From Maritime Asia to Continental Asia: China's Responses to the

1

The Impact of MAC Buffer Size on the

Throughput Performance of IEEE 802.11

Kamil H. Suleiman, Tara Javidi, Mingyan Liu, and Somsak Kittipiyakul

Abstract

The medium access control protocol of IEEE 802.11 networks has been extensively studied to

explore its throughput performance. A popular regime of study is thesaturation regimewhere users

are assumed to be saturated with information bits. The throughput achieved in this regime, called

the saturation throughput, is commonly interpreted as the maximum achievable throughput for any

given system. In this paper, we formalize the conditions under which saturation throughput is indeed

the maximum achievable throughput. We provide specific settings which may increase the maximum

aggregate throughput of the system beyond the saturation throughput. Furthermore, we observe and prove

that reducing the MAC buffer size significantly increases the maximum aggregate throughput, beyond

the saturation throughput, a fact that seems counter-intuitive. We formally establish that under small

buffer conditions and under UDP-type traffic, a reduction ineffective collisions due to the buffer size

choice has a positive effect on the throughput performance.This is despite the fact that some packets are

dropped because of likely buffer overflow events. In other words, by identifying the notion of saturation

throughput as an inherently pessimistic notion, this paperbrings to the attention the significant impact

of an optimized choice of MAC buffer size on the performance of 802.11 networks.

Index Terms

IEEE 802.11, medium access control, statistical multiplexing, saturation throughput.

I. INTRODUCTION

With the wide deployment of wireless LAN, its core enabling technology, the IEEE 802.11

medium access control (MAC) protocol, has been extensivelystudied in recent years. These stud-

Parts of the results were presented at the 2005 Allerton Conference

K. Suleiman is with the University of Cape Town; T. Javidi andS. Kittipiyakul are with the University of California, San

Diego; M. Liu is with the University of Michigan, Ann Arbor.

January 14, 2008 DRAFT

2

ies include the performance as well as fairness properties of 802.11 basic and DCF (distributed

coordination functions) options. Many of these studies examine the behavior of a fixed number

of 802.11 users (or stations/clients) under a special operating regime known as thesaturation

regime; notable examples include [1]. This is a scenario where all users in the system areinfinite

sources, i.e., they always have packets to send or equivalently, they have infinitely many packets

waiting in the queues, thus the term saturation. Saturationstudies typically characterize the

saturation throughputof a system, which is the throughput that each queue or the system as a

whole can achieve under the saturation scenario. Saturation throughput is shown to vary with

the number of users in the system [1]; they reflect in a sense the capacity of the system and

provide significant insights in understanding the limitingbehavior of 802.11. Bianchi in [1] first

proposed a Markov chain based modeling scheme to estimate the saturation throughput (these

quantities were then used to optimize the backoff window size). Similar models and extensions

have since been used for a variety of purposes. Examples include to tune the protocol [2], to

study the retry limit [3], or to study different aspects of the saturation throughput, e.g., in the

presence of transmission error [11]. The notion of saturation throughput was also studied in [4]

as a fixed point problem where its existence and uniqueness were examined.

More recently, several studies have considered a differentsystem operating regime, where user

queues are fed with finite arrival rates. This means that any given user might not always have

a packet to send. We refer to this type of queues asfinite sourcesto distinguish them from the

infinite sources/queues used in the saturation studies. These include studies that propose similar

Markov chain based models as originally proposed in [1] while taking into account the fact that

the sources may be finite; examples include [5], [6], [12]–[19]. In particular, in our previous

work [5], [7], we investigated how the system behaves when these finite arrival rates approach

the saturation rate (throughput)from below, and made the following interesting observation: The

queues have very good delay performance even when all queueshave arrival rates approaching

the saturation throughput1.

Building on the above observation, the present paper is an attempt to achieve higher than

saturation throughput. This idea builds on our prior work in[5] where we first proposed practical

settings to achieve the saturation throughput. Specifically, in the first part of the paper, we answer

1This is consistent with other non-saturation studies in literature [6].


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the following question first posed in [5]: Under the more realistic operation scenario of non-

saturation, is it possible for every user to achieve a throughput higher than that of saturation?

