (DCF) as the primary mechanism for transmit. The distributed coordination function (DCF) mode
accessing the medium. DCF has two modes: the basic broad- makes use of “carrier sense multiple access with collision
cast mode, and the MACAW [2], [13] based RTS/CTS mode avoidance” (CSMA/CA [13], [2]). This paper focuses on
(Request To Send/Clear To Send). The efficiency of the DCF. DCF allows automatic and adaptive medium sharing
IEEE 802.11 protocol directly affects utilization of channel between compatible physical layers (PHYs) through the use
capacity and system performance. Performance analysis of of CSM A/CA and a random backoff procedure. Carrier
IEEE 802.11 has been done experimentally and analytically: sense is performed both through a mechanism at the physical
saturated throughput of IEEE 802.11 has been extensively layer and a virtual mechanism at the MAC layer. The virtual
investigated [3], [5], [7], [16], [19]. Bianchi [3] proposed carrier sense mechanism is achieved by distributing reservation
a two-dimensional Markov chain model to analyze the perfor- information announcing the impending use of the medium.
mance of the IEEE 802.11 exponential backoff scheme, and The exchange of RTS and CTS frames prior to the actual data
to evaluate the saturated throughput. There are inaccuracies frame is one means of distribution of this medium reservation
in Bianchi’s model, mentioned in [19] which also proposes information. A wireless station that needs to send a data frame
modifications. should invoke the carrier sense mechanism to determine the
Other performance metrics such as message delay, data loss, state of the medium. If the medium is idle for a specific length
power consumption, and scalability, were investigated in [4], of time, the DCF interframe space (DIF S), the wireless
[6], [8], [10], [14], [15], [18]. station should generate a random time period for an additional

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deferral before transmission. The backoff procedure is invoked of this state can be easily calculated. Figure 1 outlines our
when the medium is sensed busy. The MAC sets its backoff model.
timer to a random interval using the formula, B. The System Model
Count = Random() ∗ σ In order to analyze the protocol under unsaturated traffic,
we make the same assumption as is done in [17]. We assume
where Random() returns a random integer within
that stations are statistically identical, each station has idle
[CWmin , CWmax ] where CWmin and CWmax are the min-
periods that are exponentially distributed, and packet length is
imum and maximum contention window sizes respectively.
constant. For a station under unsaturated traffic, the transition
σ is the system time slot set by the physical layer. The
from state (b, 0) to state (0, c), which means the station reaches
binary exponential backoff mechanism increases the range of
the next transmission cycle after successfully sending out a
[CWmin , CWmax ] as contention increases, with the objective
packet, is not guaranteed, as it is in Bianchi’s model. This is
of staggering the conflicting transmissions. A station perform-
only true when the station has at least one buffered packet.
ing the backoff procedure uses the carrier sense mechanism to
We add an additional state (q = 0) in our model to handle
determine whether there is activity during each backoff slot. If
the situation in which the station has no buffered packet. Let
no medium activity is detected, the backoff procedure decre-
λ be the offered load of each station, and q0 the probability
ments Count by σ. Otherwise, Count is not decremented
that a station has no buffered packet. In Figure 1, all states
for that slot. The minimum time between transmission of
and state transitions, except the state (q = 0), are based on the
interactive packets (RTS or CTS) is the short interframe space
condition that there is at least one packet to be sent. When a
(SIF S). Since DIF S > SIF S, the protocol provides higher
station gets to state (b, 0), and sends a packet, it will reach state
access priority to RTS and CTS frames.
(b + 1, c) if the packet collides and needs to be retransmitted.
If a transmission succeeds, the wireless station will follow
If the packet is successfully sent, it will reach state (q = 0) or
the same procedure for the next transmission. If a transmission
state (0, c) depending on whether or not there is any buffered
fails, the DCF procedure will be repeated with an exponential
packet. When a station is in state (q = 0), which means it
backoff mechanism. At the first transmission, the range of
currently has no packet to send, it will stay there until a packet
Random(0) is from zero to W0 , where W0 is the maximum
arrives. Then it will reach one of the (0, c) states and start a
contention window at stage 0. At the ith failure, the range of 1
transmission cycle. The average packet arrival interval is λ . So
Random() is extended from zero to Wi , where Wi = 2i−1 ∗
the transition from state (q = 0) to state (0, c) has transition
W0 . i is called the backoff stage. So, as the stage increases, 1 1
probability W0 and transition duration λ . The state transition
the range of possible contention window sizes increases. After
diagram shown in Figure 1 is governed by the following
a successful transmission, the stage is reset to 0.
transition probabilities and durations.
III. M ODEL FOR U NSATURATED T RAFFIC 1) The backoff counter decrements, and the station makes
a transition from state (b, c) to state (b, c − 1) when the
A. Related Work medium is idle
Bianchi [3] proposed a two-dimensional Markov chain P {(b, c − 1)|(b, c)} = Pidle
model to analyze the performance of the IEEE 802.11 protocol t{(b, c − 1)|(b, c)} = σ
in single hop wireless networks. Two parameters, backoff stage 2) The backoff counter suspends, and the station stays in
and backoff counter value, are used to describe the state of an state (b, c) when the medium is busy
IEEE 802.11 station. The pair (backoff stage, backoff counter P {(b, c)|(b, c)} = 1 − Pidle
P ∗Ts +Pf ∗T
value), referred to as (b, c), describes the state of a station, t{(b, c)|(b, c)} = succ 1−Pidleail f
where backoff stage b varies from 0 to a maximum backoff 3) The station sends a packet and the packet collides, the
stage, B and the counter value c takes any value between 0 and station reaches state (b + 1, c)
Wb . If a station reaches state (b, 0) (i.e., the backoff counter P {(b + 1, c)|(b, 0)} = Wcoll 0 ≤ b ≤ (B − 1)
P
b+1
value becomes 0), the station will send out a packet. If the P {(B, c)|(B, 0)} = WB Pcoll

