PROBABILISTIC RETRANSMISSION STRATEGY FOR

SINGLE-RELAY COOPERATIVE ARQ

Juan J. Alcaraz, Joan Garc´ıa-Haro and Fernando Cerd´an

Department of Information Technologies and Communication, Technical University of Cartagena

Plaza Hospital 1, Cartagena, Spain

Keywords:

Automatic repeat request (ARQ), cooperative diversity, multi-objective optimization.

Abstract:

In wireless networks with cooperative automatic repeat request (C-ARQ) protocols, a relay node, placed within

the range of the sender node and the destination node, assists the sender in the process of frame retransmis-

sion. In a collision-free scenario, the sender and the relay use different physical channels for retransmissions.

This paper highlights the tradeoff between throughput increment and efﬁciency in the use of radio resources.

By using a probabilistic retransmission strategy, the sender only retransmits in some time-slots after a frame

error notiﬁcation. At the other time-slots, the source can assign the radio resources to other communication

processes, resulting in more efﬁcient use of the bandwidth. The retransmission probability must be carefully

adjusted according to the network parameters. In this paper we propose a Markov model to compute the

throughput performance and a complementary reward model to compute the retransmission rate of the source.

In order to keep the throughput at a high value and to reduce the retransmission rate at the same time, we

present a multi-objective optimization method that is capable of balancing both objectives in any scenario. It

is shown that the increment in bandwidth efﬁciency can be very high, especially for degraded links, compen-

sating the small throughput reduction associated with a probabilistic retransmission at the source.

1 INTRODUCTION

Cooperative automatic repeat request protocols, C-

ARQ, are attracting increasing research attention.

These type of protocols apply the concept of cooper-

ative communication to improve the performance of

link-layer protocols in wireless networks. In cooper-

ative communications, each node not only transmits

and receives data for its own application, but can also

act as a relay node providing an alternative path for

other pairs of communicating nodes (A. Nosratinia,

2004). This idea is known as cooperative diversity

and is commonly presented as an extension of the

spatial diversity concept of multiple-input multiple-

output (MIMO), where each one of the multiple an-

tennas are located at each cooperative node instead of

in a single node. Future evolutions of mobile access

networks are expected to make use of cooperative di-

versity using relay nodes to improve the connectivity

of the terminal nodes, see (R. Pabst, 2004), (F. Fitzek,

2006) or (K. Doppler, 2007).

Classical (non-cooperative) ARQ protocols are

widely used in wireless links to increase the relia-

bility of the data frame delivery process between a

sender node and a destination node. Several factors

of the wireless channel, e.g. path loss, fading and

noise, can degrade the quality of the received sig-

nal so that received frames can not be correctly de-

coded at the destination node. ARQ protocols spec-

ify how to retransmit data frames when frame losses

are detected. C-ARQ exploits the broadcast nature

of the wireless channel, involving additional nodes

(relay nodes) in the retransmission process. A re-

lay node is located within the transmission ranges of

both the sender node and the destination node. If

the relay node overhears a frame that the destination

is unable to decode, it can assist the sender by re-

transmitting the same copy of the lost frame. Pre-

vious works (M. Dianati, 2006), (L. Xiong, 2008),

(I. Cerutti, 2007) have shown that C-ARQ increases

the probability of successful retransmission, resulting

in higher throughput between the sender and the re-

ceiver nodes.

In general, C-ARQ protocols are evaluated in a

slotted radio channel, where the destination node can

receive simultaneously from the sender and the re-

lay nodes. These nodes use different physical chan-

nels to communicate with the destination node, and

J. Alcaraz J., Gar

cıa-Haro J. and Cerdán F. (2008).

PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 21-28

DOI: 10.5220/0002024600210028

 SciTePress

therefore signals do not collide. In CDMA-based net-

works, this requires the use of different scrambling

codes; in OFDM networks, different orthogonal fre-

quencies and, in TDMA, different time-slots. C-ARQ

applied to these types of networks provides higher re-

liability at the cost of a more extensive use of wireless

resources, assuming that both the sender and the relay

node retransmit the lost frame.