Unfortunately, the answer to this question is negative. We show that, in fact, the low delay

behavior is due to an extremely long, transient phase in a typical simulation study and is due to

the existence of a broken ergodicity phenomenon. Instead oflimiting the above observation to

a practical lesson on how to set up simulations correctly, wetake a further step. The mentioned

broken ergodicity phenomenon motivates the main contribution of the second part of the paper:

We show that, in the case of realistic traffic (both TCP and UDPsources), reducing buffer

sizes of each user significantly increases the throughput ofthe system! This increase in overall

throughput with the reduction of buffer size might seem counter intuitive at the first glance, but

is explained as follows: The limitation on the buffer space for each user imposes a regular visit to

the all-empty queue state and, consequently, to the desirable transient phase with desirable delay

behavior. In fact, through a simple Markov chain model, we prove that, even for a buffer size

of 1, the total throughput higher than the saturation throughput can be guaranteed for Poisson

(UDP-type) source, despite an increase in packet drop probability.

One might wonder how the above result depends on the reactivebehavior of the arrival stream,

the size of the MAC buffer, or the bursty nature of the traffic.The contribution of the present paper

is to provide answers to these questions. In the case of TCP traffic, we present some simulation

results quantifying the impact of small buffer on the performance of multiple concurrent TCP

flows. We will see that even though the packet drops due to MAC buffer limitations result in

smaller congestion windows for TCP flows, the consequent lower level of contention achieved

by limiting the MAC buffer results in significantly smaller RTT values, which keep the TCP

throughput at roughly similar levels, across various choices of MAC buffer size. This highlights

an improved cross-layer interaction via TCP’s adaptive mechanism.

The rest of the paper is organized as follows. In Section II, we describe our network model and

motivate our study using experimental results. Specifically, we consider the behavior of a system

with symmetric users as the input traffic rate approaches thesaturation throughput from below.

We shall see that the system has very good delay performance.This prompts the question of

whether the notion of saturation throughput is too pessimistic and whether higher than saturation

throughput might be obtainable. We attempt to address this question in Section III, and show

that for an infinite-buffer scenario the answer is negative.We then present a detailed explanation


4

ClientNode 1

ClientNode 2

802.11AccessPoint

ClientNode N

ClientNode 3

DestinationNode

802.11 Network

Wire

Fig. 1. Network model.

of the good-delay-performance-paradox, and motivate the idea of reducing the MAC buffer size.

Then, in Section IV, we theoretically show, using a simple Markov model, how the reduction

in the MAC buffer size leads to significant improvement in throughput (higher than saturation

throughput). The same is examined using numerical simulation in Section V for both UDP and

TCP traffic sources. We conclude the paper in Section VI.

Before we close this section, we would like to acknowledge many important works in redesign-

ing the 802.11 MAC mechanism in general, such as [20], and more specifically in improving

its throughput performance, e.g., by using rate adaptation[10], by reducing the amount of time

spent in backoff [9], and so on. Some of these schemes requiremodification to the current

standard. By contrast the solution presented in our paper does not require any changes, and can

be used in conjunction with other solutions. The clean slateredesign of decentralized MAC layer

mechanisms with improved performance remains an interesting area of future work.

II. NETWORK MODEL

In this paper, we consider the network scenario illustratedin Figure 1. It consists of a fixed

number ofN wireless nodes that serve as traffic sources, a single accesspoint (base station),

and a destination node connected to the base station througha wire (for simplicity). We assume

that users have symmetric channels (with negligible error in transmission) and a finite buffer

size, ranging from2 to 10, 000 packets.


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TABLE I

IEEE 802.11 PARAMETERS

slot time 20 µs

SIFS 10 µs

DIFS 50 µs

CWmin 31

CWmax 1023

retry limit 7

physical layer data rate 11Mbps

A. Simulation Setup

The network simulator (ns2) release 2.28 is used for all the simulation presented here. In a

single simulation, the client nodes send theirs packets to the access point, using IEEE 802.11

MAC scheme. Each client node sends packets with an average rate of λ. The burst of data

packets from each node is generated according to the traffic model under study and the size of

each packet is fixed at 1024 bytes. The aggregate throughput of the wireless LAN was measured

by counting all the data bits that arrive at the wired node (orequivalently the base station). In

the simulation, RTS/CTS is disabled. This means that the basic distributed coordination function

or DCF of 802.11 is used. In all of the scenarios, the buffer size at the base station node was

fixed at 109 packets. In each simulation, all the client buffers were initialized to empty. The

relevant simulation parameters used are listed in Table I.

B. Saturation Throughput

In Figure 2, we show the dependence of aggregate throughput on the number of client nodes for

a buffer size of 10,000 packets which is large enough to be consideredinfinity for our simulation

time and topology (the throughput data were collected untilall the buffers were nonempty or

saturated in our simulations). Thesaturation throughputor saturation rateis defined as the

instantaneous throughput of the overall system when all users at all times have infinite number

of packets to send. For instance, we note that the saturationthroughput forN = 25 client nodes

is approximately 4.41 Mbps. Note that, as shown in Figure 2, this quantity is a function of the


6

0 5 10 15 20 254.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

5.3x 10

6

Number of client nodes

Sat

urat

ion

thro

ughp

ut (

bps)

Fig. 2. Saturation throughput for different number of client nodes.

total number of sources in the system. Also note that these results are essentially a reproduction

of the saturation throughput results reported in [1].