packet collides (with probability Pcoll ) then the station will t{(b + 1, c)|(b, 0)} = t{(B, c)|(B, 0)} = Tf
transit with probability Wcoll to some state (b + 1, c) with a
P
b+1
4) The station sends a packet successfully, and the station
higher backoff stage. If the packet does not collide, the station reaches state (0, c) since it has more packets to send.
will return to some state (0, c) (recall that in such a state, c P {(0, c)|(b, 0)} = (1−q0 )∗(1−Pcoll ) 0 ≤ c ≤ W0
W0
can be any value between 0 and W0 ) with probability 1−Pcoll .W0 t{(0, c)|(b, 0)} = Ts 0 ≤ b ≤ B
One difference between Bianchi’s model and ours is the 5) The station sends a packet successfully, and the station
transition probability from state (b, c) to state (b, c − 1), which reaches state (q = 0) since it has no more packets to
is also addressed in [19]. Bianchi’s model assumes that the send.
probability of the transition from state (b, c) to state (b,c-1) is P {(q = 0)|(b, 0)} = q0 ∗ (1 − Pcoll ) 0 ≤ b ≤ B
1.0. Also, for each transition, transition duration is specified t{(q = 0)|(b, 0)} = Ts
along with transition probability. With this feature, the average 6) The station has an arrival packet, and leaves state (q =
time that a station stays in one state and the time proportion 0)



q=0 1/W0

(1−q0)*(1−Pcoll)/W0
q0*(1−Pcoll)