The idea proposed in this paper is that, in certain

circumstances, it may be beneﬁcial that the sender

does not retransmit in every time-slot after a frame

loss notiﬁcation. This way, in a time-slot not assigned

to retransmission, the radio resources assigned to the

link between the sender node and the receiver node

are released. Therefore, the sender node can re-assign

this resources temporarily to other links, introduc-

ing new data in the network and making a more ef-

ﬁcient use of radio resources. In many existing and

future radio access networks this is possible because

resource allocation is done slot by slot. Two examples

of this are the high speed downlink data access (HS-

DPA) (H. Holma, 2006) and the WINNER 4G concept

(K. Doppler, 2007).

There exists a clear tradeoff between retransmis-

sion probability and efﬁciency in bandwidth use.

Our approach consists of adjusting the retransmission

probability of the sender node in order to reduce its

retransmission rate, while trying to keep the through-

put close to its maximum. The amount of resources

that this strategy is able to release compensates the

slight reduction of the throughput compared to the de-

terministic strategy, especially when the link between

the sender and the destination is highly degraded.

This paper shows how to ﬁnd an optimal working

point that balances throughputand resource efﬁciency

according to the parameters that characterize the net-

work. The proposed strategy provides a new view of

cooperativediversity, in which the relay node not only

assists the sender node in the retransmission process,

but it also allows the sender to release radio resources

increasing the overall utilization of the bandwidth.

Probabilistic retransmission has been previously

considered in a very recent work (L. Xiong, 2008) as

a strategy to balance cooperation and collision prob-

ability in order to achieve smaller latencies. In con-

trast, our work is focused in collision-free networks,

and therefore its results are applicable to mobile ac-

cess networks. Other works like (M. Dianati, 2006),

(I. Cerutti, 2007) and (I. Cerutti, 2006) consider a de-

terministic retransmission scheme at the source node.

The contributions of this paper are:

• We develop an analytical model based on a dis-

crete time Markov chain (DTMC), useful to com-

pute the throughput. The simplicity of this model

allows a closed-form solution, which is of great

utility for the optimization analysis.

• The Markov model is complemented with a re-

ward model for the derivation of the retransmis-

sion rate of the sender node.

• We propose a multi-objective optimization ap-

proach to adjust the retransmission probability

balancing bandwidth efﬁciency and throughput.

• It is shown that it is possible to achieve a notable

reduction of the retransmission rate of the sender

node while keeping the throughput very close to

the deterministic scheme.

The rest of the paper is organized as follows. In

Section 2 we describe the system under study and its

model as a DTMC. This model is used in Section 3

to analyze the performance of the system in terms

of throughput and retransmission rate. The multi-

objective optimization approach is presented in Sec-

tion 4, and numerical results are discussed in Sec-

tion 5. Finally, the implications and future research

lines derived from this work are outlined in Section 6.

2 SYSTEM MODEL

The system under study, illustrated in Figure 1, con-

sists of a sender node (S) that transmits data frames

to a destination node (D), and a relay node (N) that

receives the data frames directed to D, so it can as-

sist S in retransmissions of lost frames. The physical

layer consists of slotted radio interface. A time-slot is

deﬁned as the time from a frame transmission to the

completion of its ACK/NACK. Slots are of ﬁxed du-

ration and synchronized at all the nodes. This kind of

radio interface is characteristic of mobile access net-

works.

Figure 1: C-ARQ system.

We assume a simple channel model, similar to

(L. Xiong, 2008), where the channel can be in one of

two states: either “on”, in which transmitted signals

arrive with sufﬁcient power to be decoded without er-

ror, or “off”, in which a transmitted signal can not be

decoded. The probability of the channel being “on”

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

or “off” in a given time-slot is independent of its state

in previous time-slots, and independent of the chan-

nel states of different node pairs. The probability of

being in the “off” state is denoted by p

for the chan-

nel between S and D (direct link), p

for the channel

between S and N, and p

for the channel between N

and D (relay channel).