In the next section, we discuss the throughput behavior of the system when the users do not

always have packets to send, due to their finite buffer sizes and random traffic arrivals. We call

these usersfinite users or sources.

III. T HE FINITE SOURCE PARADOX AND ITS EXPLANATION

In this section, we provide an interesting observation: Thenetwork outlined above in presence

of finite rate sources enjoys very good delay performance even when all sources have arrival rates

approaching the saturation throughput. At first glance, this counter intuitive and rather surprising

observation seems to suggest that higher than saturation throughput can be achieved for finite

sources. However, we prove this is not the case and provide anintuitive explanation behind this

phenomenon. Despite the fact that this is a negative result,our explanation motivates a method

for inducing higher than the saturation throughput, which we explore in the subsequent section.

Consider the network shown in Figure 1 with symmetric clients and infinite buffers. Figure 3

shows the simulated expected number of backlogged clients (out of a total ofN = 25 clients),

as the arrival rate (load) increases. Here the aggregate arrival rate is normalized by the saturation


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0 0.2 0.4 0.6 0.8 1 1.2 1.40

1

2

3

4

5

6

7

8

Aggregate Arrival Rate

Ave

rage

Num

ber

of B

ackl

ogge

d Q

ueue

s

Fig. 3. Expected number of clients backlogged (out of a totalof 25) versus arrival rate normalized to the saturation rate.

throughput of a system of 25 users (roughly 4.41 Mbps). All queues are initially empty and the

average number of backlogged queues is computed by collecting data over a simulation run time

of 60 minutes. What we see here is that the observed average number of of backlogged queues

is much lower than anticipated even when the arrival rate is at or slightly above the saturation

throughput. In other words, for a system ofN symmetric users, given an empty initial state,

even at the aggregate arrival rate ofNλ = µsat(N) + ǫ, for ǫ ≈ 0, we do not see, more than

eight backlogged queues (less than1/3 of all queues). Similar results were also reported in [6],

where the authors report a large gap between simulated and analytic calculations. This is a rather

surprising result in the context of queuing systems’ operation at heavy loading.

One might prematurely interpret Figure 3 to suggest that a throughput higher than saturation

is achievable, since the observed average delay is much lower than expected. This, however, is

not true. The following result shows that each finite user is limited to its share of saturation

throughput despite the above observed good delay behavior.

Proposition 1: For any Markovian arrival process, which is independent across queues, the

maximum achievable average throughput per user isµsat(N)/N .

Proof: Obviously, for∑N

i=1 λi ≤ µsat(N), we get∑N

i=1 µi ≤ µsat(N), whereµi is the

throughput of useri. This is because aggregate throughput can never be greater than aggregate

arrival rate. Therefore we only need to show that for∑N

i=1 λi > µsat(N), the maximum


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achievable average throughput for each user isµsat(N)/N .

Consider anN-queue system whose states at timet are given by the queue backlog vector

q(t) = [q1(t), q2(t), · · · , qN(t)],

and the embedded Markov chain wheret takes integer values. Consider some timet where all

queues are backlogged, i.e.,mini qi(t) > 0, the instantaneous total service rate of the system is

given byµsat(N). Since∑N

i=1 λi > µsat(N), i.e., the total arrival rate exceeds the service rate,

at timet there is a strictly positive drift with respect to the state of the system. In other words,

there exist someδ > 0 andM > 0 such that for alli, we have

E{

|qi(t + 1) − qi(t)|∣

∣

∣min

iqi(t) > M

}

> δ . (1)

Define the stopping time

T = min {t : qi(t) ≥ M, ∀i} . (2)

From the irreducibility of Markov chain, we have

P (T < ∞) > 0. (3)

Combining (1)-(3), we conclude that this Markov chain consists of only transient states, i.e.

E(mini

qi(t)) = ∞ . (4)

This completes the proof.

The above result says that no collection of finite sources with symmetric traffic can attain

throughput higher than the saturation rate. However, our earlier simulation result suggests that the

source could sustain arrival rates higher than the saturation rate without significant queue buildup

for a while (rather long durations even). This presents an apparent contradiction. Understanding

this discrepancy turns out to be critical in designing mechanisms that allow us to obtain higher

throughput as we detail in the next section.

