Secured operating regions of Slotted ALOHA in the presence of … · 2017-02-14 · Secured operating regions of Slotted ALOHA in the presence of interfering signals from other networks

Journal of Advanced Research (2011) 2, 207–218

Cairo University

Journal of Advanced Research

Secured operating regions of Slotted ALOHA

in the presence of interfering signals from other networks

and DoS attacking signals

Jahangir H. Sarker, Hussein T. Mouftah *

School of Information Technology and Engineering (SITE), University of Ottawa, Ottawa, Ontario, Canada K1N 6N5

Received 14 October 2010; revised 8 April 2011; accepted 10 April 2011Available online 14 May 2011

*

56

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uo

20

El

Pe

do

KEYWORDS

Ad Hoc networks;

Attacking noise packets;

Interfering signals;

Multiple channels;

New packet rejection;

Retransmission trials;

Other networks;

Sensor networks;

Slotted ALOHA

Corresponding author. Tel.:

2 5664.

mail addresses: jsarker@site

ttawa.ca (H.T. Mouftah).

90-1232 ª 2011 Cairo Un

sevier B.V. All rights reserve

er review under responsibilit

i:10.1016/j.jare.2011.04.008

Production and h

+1 613

.uottawa

iversity.

d.

y of Cair

osting by E

Abstract It is expected that many networks will be providing services at a time in near future and

those will also produce different interfering signals for the current Slotted ALOHA based systems.

A random packet destruction Denial of Service (DoS) attacking signal can shut down the Slotted

ALOHA based networks easily. Therefore, to keep up the services of Slotted ALOHA based sys-

tems by enhancing the secured operating regions in the presence of the interfering signals from other

wireless systems and DoS attacking signals is an important issue and is investigated in this paper.

We have presented four different techniques for secured operating regions enhancements of Slotted

ALOHA protocol. Results show that the interfering signals from other wireless systems and the

DoS attacking signals can produce similar detrimental effect on Slotted ALOHA. However, the

most detrimental effect can be produced, if an artificial DoS attack can be launched using extra false

packets arrival from the original network. All four proposed secured operating regions enhance-

ment techniques are easy to implement and have the ability to prevent the shutdown of the Slotted

ALOHA based networks.ª 2011 Cairo University. Production and hosting by Elsevier B.V. All rights reserved.

562 5800x2173; fax: +1 613

(J.H. Sarker), mouftah@site.

Production and hosting by

o University.

lsevier

Introduction

To improve the secured transmission over vulnerable wirelessnetworks, assessment of the wireless multiple access schemesin the presence of jamming or attacking signals is an important

issue [1]. It is well known that the Code Division Multiple Ac-cess (CDMA) system has a special resistance against the inter-ference signals from other networks and the attacking signals.

Thus the CDMA scheme may be the first choice as a multipleaccess scheme in the presence of interference signals from othernetworks or/and attacking signals. The attacker should spread

its energy evenly over all degrees of freedom in order to mini-mize the average capacity of the original signals [2,3]. In a sim-

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mailto:mouftah@site. uottawa.ca

http://dx.doi.org/10.1016/j.jare.2011.04.008



208 J.H. Sarker and H.T. Mouftah

plified CDMA transmission system, with the knowledge of

spreading code, the receiver is able to detect the users’ signalsfrom interfering signals from other networks and attacking sig-nals. Using the attacker state information and the effects offading, the channel capacity can be enhanced further. For

enhancing uplink channel capacity, the attacker state informa-tion is more important than that of the effects of fading.

Preventing the attacking signals becomes very difficult, if the

attackers use the same code as the legal users and transmit. Aspecific Frequency Hoping Speed Spectrum (FHSS) techniquecan prevent this type of attack [4]. However, a specific FHSS

technique is inefficient for a large number of mobile nodes.An innovative message-driven frequency hopping was intro-duced and analyzed to improve the system capacity [5]. The

mobile nodes can exploit channel diversity in order to createwormholes in hostile jamming or attacking environment, [6].

In infrastructure-less wireless Ad Hoc and sensor a network,mobile nodes not only behave as transmitters and receivers but

also as network elements, i.e., switches or routers, without anyestablished network infrastructure. As a result, low powerconsumption systems are becoming important for infrastruc-

ture-less wireless Ad Hoc and sensor networks. The SlottedALOHA is the most spectral and power efficient multiple ac-cess scheme [7,8]. Although, the CDMA has especial resistance

against interference and attacking signals, Slotted ALOHA is awidely used random access protocol not only for its simplicityalso for its higher spectral and power efficiency.

The Slotted ALOHA multiple access schemes is used exclu-

sively in newly developed Radio Frequency Identification(RFID) technology [9]. The Slotted ALOHA is also used asa part of different multiple access protocols especially for the

control channels in many new wireless technologies. For in-stance, it is used in the random access channels of Global Sys-tem for Mobile (GSM) communications [10] and its extension

General Packet Radio Services (GPRS) [11,12], WidebandCode Division Multiple Access (WCDMA) system [13],cdma2000 [14,15], IEEE 802.16 [16], IEEE 802.11 [17], etc. A

smart power saving jammer or attacker can attack only inthe signaling channels, instead of attacking whole channels[18–20]. Therefore, defending the control channels from exter-nal and internal attacks [21] are very important issue. If the to-

tal network is based on Slotted ALOHA based protocol, thendefending the network against the DoS attack is one of themost important factors [22,23] and has been discussed in this

paper.A special type of Denial of Service (DoS) attack, called ran-

dom packet destruction that works by transmitting short peri-

ods of noise signals is considered as attacking signals. Thisrandom packet destruction DoS packets can effectively shutdown Slotted ALOHA based networks [9] and the networks

use the Slotted ALOHA based signaling channels [10–20].One of the main drawbacks of Slotted ALOHA is its excessivecollisions at higher traffic load condition. The current anti-attack measures such as encryption, authentication and autho-

rization [24,25] cannot prevent these types of attacks. Since therandom packet destruction DoS packets increase the collisionfurther, the receiver cannot read the message packets.