It is assumed that ACK/NACKs are not lost in any

channel, therefore both S and N are informed of the

reception status of the frame in D. This assumption

is common in performance evaluation of wireless net-

works, because the shorter length of control messages

make it feasible to protect them with longer error cor-

rection codes. In the subsequent time-slots after the

original transmission, if the relay node possesses a

copy of the packet, it may decide to make a coop-

erative retransmission over its relay channel.

The probability that the relay node performs a re-

transmission in a time-slot is denoted by p

. This

probability depends on the amount of resources that

N can assign to the communication between S and

D given its trafﬁc load, its scheduling policy and its

processing limitations. In the numerical examples of

section 5, we set p

= 1, assuming a relay node fully

devoted to cooperation, in line with recent proposals

for mobile access networks where relay nodes are de-

ployed as part of the radio cell infrastructure. How-

ever, the analysis is valid for p

< 1, and the con-

clusions can be generalized to this case as well. The

model includes a probability of retransmission in the

sender node, denoted by p

. The analysis of the in-

ﬂuence of this parameter in the overall performance

and its optimization is one of the main goals of this

paper. Note that this implies that the node computing

the optimum p

(in general, the sender node) must be

informed of the link qualities and the retransmission

probability of the relay node.

For successful reception, the destination node

must decode without errors at least one frame sent by

either S or N. The radio interface is collision-free, as

explained in the introduction. We assume a stop-and-

wait operation of the protocol, similarly to (M. Di-

anati, 2006). However, due to the probabilistic re-

transmission scheme at the sender, it may transmit

new frames to the receiver in time slots not assigned

to retransmissions. Each frame transmission is then

handled by independent parallel processes in a way

similar to HSDPA, (H. Holma, 2006).

The states of the Markov chain describing the op-

eration of the system are combinations of the indi-

vidual states of N and D. Let N

represent the state

of the relay node. N

= true (or simply N

) if the

relay node has successfully decoded the frame, and

= false (or simply

) otherwise. Because the re-

lay node is assumed not to discard frames, N

= true

in every time-slot between the successful reception of

a frame at N and the reception of this frame at D. The

states of the destination node are: D

, if the frame is

correctly decoded, and

otherwise.

The DTMC comprises the following three states:

• State 0: N

, D

• State 1: N

• State 2: D

The transition diagram of the DTMC is depicted in

Figure 2. In order to describe analytically the transi-

tion probabilities let us deﬁne the following events:

• S: S retransmits a frame.

• N: N retransmits a frame.

• N

: N successfully decodes a frame sent by S.

• D

: D successfully decodes a frame sent by N.

• D

: D successfully decodes a frame sent by S.

•

S, N, N

, D

: are the complementary of the

events above.

Making use of the description of the C-ARQ protocol

and the deﬁnition of the events, the transition proba-

bilities from state 0 are given by:

= P{(S∧ D

∧ N

) ∨ S}

= P{S∧ D

∧ N

}

= P{S∧ D

}

Applying the channel state and retransmission proba-

bilities of the model we obtain the following values:

= p

+ (1− p

)

= p

(1− p

)

= p

(1− p

)

(1)

When the system is in state 1, it can not enter into state

0, because the relay node does not discard frames

= 0). The system remains in the same state with

the following probability:

= P{((N ∧

) ∨ N) ∧ ((S∧ D

) ∨ S)} =

= (p

+ (1− p

))(p

+ (1− p

))

(2)

Figure 2: Discrete Time Markov Chain model of the C-

ARQ protocol.

PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ

The system makes a transition from state 1 to state 2

with probability p

= 1 − p

. Finally, if the system

is in state 2, i.e. the destination has successfully de-

coded the frame, the source transmits a new frame,

resulting in a new transition to any of the three states.

The transition probabilities from state 2 are

= P{

∧ D

} = p

= P{N

∧

} = p

= P{N

} = 1− p

(3)

The transition matrix of the DTMC is given by

P =





0 p





(4)

3 PERFORMANCE ANALYSIS

In this section we use the proposed model to obtain

two important performance metrics of the C-ARQ

scheme: the throughput and the retransmission rate of

the source. The throughput is deﬁned as the average

number of frames successfully received in the destina-

tion node per time-slot. According to the model, the

throughput is the average number of time-slots that

the DTMC spends in state 2. The retransmission rate

is deﬁned as the number of retransmissions from the

source, normalized by the total number of time-slots.