To understand the gap between the theoretical result and thesimulation observations in

Figure 3, consider again the state of the underlying Markov chain describing the queue state of

our N-user system, given by the queue backlogq ∈ ZN . Note that in such a network, as some

queues become empty, they stop competing for the channel, allowing other users to adaptively

choose smaller average back-off windows. This results in a strong negative drift on subspaces


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of form S0 = {q : ∃i s.t. qi = 0}, whereqi is the backlog of queuei. When the total arrival

rate λ > µsat(N), this negative drift creates abroken ergodicityphenomenon: although the

system consists of all transient states, the time averages computed over a simulation run time

are significantly different from the ensemble averages. More precisely, there are effectively two

classes of states, those with negative drift,S− (S0 ⊂ S−), and those with positive one,S+.

If the arrival rate is greater thanµsat, all states are transient; however, when starting with all

queues empty (inS−), the time it takes to first hit a positive-drift state can be significantly

longer than the simulation time. Indeed, we have never observed such a transition in any of our

simulation, which typically runs on the order of hours in simulated time. In other words, for

realistic simulation times the ensemble average one wishesto obtain can be drastically different

from the computed time average that one ends up getting. To compute the ensemble average,

a randomization of initial queue state is required. However, from (4), it has been shown that

the mean queue length in each buffer is infinity. Another alternative to computing the ensemble

average is to allocate a large initial queue length.

One might argue that the above phenomenon and explanation are lessons in running credible

simulations and reading the results (after all, one needs tounderstand the underlying random

processes before replacing ensemble averages by time averages). But in addition, these results do

lead us to think differently about our system. One can essentially view the system as a globally

unstable one with a desirable (high throughput) operating point which is, given a particular set

of initial conditions, practically “robust” (i.e., it can stay around the high throughput region for

a long time). This “robustness” depends on the statistics ofthe stopping time associated with

the first transition fromS− to S+, which itself heavily depends on the statistics of the arrival

processes (beyond the average mean) as well as the transmission and back-off policies, and

finally, is determined by the maximum of packets each user holds.

This leads to the question of whether one might be able to introduce mechanisms that stabilize

the system around the “robust” equilibrium, while maintaining high throughput, by preventing

the system from transitioning toS+. An intuitive way to force the system to stay inS− is

simply to periodically (but not simultaneously) empty the queues. This would result in a time

share among desirable (higher throughput) operating points. In practice, such a behavior may be

induced by artificially reducing the buffer size at the MAC layer. In the next section, we will

first formalize this idea. In particular, we will use a primitive model for the MAC interaction and


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queue build-ups to hypothesize about a mechanism that enables higher than saturation throughput.

In Section V, we will test our hypothesis via extensive simulation.

IV. THROUGHPUT IMPROVEMENT VIA REDUCED MAC BUFFER SIZE

In this section, we consider a symmetric network where each user has a perfect channel,

a finite arrival rateλ, and a finite buffer space. In particular, we will consider a special case

where each user’s buffer capacity is limited to one packet ata time, and show an increase in

the achievable throughput. This result suggests that even though we incur a loss when dropping

packets due to buffer overflow, we are able to compensate thisloss with an increase in the

departure rate2!

To facilitate the analysis, consider the following simplified model of the network shown in

Figure 4. This is a continuous-time extension of the models proposed in [4]: there areN identical

nodes with buffers of sizeB. Arrival rate to each node is Poisson with rateλ (if the buffer at a

node is full at the arrival time of a new packet, the packet is dropped). Furthermore, the arrivals

to nodes are assumed to be independent among nodes. Here we ignore the back-off times and

focus only on the times when successful attempts are made, i.e., we assume that when there are

k backlogged users a successful attempt leads to the channel being allocated to one of thek

contending nodes with equal probability. We also assume that the time between two successful

attempts, givenk contending nodes, is an exponential random variable with rate µsat(k). In this

paper, we assume thatµsat(·) is a strict monotonically decreasing function, i.e.,µsat(i) > µsat(j)

for any 1 ≤ i < j.

Let µ(λ) denote the average departure rate (average throughput). Note that from previous

sections we know that ifB = ∞, then the maximum achievable average throughput isµsat(N).

In what comes next, we calculateµ(λ) for the generalB ≥ 1 case. A straight-forward, albeit

computationally-intensive, approach is to use the the number of packets in each queue as the

state vector. This approach requires(B + 1)N states and is given as follows: we represent the

2Note that in practice this loss may not be real, in that packets are typically stored in buffers of higher layers, e.g., transport

layer TCP/UDP buffers, before they are moved to and acceptedby the MAC buffer. Therefore, a very small MAC buffer could

simply mean that packets may only be transferred into the MACbuffer in very small quantities at a time, e.g., resulting ina

small TCP window size as we shall see in the next section.