The effect of attacking noise packet signals on the SlottedALOHA scheme without autonomic is investigated [26–28].The stability of Slotted ALOHA in the presence of attacking

signals is presented in Sarker and Mouftah [29], where dy-namic channel load and jamming information are needed to

maximize the channel throughput, which makes the system

implementation difficult. Recently, there has been an increas-ing interest in the autonomic networks, i.e., networks shouldbe self-stabilized without the use of feedback information[30]. Excellent work in self-stabilized Slotted ALOHA without

the use of feedback information is presented in Bing [31],where the effect of attacking signals is not considered. Aself-stabilized random access protocol in the presence of ran-

dom packet destruction DoS attack for infrastructure-lesswireless autonomic networks is presented in Sarker andMouftah [32]. In this paper we have investigated the combined

effect of the interfering signals from other networks and theDoS attacking signals on Slotted ALOHA. Three differenttypes of noises are considered in this paper. First, noise related

to interfering packets from the same network. Second, noiserelated to interfering packets from the other networks andthird, noise related to attacking packets from DoS attack.The contributions of this paper are outlined as follows.

(1) The throughput of Slotted ALOHA in the presence ofthe interfering signals from other networks and the ran-

dom packet destruction DoS attack is presented.(2) It is shown that for any positive value of message packet

arrival rate, the throughput decreases with the increase

of the interfering signals from other networks’ signalrate. Similarly, the throughput decreases with theincrease of the random packet destruction DoS attack-ing packet rate.

(3) A sufficient number of channels can prevent the shut-down of Slotted ALOHA in the presence of interferingsignals from other networks or/and the random packet

destruction DoS attack by reducing the collisions.(4) In the presence of other message packets, a message

packet is captured, if its power is higher than the message

capture ratio times of all other interfering message pack-ets’ power for a certain section of time slot to lock thereceiver. Similarly, a message packet is captured, in the

presence of interfering packets from other networks, ifits power is higher than the interfering capture ratio timesof the power of the interfering packets from other net-works. At the same way, a message packet is captured,

in the presence of attacking noise packets, if its poweris higher than the attacking capture ratio times of otherattacking noise packets’ power. Results show that a

lower value of the message capture ratio is the mosteffective solution comparing with the interfering packetcapture ratio or the attacking packet capture ratio.

(5) The approximate value of the number of channels thatprovides the maximum throughput is derived.

(6) The security improvement region using the number of

retransmission trials control is presented.(7) The security improvement region using the new packet

rejection is also presented.

Rest of the paper is organized as follows. The system modeland assumptions are described in the next section. The thirdsection shows the security improvement using multiple chan-

nels and capture effects. The security improvement by limitingthe number of retransmission trials is evaluated in the fourthsection. The fifth section presents the security improvement

by new packet rejection. The conclusion is provided in the lastsection.

ActiveL- parallel channels

Retransmission trials <=r

+

+

Total rejection

Retransmission rejection =

Retransmissions =

Yes

No

Success

G/L( )αλ −1L

L

λα

L

λ

( ) { }∑=

−−r

i

iPL 0

)Su(11 αλ

( ){ } 1)Su(11 +−− rPL

αλ

Attacking signal with rate J

Other networks’ jamminging signal I

Fig. 1 System model and assumptions.

Secured operating regions of Slotted ALOHA in the presence of interfering signals from other networks and attacking signals 209

System model and assumptions

Let us consider a system, where a base station is located in the

middle of a very large number of users having mobile units(nodes). Assume that the average value of the new messagepacket arrival rate from all active mobile nodes per time slotis k packet per time slot. In Slotted ALOHA, the throughput

initially increases with the increase of the new packet genera-tion rate, k. The throughput reaches its maximum value fora certain value of the new packet generation rate from all ac-

tive nodes. The throughput collapse and reaches to zero, ifthe new packet generation rate increases further. The through-put collapse is known as the security or stability problem in

Slotted ALOHA. The reason for throughput collapse is exces-sive collision. The throughput collapse can be prevented byreducing the new packet arrival rate per slot. The packet rejec-

tion can provide one of the solutions and is considered in thispaper.

Assuming that the new packet rejection probability is a.The new packet transmission rate per time slot is kð1� aÞ.Let there be L parallel Slotted ALOHA based channels. Themobile nodes can transmit their packets selecting any of theL channels by random selection, without the knowledge of

other mobile units’ activeness. During the transmission ofpackets, each mobile node adjusts their packet size to fit intothe time slots. Since the average new message packet transmis-

sion rate from all active mobile nodes per time slot is kð1� aÞpacket per time slot and the channel selection is random, thenew packet transmission rate from all mobile nodes iskLð1� aÞ packets per time slot.