0,0 0,1 0,2 0,W0−2 0,W0−1
P idle
1−Pidle 1−Pidle 1−Pidle

(1−q0)*(1−Pcoll)
i−1,0
q0*(1−Pcoll) Pcoll/Wi

i,0 i,1 i,2 i,Wi−2 i,Wi−1
P idle
1−Pidle 1−Pidle 1−Pidle

Pcoll/Wb

(1−q0)*(1−Pcoll)
B,0 B,1 B,1 B,Wb−2 B,Wb−1

1−Pidle 1−Pidle

Fig. 1. Overview of the Station Model

1
P {(0, c)|(q = 0)} = W0 0 ≤ c ≤ W0 C. Solutions and Results
1
t{(0, c)|(q = 0)} = λ With the diagram and conditions mentioned above, we could
Let us denote P(b,c) as the probability that the station obtain the stationary probability distribution of the model,
reaches state (b, c). From the model, we can compute that except that there is still an unknown, Daccess . Suppose that
under the condition that there is at least one packet to send, a packet is successfully sent on the ﬁrst try, and the time
the station has probability τ to send a packet in any time slot. it takes is T S. Otherwise, if it fails on the ﬁrst try, which
τ=
B
P(b,0) takes time T F , then it will have to wait for the station to
b=0
reach the next sending state (b, 0) before it is sent again. In
Then the probability that a station will send a packet in any order to derive Daccess , we need to express the average time
time slot is, between two sending states. Let us denote D as the average
p = (1 − q0 ) ∗ τ time between two sending states. In practice, D is also the
time that a station takes to complete a backoff procedure after
In a system that consists of n stations, the probability that a a failed transmission.
sent packet collides is, Consider that each transmission starts with a backoff pro-
Pcoll = 1 − (1 − p)(n−1) cedure. We have,
For the whole system, the probabilities of a successful T F = Tf + D
packet, failed packet and no packet in any time slot are Psucc , T S = Ts + D
Pf ail and Pidle , respectively,
Let Rτ be the set of sending states, i.e.,
Psucc = n ∗ p ∗ (1 − Pcoll )
Pidle = (1 − p)n Rτ ={(b; c) : c = 0}
Pf ail = 1.0 − Psucc − Pidle The probability that a station is in Rτ is τ . Suppose τi ∈ R
As for probability q0 , let us denote the average access delay, and τj ∈ R are two consecutive states (in Rτ ) that the station
the time between when a packet reaches the M AC layer and goes through. Then between two consecutive visits to Rτ (τi
when it is successfully sent, Daccess . Daccess is also the packet and τj ), the expected number of visits to any state k ∈ Rτ is
/
Pk
service time if we treat each station as a M/M/1/N queue τ . Assume that the average time a station will stay in state
system, in which N is the maximum queue length of the k is µk . We can derive the time D between two consecutive
queue. For a M/M/1/N queue, the probability that there is sending states as
no packet in the queue is, D= Pk µk
k;k∈R,k∈Rτ
/ τ
ρ = λ ∗ Daccess D is also the time between two consecutive transmissions of
1−ρ
q0 = 1−ρN +1 any packet. The probability that a packet would be successfully



0.06 0.4 2
n=5
0.35
Transmission Probability

n=30

Average Access Delay
0.05

Average Throughput
0.3 n=50 1.5
0.04
0.25
0.03 0.2 1
0.15
0.02
n=5 0.1 0.5 n=5
0.01 n=30 n=30
0.05
n=50 n=50
0 0 0
0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2
Offered Traffic Load Offered Traffic Load Offered Traffic Load

(a)Transmission Prob. (b)Average Access Delay (c)Average Throughput
Fig. 2. Analytic Results from the Model

0.05 0.1 2 2
Simulation Simulation Simulation Simulation
Model Model Model Model


Average Throughput

Average Throughput
0.04 0.08
1.5 1.5

0.03 0.06
1 1
0.02 0.04

0.5 0.5
0.01 0.02

0 0 0 0
0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2
Offered Traffic Load Offered Traffic Load Offered Traffic Load Offered Traffic Load

(a) Average Access Delay n = 5 (b) Average Access Delay n = 10 (c)Average Throughput n = 5 (d)Average Throughput n = 10
Fig. 3. Results from the Simulation

sent on the first try is (1 − Pcoll ), on the second try is Pcoll ∗ show that the probability a station sends a packet in any time
(1 − Pcoll ), and so on. The probability that a packet would slot when it has packets to send, τ , is not independent of the
be sent successfully on the ith try is Pcoll ∗ (1 − Pcoll ). If a
i−1
offered traffic load. As the offered load increases, τ decreases.
packet is sent successfully on the first try, it takes T S. If on For network size less than 50, the breaking point is around
the second try, it takes (T F + D + Ts ), which is (T F + T S), 0.65. After the overall traffic load exceeds 0.65, the average
and so on. If a packet is sent successfully on the ith try, it access delay increases steeply, and the throughput becomes
takes ((i − 1) ∗ T F + T S). The average access delay can be saturated. After the load exceeds 0.8, the average access delay
derived as and τ do not change much. Figures 3(a)-(d) plot both ns-
N 2 simulation results And analytical results for network size
n=1 Pcoll (1 − Pcoll )(T S + (n − 1) ∗ T F ).
n−1
5 and 10. The simulation results fit quite well the analytic
where N is the number of retransmission times minus one. results. When the network size increases, the ns-2 simulation
When N goes to infinity, the access delay will be results fit well with the analytic results when the offered load
Pcoll ∗T F is less than 0.65 or greater than 0.80. However, they show
Daccess = T S + 1−Pcoll .
a relatively large deviation from the analytic results when the
Daccess can be expressed through Pcoll , and the stationary load is between 0.65 and 0.8. This is because when the offered
distribution can thus be obtained. load is greater than 0.65, the system is close to the saturation
The average system throughput should be the sum of condition. The average access delay of each station is close
throughputs of all stations. For a single station, the throughput to or greater than the packet arrival rate. The estimation on ρ
should be the throughput it has during the time it has packets to and q0 may not be accurate any more.
send averaged over the total time that it has or has no packets In [9], Feeney and Nilsson gave a linear model for Lucent
to send. IEEE802.11 2M bps P C cards. According to this model,
the energy consumption in IEEE802.11 networks can be
Tslot = i Pi µi
(1−P(q=0) )∗τ (1−Pcoll )∗n associated with the size of sent packets.
T hr = 8 ∗ L ∗ { Tslot }
where L is the payload length. E = a ∗ Size + b
From a single station’s point of view, there are four kinds of a is the energy consumption per byte, and b is the overhead for
time slots. A slot in which there is a successful packet, a slot sending a packet. a and b are different for sending, receiving,
in which there is a collided packet, a slot in which the backoff and overhearing conditions. They also depend on whether or
counter decrements, and a slot in which there is no packet to not the station is within the range of the data source and
send. Tslot can be seen as the average slot time. Figures 2(a)- data destination. The idle state energy consumption does not
(c) show some analytic results from the model. The x-axis in depend on the packet size. The paper gives an estimation
each figure is the normalized offered traffic load. Figure 2a) of idle state consumption rate e. We borrow this model for