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λ

λ

λ

λ

λ

Randomly select 1 out of nt backlogged queues at rate µsat(nt)

nt = number of backlogged queues at time t

Fig. 4. A simple queuing model to approximate 802.11 MAC. In this illustration,nt = 4.

system as a time-homogeneous continuous-time Markov chain[8] with state vectors

s = (s1, s2, . . . , sN) ∈ S := {0, 1, . . . , B}N .

Here sn is the number of packets in queuen ∈ {1, . . . , N}. The time-homogeneous transition

ratequv from stateu ∈ S to statev ∈ S is given as follows:

quv =

λ, if v = u + en for somen ∈ {1, . . . , N}

µsat(|u|)|u|

, if v = u − en for somen ∈ {1, . . . , N}

−∑

s∈S:s6=u

qus, if v = u

0, otherwise,

where we define|u| :=∑N

m=1 1{um 6=0}, indicator1A =

1, if A

0, if not A, anden denotes a vector

whoseN elements are all zero except one in thenth position. We let a matrixQ = [quv] to

denote the infinitesimal generator matrix.

Since the above continuous-time Markov chain is irreducible and has a finite number of states,

there exists a unique steady-state probability vectorπ̂ = [π̂s]s∈S such that

0 =∑

u∈S

π̂uquv, ∀v ∈ S,

or in vector-matrix form,

0 = π̂Q.


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Therefore, the average throughput is given as

µ(λ) =∑

s∈S

µsat(|s|)π̂s =N∑

m=1

µsat(m)∑

s∈S:|s|=m

π̂s =N∑

m=1

µsat(m)πm(λ),

whereπm(λ) :=∑

s∈S:|s|=m

π̂s is the steady-state probability when there arem backlogged users

in the system.

Due to the large state space, the above calculations have a large computation complexity. On

the other hand, it is not difficult to calculate for the special case ofB = 1. WhenB = 1, the

number of backlogged users,m(t), also forms a continuous-time Markov chain. This allows a

closed form characterization ofµ(λ). The following theorem shows thatµ(λ) can be strictly

greater thanµsat(N) whenB = 1.

Theorem 1:AssumeB = 1. There exists a rate of arrival,λ∗ such that for allλ ≥ λ∗ the

achievable average throughputµ(λ) is strictly greater thanµsat(N).

Proof: The number of backlogged users in the system forms a birth-death continuous-time

Markov chain with statem ∈ {0, 1, . . . , N}. The state transition diagram for such a system is

shown in Figure 5.

Note that the total departure rate in this model is

µ(λ) =N∑

m=1

µsat(m)πm(λ), (5)

whereπm(λ) is the stationary distribution for statem, given the arrival rateλ.

On the other hand, from the balance equations, we obtain the following:

πm(λ) = πN(λ)

∏N

k=m+1 µsat(k)

(N − m)!λ(N−m), m = 0, 1, . . . , N − 1. (6)

This together with the fact that∑N

m=0 πm(λ) = 1 leads to the following expressions forπN

andπm, m = 0, . . . , N − 1:

πN(λ) =

(

1 +N−1∑

j=0

∏N

k=j+1 µsat(k)

(N − j)!λ(N−j)

)−1

=N !λN

N !λN +∑N−1

j=0 [N ]jλj∏N

k=j+1 µsat(k)(7)

πm(λ) =[N ]mλm

∏N

s=m+1 µsat(s)

N !λN +∑N−1

j=0 [N ]jλj∏N

k=j+1 µsat(k), (8)


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0 1 m N

Nλ (N-1)λ

µsat(m)

λ

µsat(N)µsat(1)

(N-m)λ(N-m+1)λ

µsat(m+1)µsat(2)

Fig. 5. Continuous-time Markov chain describing the numberof backlogged users.

where[N ]m denotes N !(N−m)!

.

Inserting (7) and (8) into (5) gives the achievable average throughput:

µ(λ) =

∑N

m=1 µsat(m)[N ]mλm∏N

s=m+1 µsat(s)

N !λN +∑N−1

j=0 [N ]jλj∏N

k=j+1 µsat(k), (9)

where we use the convention that∏N

s=N+1 µsat(s) ≡ 1. Note that, by rearranging the terms, we

have

µ(λ) = µsat(N)N !λN +

∑N−1m=1[N ]mλmµsat(m)

∏N−1k=m+1 µsat(k)

N !λN +∏N

k=1 µsat(k) +∑N−1

m=1[N ]mλmµsat(N)∏N−1

k=m+1 µsat(k). (10)

It is easy to see thatµ(λ) → µsat(N) as λ → ∞. In addition, because of the monotonic

decreasing property ofµsat(·), we note that the numerator in (10) is greater than the denominator,

for sufficiently largeλ. That is, there existsλ∗ for which

µ(λ) > µsat(N),

for any λ > λ∗.