It is well known that the Slotted ALOHA’ performance isdegraded due to excessive collision. The interference fromother networks can produce packets to increase the collision

farther. Let the interference from other networks’ packet arri-val to the base station be Poisson Point Process with an aver-age rate of I packet per time slot. The probability that m

packets are transmitted to the same slot from other networksas jamming is

INm ¼Im

m!e�I ð1Þ

In the first collision reducing technique, we have used multi-ple parallel Slotted ALOHA Slotted channels instead of singlechannel Slotted ALOHA channel. For doing that the message

packets can be transmitted in a multiple L-channel SlottedALOHA system. Then we have the possibility of reducing col-lisions. In multiple L-channel Slotted ALOHA system, inter-

ference from other networks’ jamming packets will transmitto all L channels uniformly. Let the probability that i interfer-ence from other networks’ jamming packets out of m jammingpackets be transmitted at the same slot of an L-channel Slotted

ALOHA system

INmji ¼m

i

� �1

L

� �i

1� 1

L

� �m�ið2Þ

Now form total probability theory, the probability that iinterference from other networks’ jamming packet are trans-mitted to the same slot is

INi ¼X1m¼i

Jm

m!e�I

m

i

� �1

L

� �i

1� 1

L

� �m�i

¼ ðI=LÞi

i!e�ðI=LÞ ð3Þ

The attacking noise packets can also collide with message

packets to reduce the performance of Slotted ALOHA. There-fore, attacking signals are made to produce dummy packets/noise packets of the same size to increase the collision farther[22,23]. In addition, assume that the attacking signals are not

producing noise packets in each slot for two reasons. First, itwill be detected immediately and will be removed. Second, itwill dissipate more energy and will die soon. Let the attacking

packet arrival to the base station be also Poisson Point Processwith an average rate of J packet per time slot. The probabilitythat n packets are transmitted to the same slot from the attack-

ing node (or nodes) is

An ¼Jn

n!e�J ð4Þ

In multiple L-channel Slotted ALOHA system, the attacker

packets need to transmit all L channels separately. The attack-er should spread its energy evenly over all degrees of freedomin order to minimize the average capacity [2,3]. Let us assume

that the attacking packets also transmitted at L parallel SlottedALOHA channels to increase the collision. The effect of recei-ver noise has not been considered in this analysis, since it is

very small compared to the collision.The probability that j attacking noise packets out of n

attacking noise packets will be transmitted at the same slotof an L-channel Slotted ALOHA system is

Anjj ¼n

j

� �1

L

� �j

1� 1

L

� �n�jð5Þ

From total probability theory, the probability that j attack-ing noise packets are transmitted to the same slot is

Aj ¼X1n¼j

Jn

n!e�J

n

j

� �1

L

� �j

1� 1

L

� �n�j

¼ ðJ=LÞj

j!e�ðJ=LÞ ð6Þ

If the base station can receive only one message packet per

time slot in the presence of interfering packets from other net-works and attacking noise packets, then the slot is consideredas successful. Let a maximum of r retransmission trials be al-

lowed. Assume the retransmitted packets are also Poisson ar-rival [33]. Thus, the aggregate message packet arrival rate isG packet per time slot. If any message packet also selects Lchannels by random selection, the aggregate message packet

arrival rate per time slot is G/L. The system model andassumptions is presented in Fig. 1.


Probability of success

The radio channel is characterized by fading of the receiving

signal, resulting from vector addition of several reflected, scat-tered or diffracted multi-paths. The fading is assumed to beslow, affecting all bits in a packet in the same way, and flat,implying sufficiently low bit rates. With these assumptions

the received signal envelop r is constant over each packetand approximately Rayleigh distributed [34]

fðrÞ ¼ 2r

P0

exp � r2

P0

� �r � 0 ð7Þ

PðSuÞ ¼ Pðthe selected packet will be a message packetÞ� Pða message packet is captured in the presence of interfering packets from other networksÞ� Pða message packet is captured in the presence of attacking noise packetsÞ� Pða the message packet is captured in the presence of other interfering message packetsÞ

¼ PM � PCI � PCA � PCM ð10Þ

where P0 is the average power of the received packets. The cor-responding instantaneous power distribution (i.e., power dis-tribution of the packets) can easily been shown to be [34]

fðpÞ ¼ 1

P0

exp � p

P0

� �p � 0 ð8Þ

In the following analysis it is assumed that packet colli-sion in a slot is the sole cause of packet loss. This, of

course, is not strictly true since deep fades also contributeto packet loss, due to an increase error rate, even withoutpacket collision. In a well-designed system, the probability

of such events is generally order of magnitude smaller thanthat of packet collision.

In a Rayleigh fading channel the probability that the

power of a message packet is higher than that of the powerof an attacking packet is ½ [32]. In the same way, it can beshown that the probability that the power of an attackingpacket is higher than that of the power of a message packet

is also ½.The probability that a test message packet will be se-

lected from all three types of packets is the ratio of the total

number of message packets per time slot and the total num-ber of message packets per time slot plus the total numberof interfering packets from other networks per time slot

and plus the total number of attacking noise packets pertime slot. Therefore, the probability that a selected testpacket is a message packet is

PM ¼ Pðthe selected packet is a message packetÞ

¼ Total number of message packets

Total of message packetsþ Total of interfering packets from other networksþ Total of attacking packets

P1a¼0

a ðG=LÞa

a!e�ðG=LÞ

P1a¼0

a ðG=LÞa

a!e�ðG=LÞ þ

P1b¼0

b ðI=LÞb

b!e�ðJ=LÞ þ

P1c¼0

c ðJ=LÞc

c!e�ðJ=LÞ

¼ G=L

G=Lþ I=Lþ J=L¼ G

Gþ Iþ Jð9Þ

Amessage packet is successfully received in a time slot, if four

conditions are fulfilled. First, the receiver will select a messagepacket in the presence of message packets from the same net-work, interfering packets from other networks and attackingnoise packets. Second, there exists the probability that the mes-

sage packet is captured in the presence of interfering packetsfrom other networks. Third, there exists the probability thatthemessage packet is captured in the presence of other attacking

noise packets. Fourth, the probability that themessage packet iscaptured in the presence of other interfering message packetsfrom the same network exists. Therefore, the probability that a

message packet is successfully transmitted can be written as

According to our assumption, the power distribution of amessage packet, the power distribution of an interfering packetfrom other networks and the power distribution of an attack-ing packet are the same. The capture effect of a message packet

in the presence of interfering packets from other networks isdefined in the following way. In case of a message packet col-lision with interfering packets from other networks, a message

test packet is captured if its power is zf times higher than thecombined power of all interfering packets from other networkstransmitted on the same slot as message (selected by receiver)

packet is being transmitted, during a ‘certain section of timeslot’, to lock the receiver. Note that, capture ratio zf and‘certain section of time slot’ both are affected by modulationand coding technique [34]. Using the procedure presented in