This measurement reﬂects the amount of resources al-

located to retransmissions. Therefore, for an efﬁcient

use of the bandwidth, the goal is to reduce this rate.

For the computation of the retransmission rate, a re-

ward model is constructed.

3.1 Throughput Performance

Let

π = {π

, π

} be the steady-state distribution of

the DTMC, where π

is the steady-state probability of

state i ∈ {0, 1, 2}.

π is obtained by solving the follow-

ing system of linear equations:

π = πP

∑

i∈Ω

= 1

(5)

where Ω = {0, 1, 2}, and P is given by (4). Solving

(5) for

π we obtain the following solution:

1− p

(1− p

)(1− p

)

1− p

−1

(1− p

)(1− p

)

1− p

(6)

From the transition probabilities obtained in Sec-

tion 2 we can compute

π as π(p

, p

). Be-

cause we focus on ﬁnding the optimal p

, we use,

for convenience, a simpler notation:

π(p

). The

throughput of the system is denoted by T(p

) =

). It is obvious that, for any given set of val-

ues {p

, p

}, the maximum throughput is ob-

tained when the source retransmits in every time-slot

after a frame loss notiﬁcation (p

= 1). Therefore we

deﬁne the maximum throughput as T

= T(1). T

taken as a reference to evaluate different values of p

3.2 Retransmission Rate of the Source

In this subsection we develop a reward model to com-

pute the average retransmission rate in the source

node. This approach has been previously applied to

the analysis of ARQ protocols. See (M. Zorzi, 1996)

for a description of this technique.

In the DTMC considered, let X

→ X

represent a

transition from state i to state j. Let R

be the reward

associated to this transition. In our context, R

rep-

resents the average number of retransmissions from

S, in the time-slots where X

→ X

. Analytically, it

is expressed as R

= rP{S|X

→ X

}, where r is the

number of frames in a retransmission time-slot. In the

system under study, r = 1 because only one frame can

be transmitted per time-slot.

The reward associated to a transition is 1 if the

transition can only take place when the source retrans-

mits the frame. Therefore, any transition from state 0

to a different state involves a single reward:

= R

= 1

(7)

The ﬁrst transmission of a frame is not considered a

retransmission, therefore the transitions from state 2

involve a null reward:

= R

= 0

(8)

The reward associated to X

→ X

is given by

= P{S|X

→ X

}

which, making use of the deﬁnition of conditional

probability can be expressed as

P{S|(X

→ X

)} =

P{S∧

∧ D

}

P{X

→ X

}

Applying the probabilities of each event, we obtain

the following value:

(9)

Similarly, R

equals the following conditional prob-

ability:

P{S|(X

→ X

)} =

P{(S∧

) ∧ ((N ∧ D

) ∨ N

)}

P{X

→ X

}

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

which, according to the model results in

+ 1− p

)

(10)

Finally, R

is given by

P{S|(X

→X

)} =

P{(S∧

) ∧ ((S∧ D

) ∨ (N ∨ D

))}

P{X

→ X

}

which results in

(1− p

) + p

(1− p

)

(11)

The retransmission rate associated to a reference

state, i, is computed with the following expression:

∑

j∈Ω

(12)

The average retransmission rate from S is given by a

weighted sum of the rates obtained in (12), where the

weighting factors are the steady state probabilities of

the Markov chain:

R =

∑

i∈Ω

(13)

Applying the rewards (7), (8), (9), (10) and (11) in

(12), it can be easily checked that R

= R

= p

and

= 0. For convenience, we can write R in terms

of p

as R(p

) = p

(1 − π

)). At the maximum

throughput, obtained with p

= 1, the retransmission

rate is R

= R(1).

4 MULTI-OBJECTIVE

OPTIMIZATION STRATEGY

There exists a clear tradeoff between the two per-

formance measurements derived in previous section.