Figure 6 compares the above calculation with the simulationresult for N = 25 users with

B = 1. Even though, as expected, the simple MAC model proposed earlier fails to capture the

precise departure rate, our simulations confirm the generaltrend specified by Theorem 1. In

other words, limiting the buffer size to 1 unit improves the maximum achievable throughput of

the system. Note that such a buffer constraint, on the other hand, causes packet drops in the

admissible regime (whenNλ < µsat(N)) which are nonetheless compensated by the increase in

the overall throughput rate. It clearly confirms the result of Theorem 1, suggesting thatλ∗ is 5.2

Mbps from calculation and 4.4 Mbps from simulation. This discrepancy between the two graphs

is attributed to the overly simplified model of 802.11 MAC. However, the above simple analysis

allows us to hypothesize the following interesting and rather counter-intuitive phenomenon: in


14

0 1 2 3 4 5 6 7 8 90

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Aggregate arrival rate Nλ (Mbps)

Agg

rega

te th

roug

hput

µ(λ

) (M

bps)

simulationcalculationµ

sat(N)

Fig. 6. Dependence of aggregate throughput on aggregate sending rate for a system ofN = 25 client-nodes. Each client node’s

MAC buffer is reduced to one packet. The horizontal dotted line shows the saturation throughputµsat(N).

spite of the introduction of buffer overflow and packet loss,the overall throughput of the system

increases as the MAC buffer size is reduced. In the next section, we provide numerical and

simulations studies, confirming this hypothesis.

V. SIMULATION RESULTS AND DISCUSSIONS

In this section, we demonstrate the validity of our small buffer proposal via simulating a

network of 25 users/nodes with finite arrival traffic rates. Parameters are the same as those

given in Section II, and the specific values ofµsat(·) are obtained from Figure 2. We distinguish

between sources of traffic that are reactive (e.g. TCP) and those that are not (e.g. UDP). In

subsequent subsections, we first consider the case of UDP traffic and then the case of TCP

traffic.

A. Sending UDP Packets

Here, we study the dependency of the system throughput on buffer size when the client nodes

send UDP packets via the base station. At the MAC layer, we allocate different buffer sizes to

client nodes to see the dependency of the aggregate throughput on the buffer size of each node.

Figure 7 shows a graph of aggregate throughput versus arrival rate when each client node is

allocated with buffer size 1 and 10000, respectively. The arrival process to each node is Poisson.


15

0 1 2 3 4 5 6 7 8 9

x 106

0

1

2

3

4

5

6x 10

6

Aggregate arrival rate (bps)

Agg

rega

te th

roug

hput

(bp

s)

1pkt10000 pkts

Fig. 7. Throughput performance for buffer size 1 and 10000 packets, respectively, with Poisson arrivals.

Here, we notice that when the buffer size is 10000, the aggregate throughput is basically the

same as the aggregate arrival rate until it peaks at saturation (around 4.6 Mbps). It then follows

a similar flat curve that is consistent with the saturation curve.

In the case of 1-packet buffer size, we notice that the curve overlaps with that of 1000-packet

buffer size until the arrival rate exceeds the saturation throughput. At this point, unlike in the

previous case, the throughput continues to increase past the saturation point at 4.6 Mbps and

starts to drop around 5.2 Mbps (close to a 10% increase in throughput) and gradually returns

to the saturation throughput when the arrival rate exceeds 8.5 Mbps. Here we see a significant

increase in throughput when we compare the maxima of the two curves. In particular, the range

between 4.6 Mbps (the saturation point) and 8.5 Mbps is the ideal range in which the system

should be operated; it is in this range we achieve higher thansaturation throughput.

Similar results can be obtained for various choices of buffer sizes. Figure 8 shows a zoomed-

in plot of the system throughput versus arrival rates aroundthe saturation rate. The conclusion

remains the same: for arrival rates less than the saturationrate we get essentially the same values

of system throughput; for arrival rates higher than the saturation rate smaller buffer sizes result

in higher system throughput than the saturation rate.