200 20 40
Average Energy Per Bit (uw/bit)


180 n=5 Simulation Simulation
n=30 Model 35 Model
160 n=50 15 30
140
120 25
100 10 20
80 15
60
5 10
40
20 5
0 0 0
0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2
Offered Traffic Load Offered Traffic Load Offered Traffic Load

(a)epb. (b)epb. n = 5 (c)epb. n = 10
Fig. 4. Energy Consumption Analysis

calculating per-packet energy consumption. In addition to other stations’ data. In this case, it is inappropriate to model
the transition duration for each state, our model gives the every station as a saturated data source at all times.
transition energy consumption for each state. For example, We propose a general scenario for the modeling of mutli-
in the source station model, the transition from state (b, c) to hop wireless networks. We make the following assumptions.
state (b, c−1) will consume e∗σ(w.sec) . The transition from At any given time, statistically, a certain number of stations
state (b, 0) to state (0, c) will consume a ∗ L + b(w.sec), and within a given station’s transmission range act as data sources
the transition from state (b, 0) to state (b + 1, c) will consume that inject data traffic. These are called source stations. Other
a ∗ l + b (w.sec), where l is the number of bytes sent during stations act as data relays that forward traffic within the
a failed transmission. The average consumption in each state network. These are called relay stations. Source stations do
Ei can be calculated in the same way as the average state not forward data and relay stations do not generate data.
duration, µi .
For the source stations, our two dimensional model is
The energy consumption of a station during queue empty
sufficient to describe the behavior of the IEEE 802.11 MAC
state is not very explicit. For source stations, when they are
protocol under different traffic loads. For the relay stations,
in the empty queue state there are two cases affecting energy
the above model fails to correctly describe how packets are
consumption. In the first case, other stations have packets and
queued. The above model represents the situation where orig-
there is transmission activity on the medium; the station’s
inal traffic is generated at the station, which is not true for relay
energy consumption includes the overhearing of packets in the
stations. A relay station listens to the medium, gets packets
medium. In the second case, all stations are empty and there
from it and forwards the packets it receives. The number
is no transmission activity in the medium; the station’s energy
of packets a relay station receives and accepts to forward
consumption only includes idle energy consumption. Let ei
depends on the upper layer routing protocol. For example, in
denote the average energy consumption rate of any state i,
the flooding protocol, a station broadcasts all its own packets
and πi denote the time proportion of each state i, then the
and forwards packets from/to all its neighbors. A station will
average energy consumption rate of the station, e, is,
accept 100% of the traffic within its range. In the diffusion
ei = Ei
µi e= i πi ∗ ei routing protocol [12], as well as most routing protocols, a
station will forward most of its traffic to the neighbor station
Figure 4.a) shows the analytic results for energy consumption on its estimated shortest path to the destination, and very little
of all source station networks under different traffic loads. traffic to other neighboring stations. So the station on the
Figures 4.b) and 4.c) show the simulation results when n is shortest path will accept a packet with a probability that is
5 or 10. epb in the figures means energy per bit. epb increases much higher than that of the other stations. Thus, for a multi-
as the network size increases, decreases as the traffic load hop data transaction, the upper layer protocol determines the
increases. traffic load on the relay stations that are involved. Due to the
different traffic loads that fall on each station, the status of
IV. M ULTIHOP W IRELESS N ETWORK M ODEL
each station’s link layer queue is different and undetermined.
D EVELOPMENT
The assumption that at any time there is at least one packet
A. Multi-hop Wireless Network Scenario in the queue is not appropriate.
In the IEEE 802.11 protocol model for single-hop wireless Since our work focuses on the analysis of the MAC proto-
networks, every station is assumed to be equivalent. In most col, we need to find a way to isolate or take into account
previous work described above, every station is assumed to be the upper layer protocol. That is what we propose in our
a data source that sends out saturated traffic. In a multi-hop three dimensional model for the relay stations in the multi-
wireless network, each station in the whole network is not hop wireless network. We introduce a probability Pin . Pin
necessarily a data source. A station may act as a data source is the probability that a relay station will accept to forward
for a period of time when it has original data to send, while at (receive and later forward) a packet under the condition that
other times it may act as a relay station that simply forwards there is a successful packet from other stations in the medium.