Sarker and Mouftah [32], it can be shown that the probabilityof a message packet is captured against all interfering packetsfrom other network transmitted to the same slot is

PCI ¼ exp � I=L

1þ 1=zf

� �ð11Þ

The capture effect of a message packet in the presence ofattacking packets is defined in the following way. In case of

a message packet collision with attacking packets, a messagetest packet is captured if its power is za times higher than thatof all attacking interfering packets transmitted on the same

slot as message (selected by receiver) packet is being transmit-ted, defined as the attacking packet capture ratio, during a

‘certain section of time slot’, to lock the receiver. The probabil-ity that a message packet is captured against all attackingpackets transmitted to the same slot is [32]

PCA ¼ exp � J=L

1þ 1=za

� �ð12Þ


The evaluation procedure of ‘‘za’’ is presented in Sarker and

Mouftah [32]. At the same way, a message test packet is cap-tured, if its power is zm times higher than that of all other inter-fering packets transmitted from the same network defined asthe attacking packet capture ratio, during a ‘certain section

of time slot’, to lock the receiver. The probability that a mes-sage packet is captured against all other interfering packetstransmitted from the same network is [32,34]

PCM ¼ exp � G=L

1þ 1=zm

� �ð13Þ

Finally the probability of success of a message packet in the

presence of interfering packets transmitted from the other net-works, attacking noise packets and interfering packets trans-mitted from the same network is

PðSuÞ ¼ PM � PCI � PCA � PCM ¼G

Gþ Iþ Jexp � I=L

1þ 1=zf

� �

� exp � J=L

1þ 1=za

� �exp � G=L

1þ 1=zm

� �: ð14Þ

The probability of failure of any message packet is1� PðSuÞ. This unsuccessful part k

Lð1� aÞf1� PðSuÞg will be

transmitted during first retransmission time. The probability

of two successive failures is f1� PðSuÞg2. So the second timeretransmission part is k

Lð1� aÞf1� PðSuÞg2, and so on. In gen-

eral, kth time retransmission part is kLð1� aÞf1� PðSuÞgk. Let

the total number of retransmissions of a packet be r (one trans-mission followed r retransmission trials). The totalmean offeredtraffic from all active users is then given by

G

L¼Xrk¼0

kLð1� aÞf1� PðSuÞgk ð15Þ

Simplifying Eq. (15) and combining with Eq. (14), we can

write

G

LPðSuÞ¼ k

Lð1�aÞ½1�f1�PðSuÞgrþ1�)G

L

G

GþIþJ

�exp � I=L

1þ1=zf

� �exp � J=L

1þ1=za

� �exp � G=L

1þ1=zm

� �

¼ kLð1�aÞ 1� 1� G

GþIþJexp � I=L

1þ1=zf

� ��

�exp � J=L

1þ1=za

� �exp � G=L

1þ1=zm

� ��rþ1#

ð16Þ

Eq. (16) is the basic equation of retransmission cut-off andnew packet rejection algorithm of multiple L-channels SlottedALOHA in the presence of interfering packets transmitted

from other networks and attacking noise packets.

Security improvement using multiple channels and capture

effects

The probability of success of L-channel Slotted ALOHA sys-

tem in the presence of interfering packets transmitted fromother networks and attacking noise packets is derived in Eq.(14). The throughput per slot of L-channel Slotted ALOHA

system is defined as the multiplication of average traffic arrivalrate per time slot and the probability of success in the presenceof interfering packets transmitted from other networks and

attacking noise packets. Thus, the throughput is

S¼ G

LPðSuÞ¼ G2

LðGþIþJÞ exp �I=L

1þ1=zf

� �exp � J=L

1þ1=za

� �

�exp � G=L

1þ1=zm

� �¼ kLð1�aÞ 1� 1� G

GþIþJ

��

�exp � I=L

1þ1=zf

� �exp � J=L

1þ1=za

� �exp � G=L

1þ1=zm

� ��rþ1#ð17Þ

Eq. (17) is the basic equation for the throughput of a mes-sage packet. Articulately, the new packet generation rate k,number of channels L, new packet rejection probability a, cap-ture ratios, zf, za, zm, interfering packets from other networks’generation rate, I, attacking signal generation rate, J, andnumber of retransmission trials, r, play important role in thisequation.

Fig. 2 shows the throughput of Slotted ALOHA in the pres-ence of interfering packets from other networks and attackingsignals. But in this section, we will limit our discussion only to

the effect of L-channels and capture ratios. Therefore, we willconsider only the first two methods of secured transmission inSlotted ALOHA. The first method is to use multiple channels

and the second method is to lower the capture ratios.Fig. 2 shows the throughput per slot, S with the variation of

aggregate message packet arrival rate, G for different values of

attacking packets rates of J. From Fig. 2 we can make the fol-lowing conclusions:

1. The throughput per slot S of 1-channel without capture

effects, za ¼ 1; zf ¼ 1; zm ¼ 1, Slotted ALOHA systemis very low in the presence of interfering signals from othernetworks and attacking noise packet signal (Fig. 2b com-

paring with Fig. 2a). Because of that the current 1-channelwithout capture effects Slotted ALOHA based networks [9–17] can be shut down very easily. A lower message capture

ratio, zm ¼ 1, can increase the channel throughput signifi-cantly at all traffic load (Fig. 2c).