Table II lists the maxima of the throughput curve for the different buffer sizes considered


16

4.5 5 5.5 6 6.5 7 7.5 8 8.5 94.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

Aggregate arrival rate (Mbps)

Agg

rega

te th

roug

hput

(M

bps)

1 pkt4 pkts9 pkts)30 pkts10,000 pkts

Fig. 8. Throughput performance for different buffer size values

TABLE II

COMPARISON OF THE MAXIMUM THROUGHPUT ACHIEVED FOR DIFFERENTBUFFER SIZES AND THE RESPECTIVE INCREASE

IN THROUGHPUT OVER THE SATURATION THROUGHPUT

Buffer size Approximated maximum Percentage increase in throughput

1 5064913 14.56

4 4959693 12.19

6 4877423 10.31

9 4841981 9.50

30 4497785 1.71

100 4497785 1.71

10000 4497785 1.71

in the above simulation. Note that these maxima are approximate values as the data points are

discrete.

We also experimented with arrival processes that are more bursty than Poisson. In particular,

we also used arrivals that occur in bursts of average size 20 packets, with an exponential inter-

burst time. The results are shown in Figure 9, with a similar observation and conclusion. Note


17

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Aggregate arrival rate (Mbps)

Agg

rega

te th

roug

hput

(M

bps)

20 pkt10,000 pkts

Fig. 9. Throughput performance for buffer size 20 and 10,000in which packet arrival process is exponential and bursty (average

burst size of 20 packets)

that in bursty scenarios, the MAC buffer cannot be reduced beyond the average burst size without

the probability of packet drop becoming prohibitively large.

From the above simulation results and comparisons, we conclude that saturation throughput

is a pessimistic criteria when working with 802.11 network.We also observe that a large buffer

size in client nodes can have a negative effect on throughputperformance. The intuitive reason

is that for arrival rates beyond saturation, the higher the arrival rate, the higher the chances of

collision between competing packets. This, in turn, leads to large average window size using

exponential back off, which results in waste of bandwidth. Reducing the buffer sizes at the

client nodes effectively reduces arrival rates “seen” by the base station for arrival rates beyond

saturation.

There are two important points to make in applying the above observation to practice. The

first is that in order to fully benefit from the above result, ideally one would like to operate the

system around the region where the aggregate throughput exceeds the saturation throughput, by

allocating the right buffer size. This may not be easy in practice because one does not necessarily

know a priori the number of clients in the system or their respective arrival processes. Fortunately,

even if one cannot perfectly fit the buffer size to the traffic scenario, not much is lost in term


18

of throughput. As we have seen, a smaller buffer gives identical throughput performance as

a large buffer under all arrival rates except for the immediate region exceeding the saturation

rate, in which case smaller buffers outperform large buffers. Even more fortunate, in the case

of transporting using TCP, as we shall see in the next subsection, TCP actually adapts to the

smaller buffer size (adjusting its congestion window size)and “learns” the ideal operating point.

The second point is that the gain in throughput for UDP trafficis obtained at the expense of

higher packet losses due to buffer overflow. We note that, forall buffer sizes and at arrival rates

above the saturation rate, the higher the arrival rate, the higher the difference between arrival and

service rates. In the case of smaller buffers, this difference means packets are lost due to more

buffer overflow; whereas in the case of large buffers, this difference means packets are queued

indefinitely in the buffer (up to the buffer capacity), as well as more loss due to collision. This

distinction is important as it sheds light on the advantage of losing packets at the MAC buffer:

buffer overflow prevents excessive traffic and packet collision over the air. Therefore, reliability

mechanism (e.g., packet loss recovery/retransmission) atthe higher layers does not involve the

actual “retransmission” of packets over the air. Such a system is much more bandwidth and

energy efficient than retransmitting packets lost due to collision.

Having demonstrated the benefits of adopting smaller buffersizes at the MAC layer for UDP

traffic, we next examine whether the same approach has negative impact on TCP traffic, which

is reactive unlike UDP. We will see that the adaptive nature of TCP makes its performance (to

a large extent) impartial to the choice of the MAC buffer size.

B. Sending TCP Packets

The sending rate of TCP packets is determined by the TCP agents at both the sender and

receiver. If TCP packets are being sent by client nodes, the sender-side TCP considers any

loss of packets as a sign of network congestion and, consequently, throttles its sending rate.

The reactive response of TCP, i.e. additive-increase, multiplicative-decrease of the congestion

window, adaptively controls the rate at which packets are being lost for any reason. In our

network, two possible reasons significantly contribute to the loss of a packet: buffer overflow

and timeout (both are regulated and impacted by users’ interactions and dynamics.).