Pidle Pidle
i+1;0,1 i+1;0,2
i+1;0,0 i+1;0,W0−2 i+1;0,W0−1

(1−Pcoll)/W0 Ps Ps Ps Ps

Pidle Pidle
(1−Pcoll)/W0 Pidle
i;0,0 i;0,1 i;0,2
i;0,W0−2 i;0,W0−1
P3
Ps Ps Ps i+1;j,Wi−1
Ps
Ps

i;j−1,0

Pcoll/W
Pin*Psucc’ Pin*Psucc’
j+1 Pin*Psucc’

i+1;m,Wm−1
P2
i;j,0 i;j,1 i;j,2 i;j,Wj−2 i;j,Wj−1
Pin*Psucc’
Ps Ps Ps Ps

Ps

i;m,0 i;m,1 i;m,2 i;m,Wm−2 i;m,Wm−1
Ps Ps Ps

Pcoll/W
m

Fig. 5. Overview of the Relay Station Model

Pin could be different for different relay stations. The different stays in some state (0, b, c) that has a queue length of zero,
routing protocols distribute the traffic load among the stations then the station has no packet to send. Therefore, we assume
in different ways. Pin could represent the distribution. that states (0, b, c) must have backoff stage b = 0 and that a
For the work that has been done on the performance analysis station in one of these states will not transit to any other state
of the IEEE 802.11 protocol, all stations behave like saturated unless the station gets a successful packet from the medium.
data sources. Saturated throughput is of the utmost interest. For This feature of the relay stations is different from that of the
multi-hop wireless networks that include both source stations source stations since the source stations have new packets from
and relay stations, the average queue length, average delay, and the application layer.
energy consumption at relay stations are of great interest. In With this 3-D model, the average queue length and average
order to mathematically analyze those performance features, one hop delay can be derived. Please refer to [1] for details
we add a dimension that takes queue length into account to on this 3-D model.
our original model.
C. Conclusion
B. Model for the Relay Station
The performance analysis with saturated traffic does not
Figure 5 outlines the model for the relay stations. apply to nodes that do not originate traffic but may forward
Let us denote state space R, it in on behalf of others. Sometimes, these relay stations may
R = {(q, b, c) : Q ≥ q ≥ 0, B ≥ b ≥ 0, c ≥ 0} not have any packet to forward. Bianchi’s model applies only
to saturated traffic. We presented a two-dimensional model
where q is the current queue length, Q is the maximum queue to analyze the IEEE802.11 performance under unsaturated
length, b is the current backoff stage, and c is the current traffic conditions. Another challenge is the fact that not all
backoff counter value. relay stations receive the same amount of data to forward. This
The foreground plane in Figure 5 represents the two dimen- amount is determined by the upper layer routing protocol. We
sional Markov model with queue length q = i. The model proposed a three-dimensional model that addresses this issue
is extended in depth toward the background with increasing and allows to analyze IEEE802.11 on multi-hop networks in
queue length q. The background plane is the two dimensional which there are source stations and relay stations. Simulation
Markov model with queue length q = i + 1. Within the (b, c) results validate our analytic results.
plane with a fixed value i, the model is similar to the two
dimensional model. A station in a state on the (b, c) plane R EFERENCES
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