2. A lower interfering capture ratio, zf ¼ 1, can increase thechannel throughput slightly. A lower interfering capture

ratio is only effective, if the interfering signals rate fromother networks, I is high (Fig. 2 d comparing with Fig. 2c).

3. Similarly, a lower attacking capture ratio, za ¼ 1, can

increase the channel throughput slightly. If the attackingsignals rate, J is high only then a lower attacking captureratio is effective (Fig. 2e comparing with Fig. 2d).

4. If 5-channels are used instead of 1-channel then thethroughput per slot increases significantly, even under thehigh interfering signals from other networks and attacking

signals (Fig. 2f comparing with Fig. 2b).5. Since the throughput per slot, S, does not collapse even

with a high interfering signals rate from other networks, Iand attacking noise packet generation rate, J, with a lower

message capture ratio, zm ¼ 1, the security of SlottedALOHA system can be enhanced by lowering the captureratios Fig. 2c–e.

6. Since the throughput per slot, S, does not collapse with ahigh message packet arrival rate, G, even with a highinterfering signal rate from other networks, I and a high

attacking noise packet generation rate, J, with a highernumber of channels, L, the security of Slotted ALOHAsystem can be enhanced using multiple L-Slotted ALOHA

channels.

Message packet generation rate G

Thr

ough

put p

er s

lot S

1

J=00.10.20.30.5

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6

∞=∞=∞= mfa zzz ,,

I=0, L=1

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6


Thr

ough

put p

er s

lot S

∞=∞=∞= mfa zzz ,,

I=0.3, L=1

1

J=0

0.10.2

0.30.5

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6


Thr

ough

put p

er s

lot S

I=0.3, L=1J=0

0.1

0.2

0.3

0.5

1,, =∞=∞= mfa zzz

1

(a) 1-channel, without interference, without capture (b) I=0.3 (c) message packet capture 1=mz

1,1, ==∞= mfa zzz

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6

I=0.3, L=1

J=0

0.1

0.2

0.3

0.5

Thr

ough

put p

er s

lot S


1

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6


Thr

ough

put p

er s

lot S

J=0

0.1

0.2

0.3

0.5

1,,1 =∞== mfa zzz I=0.3, L=1

1

0 3 6 9 12 150

0.1

0.2

0.3

0.4

0.5

0.6


Thr

ough

put p

er s

lot S

∞=∞=∞= mfa zzz ,,I=0.3, L=5

1

J=00.10.20.30.5

(d) interfering packet capture 1=fz 1=az (f) 5-channel, without capture (e) attacking packet capture

Fig. 2 Throughput per slot with the variation of message packet arrival rate.


7. There exists an optimum point where throughput per timeslot, S, is maximum for given values of message packet gen-eration rate, G, interfering signals rate from other net-

works, I, and attacking packet generation rate, J.

Differentiating Eq. (17) with respect to attacking noise

packet generation rate, J, we obtain

dS

dJ¼ exp � I=L

1þ 1=zf

� �exp � G=L

1þ 1=zm

� �� 1=L

1þ 1=za

� �G2

LðGþ Jþ IÞ exp � J=L

1þ 1=za

� �� G4

LðGþ Jþ IÞ2exp � J=L

1þ 1=za

� �" #

¼ exp � I=L

1þ 1=zf

� �exp � G=L

1þ 1=zm

� �exp � J=L

1þ 1=za

� �� 1=L

1þ 1=za

� �G2

LðGþ Jþ IÞ �G4

LðGþ Jþ IÞ2

" #

ð18Þ

It is clear from Eq. (18) that for any positive value of mes-sage packet generation rate, G, and interfering packets arrivalrate from other networks, I, the throughput, S, decreases with

dS

dG¼ 1

Lexp � J=L

1þ 1=za

� �exp � I=L

1þ 1=zf

� �G2

Gþ Jþ Iexp � G=

1þ 1

�"

¼ 1

Lexp � J=L

1þ 1=za

� �exp � G=L

1þ 1=zm

� �G

Gþ Jþ I� G=L

1þ 1=z

��

the increase of attacking noise packet generation rate, J. Ex-actly in the same way, it can be shown that for any positive va-lue of message packet generation rate, G, and the attacking

noise packet generation rate, J, the throughput, S, decreaseswith the increase of interfering packets arrival rate from othernetworks, I. However, the numerical results of these two re-sults have already been depicted in Fig. 2.

Differentiating Eq. (17) with respect to message packet gen-eration rate, G, we get

L

=zm

�� 1=L

1þ 1=zm

� �þ ðGþ Jþ IÞð2GÞ � G2

ðGþ Jþ IÞ2exp � G=L

1þ 1=zm

� �#

m

�þ ðGþ Jþ IÞð2Þ � G

ðGþ Jþ IÞ

�ð19Þ


Now putting the differentiation result Eq. (19) equal to

zero, we obtain the optimum value of the message packet arri-val rate from all active mobile nodes,

Gopt ¼fLð1þ 1=zmÞ � ðJþ IÞg �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8LðJþ IÞð1þ 1=zmÞ

q2

ð20Þ

Using the value of optimum message packet arrival rate,Gopt, in Eq. (17), we can obtain the optimum throughput pertime slot as