Table III shows the aggregate throughput, number of packetsdropped, the average round trip

time (RTT) for TCP packets, and the average congestion window during the simulation for


19

TABLE III

PARAMETERS MEASURED FORTCPSIMULATION FOR DIFFERENT BUFFER SIZE VALUES

Buffer size Throughput Buffer overflow drop Drop due to timeout Average RTT (s) Average CWND

1 3276458 106862 2 0.261492 3.53879

3 3280281 18205 5 0.712183 14.2779

6 3266901 172 48 1.21481 202.856

10 3276458 12 25 1.21821 223.326

30 3275366 0 15 1.21982 224.9

10000 3275366 0 15 1.21982 224.9

different choices of MAC buffer sizes. Many important observations and conclusions are to be

made here: First, we do not see any significant differences between the net aggregate throughput

achieved across different scenarios. Moreover, while the number of packets dropped due to

timeout are quite insignificant, we see significant and consistent changes in number of packets

dropped due to buffer overflow, average RTT, and average TCP congestion window size. This

can be explained as follows. Packet losses due to timeout do not have significant impact on the

throughput performance in the system. As the buffer size increases, the probability of dropping

packets decreases significantly. This has a positive impacton the TCP congestion window size.

However, we do not see any proportional increases in aggregate throughput as the average TCP

congestion window increases. This is because, in the case ofhigher buffer size, there is a higher

competition to share the bandwidth which increases the queue delay of packets (shown by an

increase in RTT). This slows down the sending rate for a givencongestion window as TCP uses

a sliding window mechanism. That is, although a packet with such a long RTT is not dropped,

it blocks the sliding TCP window. This is exactly why the aggregate throughput does not vary

significantly with buffer sizes.

Here we note that the lower aggregate throughput in TCP traffic, relative to UDP traffic, is

somewhat expected due to the less stochastic nature of the TCP traffic streams and the lower

statistical multiplexing of the sources. This lower statistical multiplexing results in a higher level

of simultaneous use of channel and, hence, higher collisionrates. In other words, the adaptive

nature of TCP streams is both the curse and the blessing: it isa curse in smoothly adapting traffic,


20

resulting in higher collision rate and, hence, less efficient use of bandwidth; it is a blessing as

it guarantees a robust performance against variations in MAC buffer sizes.

The second issue at hand is the impact of packet loss due to buffer overflow. We note two

regimes for the operation of the network in relation to packet loss. Our studies show that, when

traffic intensity is significantly below saturation, packetloss due to overflow is negligible. With

an increase in traffic load, packet overflow loss increases. When the traffic load is strictly below

saturation, the short buffers introduce an undesirable loss phenomenon. This loss probability

can easily be combatted at high layers via FEC or packet retransmission3. In the regime where

arrival rate surpasses the saturation throughput of the system, the packet loss due to overflow

becomes insignificant compared to the packet loss due to collisions and deadline expiry. This

means that the negative impact of a short buffer, i.e., higher buffer overflow rate, is dominated by

the positive impact of short buffer on decreasing the collision rate. In other words, this highlights

a similar point we made in the case of UDP traffic: that is, for all buffer sizes, the higher the

arrival rate (beyond saturation), the higher the difference between the arrival rate and service

rate. As mentioned earlier, in the case of small buffers, this difference means packets queued

increase buffer overflow, whereas in the case of large buffers, the difference means packets

queued indefinitely in the buffer (up to buffer capacity≈ ∞) as well as increased packet loss

due to collision. This distinction is important because theformer does not introduce excessive

traffic and packet collision over the air. Therefore, any reliability (e.g., packet loss recovery and

retransmission) measures at higher layers do not involve the actual transmission of packets –

they are lost prior to transmission which is thus much more bandwidth and energy efficient.

VI. CONCLUSION

Most studies regarding 802.11 technology have focused on what is known as saturation

analysis. In this paper, we first showed that the notion of saturation is an inherently pessimistic

one as it does not fully convey the capacity of the system. Ourwork was motivated by our

observations and simulations of the 802.11 network. We usedbasic concepts from Markov chain

theory to explain a seemingly paradoxical gap between theoretical notion of throughput and

3The FEC technique is advantageous to retransmission as it does not incur an out-of-order delivery problem, but both techniques

are simple and easy to implement.


21

the simulated performance of an 802.11 network. We then relied on this insight to show that a

reduction of MAC buffer size, in fact, significantly improves the throughput performance in the

network. The main reason behind this improvement is the monotonically decreasing property of

the saturation throughput in 802.11 network with the numberof backlogged users.

While we have shown that saturation throughput does not completely capture the capability

of 802.11, it remains one of the most succinct and natural notions of performance. It would

be highly desirable if we could come up with a similarly succinct and natural notion in the

non-saturated regime (conceivably the finite buffer size will have to be counted for somehow).

This is a potentially interesting future research direction.

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