Number of channels L

Thr

ough

put p

er s

lot S

opt

Thr

ough

put p

er s

lot S

opt

J=0

1

52

1020

0,

,

=∞=

∞=∞=

Iz

zz

m

fa

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Number o

Thr

ough

put p

er s

lot S

opt

0 10 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

J=0 1 2

z

z

(a) without interference, without capture (b) with inte

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2,1

1,

==

=∞=

Iz

zz

m

fa

L

5

10

20

J=0 1 2

0 10 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Number o

Thr

ough

put p

er s

lot S

opt

J=0 1 2

(d) interfering packet capture 1=fz (e) attacking pack

Fig. 3 The maximum throughput, Sopt with

Sopt ¼ðGoptÞ2

LðGopt þ Jþ IÞ exp � J=L

1þ 1=za

� �exp � I=L

1þ 1=zf

� �exp �

�

¼Lð1þ 1=zmÞ � ðJþ IÞf g þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8L

q�

2L Lð1þ 1=zmÞ þ ðJþ IÞ þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8

q�

� exp � J=L

1þ 1=za

� �exp � I=L

1þ 1=zf

� �exp

�fLð1þ 1=zmÞ �24

The optimum throughput per time slot is shown in Figs. 3

and 4 using Eq. (21). Figs. 3 and 4 show that the optimumthroughput can be increased significantly using lower capture

ratios and multiple channels. The conclusions of Figs. 3 and4 are almost same as the conclusions drawn from Fig. 2.

Thr

ough

put p

er s

lot S

opt

Thr

ough

put p

er s

lot S

opt

f channels L L

510

20

30 40 50

2,

,

=∞=

∞=∞=

Im

fa z

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2,1

,

==

∞=∞=

Im

fa

z

zz

rference, I=2 (c) message packet capture 1=mz

J=0

J=0 1 2

510

20

1 2

510

20

2,1

,1

==

∞==

Iz

zz

m

fa

30 40 50

510

20

f channels L L0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2,1

1,1

==

==

Iz

zz

m

fa

et capture 1=az (f) with capture effects

the variation of number of channels L.

Gopt=L

1þ 1=zm

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðJþ IÞð1þ 1=zmÞ

�2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLðJþ IÞð1þ 1=zmÞ

�

ðJþ IÞg þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8LðJþ IÞð1þ 1=zmÞ

q2Lð1þ 1=zmÞ

35

ð21Þ


Now the question that may arise is: what is the optimum

number of channels, L that provides maximum throughput.To answer this question, the optimum L can be obtained bysetting Eq. (19) is equal to zero. Therefore, the optimum num-ber of channels is

Lopt ¼GðGþ Jþ IÞ

ð1þ 1=zmÞðGþ 2Jþ 2IÞ ð22Þ

Sopt ¼kopt

L1� 1�PoptðSuÞ

rþ1h i¼ ðGoptÞ2

LðGopt þ Jþ IÞ exp � J=L

1þ 1=za

� �exp � I=L

1þ 1=zf

� �exp � Gopt=L

1þ 1=zm

� �

¼fLð1þ 1=zmÞ � ðJþ IÞg þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞ2 þ 8LðJþ IÞgð1þ 1=zmÞ

q� �22LfLð1þ 1=zmÞ þ ðJþ IÞ þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8LðJþ IÞð1þ 1=zmÞ

qg

� exp � J=L

1þ 1=za

� �exp � I=L

1þ 1=zf

� �exp �

fLð1þ 1=zmÞ � ðJþ IÞgþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8LðJþ IÞð1þ 1=zmÞ

q2Lð1þ 1=zmÞ

24

35ð23Þ

Eq. (22) shows that the optimum number of channels, Lopt,increases linearly with the increase of aggregate message trafficarrival rate, G. The Lopt, increases further with the increase of

PoptðSuÞ¼Sopt=L

Gopt

¼ Gopt

GoptþJþ Iexp � J=L

1þ1=za

� �exp � I=L

1þ1=zf

� �exp � Gopt=L

1þ1=zm

� �

¼Lð1þ1=zmÞ�ðJþ IÞþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ1=zmÞ�ðJþ IÞg2þ8LðJþ IÞð1þ1=zmÞ

qLð1þ1=zmÞþðJþ IÞþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ1=zmÞ�ðJþ IÞg2þ8LðJþ IÞð1þ1=zmÞ

q

� exp � J=L

1þ1=za

� �exp � I=L

1þ1=zf

� �exp �

fLð1þ1=zmÞ�ðJþ IÞgþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ1=zmÞ�ðJþ IÞg2þ8LðJþ IÞð1þ1=zmÞ

q2Lð1þ1=zmÞ

24

35ð24Þ

message packet capture ratio, zm. However, the same decreaseswith the increase of interfering packet arrival rate from othernetworks, I, or/and attacking packet arrival rate, J.

Security improvement by limiting the number of retransmission

trials

In a normal data transmission system, every packet must betransmitted successfully. On the other hand, in the case of con-tention based access protocol or for real-time data transmis-

sion, we can cut the retransmission number, which will avoidthe undesirable stability or security problem of Slotted ALO-HA [35]. Over a long time period, the total offered traffic load

G will have an optimum value Gopt depending on the otherparameters like new packet generation rate per time slot andthe number of retransmission trials. In the case of access orreal-time traffic transmission packets are identical in nature

for each user and the access procedure is limited by time.For a secured operation of L-channels Slotted ALOHA typesystem, with a higher value of new packet generation rate

per time slot, the retransmission trials should be controlled.The purpose of the retransmission trial control is to get theoptimum value of offered traffic load from all users Gopt, which

will make the system secured or stable. Here, in this paper asimplified assumption is considered: if the traffic generation

rate from all active users in a given time slot is less than or

equal to the optimum packet arrival per time slot, the systemis secured. This assumption is reasonable for Slotted ALOHAsystem [33].

The optimum throughput per slot of L-channels Slotted

ALOHA system with and without limiting the number ofretransmission trials can be obtained from Eqs. (18 and 21) as

The optimum probability of success can be obtained fromEqs. (23) and (20) as

Therefore, the optimum throughput per slot of L-channelsSlotted ALOHA system by limiting the number of retransmis-sion trials can be obtained from Eq. (17) as

Sopt ¼ koptL

1� f1� PoptðSuÞgrþ1h i

orkoptL¼ Sopt

1� 1�PoptðSuÞf grþ1ð25Þ

where the values of Sopt and PoptðSuÞ are given in Eqs. (23) and(24), respectively. The main purpose of our system model is tomaximize the throughput per slot, S by adjusting the transmis-

sion trials, r and the new packet generation rate per slot, k=L,for a given interfering packet arrival rate from other networks,I, and attacking packet arrival rate, J. We have already derivedthe maximum throughput of L-channels Slotted ALOHA sys-

tem Sopt in Eq. (23). And it occurs when the aggregate trafficgeneration rate, Gopt, which is shown in Eq. (20).

Eq. (25) is the basic equation for the secured transmission

method. The secured transmission method can be stated as fol-lows: For a call establishment system design or for a real-timetraffic transmission, the time out is the most important param-

eter. This time out is the time to transmit the access informa-tion from mobile to base station plus the switching time. Fromthe value of the time to transmit the access information or real-

time transmission plus the propagation delay, we can find themaximum allowable retransmission trials, r, i.e., how many


retransmission trials are possible for a given time. From this

value of r, L, I, J, za, zf and zm we can find the optimumnew packet generation rate per time slot, kopt=Lper time slotusing Eqs. (23)–(25). Fig. 5 shows the variation of optimumnew packet generation rate per time slot, kopt=L, with the var-

iation of number of channels, L, using Eqs. (23)–(25).Without any retransmission attempts (r! 0 the optimum

new packet generation rate per time slot can be obtained using

Eq. (25) as

kopt

L

� �r!0

¼ Sopt

PoptðSuÞ¼

Lð1þ 1=zmÞ � ðJþ IÞ þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifLð1þ 1=zmÞ � ðJþ IÞg2 þ 8LðJþ IÞð1þ 1=zmÞ

q2L

ð26Þ

Eq. (26) shows the limit of the proposed solution withretransmission cut-off scenario.

In the other extreme, without any retransmission cut-off(r fi1) the optimum new packet generation rate per time slot

can be obtained using Eq. (25) as

UR ¼ 1

1� a

� �Sopt

PoptðSuÞ¼


q2Lð1� aÞ ð30Þ

kopt

L

� �r!1¼ Sopt ð27Þ

where the value of Sopt is given in Eq. (23). Therefore, the secu-rity improvement area by limiting the number of retransmis-

sion trials, r is

Ar ¼ kopt

L

� �r!0

� kopt

L

� �r!1¼


q2L

� Sopt ð28Þ

The shaded parts indicated in Fig. 5 show the secured re-gion by limiting the number of retransmission trials, r. Thelower most parts of the figures show the secured transmissionregion without limiting the number of retransmission trials.

Increasing the number of channel, L or/and reducing the cap-ture ratios, za, zf and zm are not enough to obtain a higher se-cured transmission operating region. Limiting the number of

retransmission trials can increase the secured transmissionoperating region significantly.

Security improvement by new packet rejection

The main purpose of this paper is to obtain the secured trans-

mission of L-channel Slotted ALOHA system. It is alreadyshown that if L-channel Slotted ALOHA system providesmaximum throughput then the system is secured. If limitingthe retransmission trials is not sufficient for obtaining a se-

cured stabilized L-channel Slotted ALOHA system, then itcan be achieved by the expense of newly generated packetrejection.

The maximum throughput per slot of a L-channel SlottedALOHA is Sopt is derived in Eq. (23), and it occurs when theaggregate traffic generation rate, Gopt, which is shown in Eq.

(20). The aggregate message packet generation rate per time

slot G/L, by limiting the number of retransmission trials and

new packet rejection is shown in Eq. (16). Combining Eqs.(16 and 17) and after simplification we can write

kopt

L¼ 1

1� a

� �Sopt

1� 1� PoptðSuÞ rþ1 ð29Þ

The secured operating region ofL-channel SlottedALOHA sys-tem with and without limiting the retransmission trials is de-

picted in Fig. 6. Please note that here the y-axis should bemultiplied by X� ¼ Gopt

1�a. The value of Gopt is given in Eq. (20).

Fig. 6 shows clearly that by increasing the value of a (new packetrejection probability), the secured operating regions with andwithout retransmission cut-off can be increased significantly.

FromFig. 6, it can be said that themaximumvalue of the newpacket generation rate per slot, kopt=Lwith new packet rejectionis

ComparingEqs. (26) and (30), the upper limit of the newpack-et generation rate per slot with new packet rejection is 1=ð1� aÞtimes higher than that of the without new packet rejection.

On the other hand the new packet generation rate per slot,

without limiting the number of retransmission trials with newpacket rejection is

LR ¼ Sopt

1� að31Þ

It can be said that the new packet generation rate per slotwithout limiting the number of retransmission trials with

new packet rejection is 1=ð1� aÞ times higher than that ofthe without new packet rejection, by comparing Eqs. (27)and (31).

From Fig. 6, we can conclude that, the aggregate messagepacket generation rate, G, never reaches its optimum point,if the new packet generation rate per slot, kopt=L, is less thanLR packet per time slot. The reason is that, we started to get

the result of Eq. (31) with the aggregate message packet gener-ation rate, Gopt. So, it is unnecessary to control the retransmis-sion attempt for a secured operation of L-channels Slotted

ALOHA, if the new packet generation rate per slot, kopt=L,is less than LR packet per time slot, where a is the newly gen-erated packet rejection probability.

Conclusions

In this paper, an analytical approach for secured operating re-gions of Slotted ALOHA in the presence of interfering signalsfrom other networks and DoS attacking signals has been

L =20

10

5

3

2

1

L =20

10

5

3

2

1

L =20

10

5

3

2

1

L =20

10

5

3

2

1

Fig. 4 The maximum throughput, Sopt .


investigated. The performance evaluations presented in thispaper are based on the numerical analysis.

The security improvement of L-channels Slotted ALOHA

in the presence of interfering signals from other networksand random attacking noise packets signals is studied in thispaper. The current security protected measures such as encryp-

tion makes the packets unreadable by unauthorized users. Theauthentication technique is used to protect the system fromillegal users and authorization separates the legal users. How-

ever, in a Slotted ALOHA based network, the interfering sig-nals from other networks and the random packet destructionDoS attacking noise packets may collide with message packetsand reduces the secured transmission. Therefore, the current

security measures such as encryption, authentication andauthorization cannot prevent those types of attack. One ofthe main drawbacks of Slotted ALOHA protocol is its exces-

sive collisions.In this paper, we have used four different techniques for

security improvement of Slotted ALOHA by reducing the

collisions. Since the interfering signals from other networksand the random packet destruction DoS attacking noisepacket increase the collision, we intend to use multiple chan-

nels in the Slotted ALOHA protocol to reduce the collisionsin the first technique. The use of multiple channels in theSlotted ALOHA protocol reduces three types of packet colli-

sions. First type of collision is the collision between two ormore message packets. The second type of collision is the col-lision between a message packet and one or more interfering

packets from other networks. The third type of collision isthe collision between a message packet and one or moreother attacking noise packets.

In the second security improvement technique, we haveshown the effects of capture ratios in the presence of interfer-ing signals from other networks and the random packet

destruction DoS attacking noise packet. A lower message cap-ture ratio can increase the throughput and maximum through-put significantly. A lower interfering capture ratio can increasethe throughput and maximum throughput only if the rate of

interfering signals from other networks’ packets rate is high.Exactly same conclusion is applied for a lower attacking cap-ture ratio.

In the third technique, we have used retransmissions cut-offby limiting the number of retransmission trials. The retrans-missions cut-off technique can limit the aggregate packet flow

and form the optimum message packet flow in the presence ofinterfering signals from other networks and the attacking noisepacket. It is possible that the third technique called retransmis-

sions cut-off technique is not enough to control the flow ofmessage packets. Because of that the fourth technique callednew packet rejection probability is introduced. The secured

1 10 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Opt

imum

new

pac

ket g

ener

atio

n

rat

e pe

r sl

ot

Retransmission trials r+1

Secured region without limiting r

X*

Secured region with limiting r

Unsecured operating region

Sopt

Gopt

λ opt /

L

Fig. 6 Secured and unsecured operating regions of multichannel

L-Slotted ALOHA in the presence of interfering signals from

other networks and attacking noise packets. The y-axis should be

multiplied by X� ¼ Gopt

1�a.

1 11 21 31 41 510

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4O

ptim

um n

ew p

acke

t gen

erat

ion

r

ate

per

slot


∞=∞=∞= mfa zzz ,,


I = 0, J = 0



∞=r

0=r

Opt

imum

new

pac

ket g

ener

atio

n

rat

e pe

r sl

ot

Number of channels L1 11 21 31 41 51

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

∞=∞=∞= mfa zzz ,,

I = 2.5, J = 0

∞=r

0=r




1 11 21 31 41 510

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4


Opt

imum

new

pac

ket g

ener

atio

n

rat

e pe

r sl

ot

∞=∞=∞= mfa zzz ,,


I = 2.5, J = 2.5



∞=r

0=r

(a) ∞=az , ∞=fz ∞=mz , I=0, J=0 (b) ∞=az , ∞=fz ∞=mz , I=2.5, J=0 (c) ∞=az , ∞=fz ∞=mz , I=2.5, J=2.5

1 11 21 31 41 510

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4



I = 2.5, J = 2.5

1,, =∞=∞= mfa zzz

Opt

imum

new

pac

ket g

ener

atio

n

rat

e pe

r sl

ot

0=r

∞=r



1 11 21 31 41 510

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4


Opt

imum

new

pac

ket g

ener

atio

n

rat

e pe

r sl

ot

1,1, ==∞= mfa zzz

I = 2.5, J = 2.5



∞=r

0=r


1 11 21 31 41 510

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

∞=== mfa zzz ,1,1

I = 2.5, J = 2.5

∞=r

0=r




Opt

imum

new

pac

ket g

ener

atio

n

rat

e pe

r sl

ot


(d) ∞=az , ∞=fz , 1=mz , I=2.5, J=2.5 (e) ∞=az , 1=fz , 1=mz , I=2.5, J=2.5 (f) 1=az , 1=fz , ∞=mz , I=2.5, J=2.5

λ opt /

Lλ o

pt /

L

λ opt /

L

λ opt /

L

λ opt /

L

λ opt /

LFig. 5 Security improvement by limiting the retransmission trials.


operating regions can be increased 1=ð1� aÞ times by usingthis fourth technique. Where a is the new packet rejectionprobability.

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Secured operating regions of Slotted ALOHA in the presence of … · 2017-02-14 · Secured operating regions of Slotted ALOHA in the presence of interfering signals from other networks