The maximum throughput, T

, is achieved setting

= 1. However, this can lead to a high retrans-

mission rate, especially if the direct link is highly de-

graded. On the other hand, if p

= 0, then the retrans-

mission rate reduces to 0. In order to ﬁnd an optimum

balance between both objectives, we propose an ap-

proach based on a multi-objective optimization tech-

nique, known as global criterion method (Rao, 1996).

This method consists of minimizing a global criterion

function, deﬁned as:

G(p

) =

∑

k=1



− f

)



(14)

where n is the number of objective functions, f

)

are the objective functions, O

are the optimum val-

ues for each objective function and α

are the factors

weighting the relative importance assigned to each

objective. In the system analyzed, we are balancing

two objectives. First, it is desirable that the through-

put approaches its maximum, T

, as much as possi-

ble, i.e. f

) = T(p

) and O

= T

. Second, it is

also desirable to reduce the retransmission rate of S,

therefore f

) = R(p

) + C, and O

= C, where C

is an auxiliary non-zero real number required to avoid

a division by 0 in the global objective. In our model

we choose C = 1 because the relative importance of

R(p

) approaching to 0 is already controlled by α

Making use of these deﬁnitions in (14) we obtain:

G(p

) = α



− T(p

)



+ α

R(p

)

(15)

Let p

∗

denote the solution to the multi-objective op-

timization problem. Because p

∗

is a probability,

the problem is subject to the constraint 0 ≤ p

≤ 1.

Therefore we have:

∗

= argmin

0≤p

≤1

{G(p

)}

(16)

Let T

= T(p

∗

) be the optimum throughput in terms

of the multi-objective optimization problem. Simi-

larly, let R

= R(p

∗

) denote the optimum retransmis-

sion rate. In the following section we compare T

and

with T

and R

in several scenarios. The weight-

ing factors chosen are α

= 1 and α

= 0.2. Addition-

ally, the effect of α

is also discussed in the following

section.

5 RESULTS

In this section we investigate the performance of the

probabilistic retransmission approach numerically. It

is shown that, with the computed probability, the sys-

tem achievesa notable reduction in the retransmission

rate of the source with a relatively small reduction of

the throughput. Moreover, we show that the two ob-

jectives are well-balanced in many different combina-

tions of link quality conditions.

In the framework of cooperative mobile access

networks, relay nodes are considered to be part of the

cell infrastructure, speciﬁcally deployed to enhance

the connectivity of mobile users. In this scenario, a

relay node is always willing to cooperate. Assuming

that there are enough resources available, p

= 1. The

frame error probability in the source-relay link can be

a network design parameter, and therefore its value

can be relatively small. In the numerical evaluations

of this section we set p

= 0.2.

First, we study the effect of p

in the performance

of the proposed strategy, and compare it with the max-

imum throughput conﬁguration (p

= 1). For this

PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ

0 0.2 0.4 0.6 0.8 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Performance vs p

Figure 3: C-ARQ performance vs. p

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

Optimum p

Figure 4: Optimum p

vs. p

evaluation, the typical situation of a good relay chan-

nel is assumed: p

= 0.1.

The results are shown in Figure 3. It is clear that,

as the quality of the source-destination channel wors-

ens, the retransmission rate of the source with the

proposed strategy, R

, is notably reduced compared

to the maximum throughput scheme, R

. The most

interesting result is that the cost of this reduction in

terms of throughput is very small. Figure 4 shows the

corresponding values of p

∗

in this scenario.

In order to evaluate the effect of the weighting fac-

tors, we can set α

= 1 and compute the performance

for a range of values of α

. Let consider the previous

conﬁguration of the system, with p

= 0.4. Figure 5

plots the performance metrics obtained with α

in the

range 10

−2

≤ α

≤ 10. While it was expectable that

both T

and R

decrease as α

is set to higher val-

ues, it is surprising to check that the throughput does

not decay dramatically when α

= 1 or even at higher

values. From the values of p

∗

shown in Figure 6, we

observe that a reduction of p

from 0.9 to 0.4 (more

than 50%), causes a reduction of about 10% in the

throughput. This fact suggests that, in practice, the

system tolerates certain inaccuracy in the computa-

−2

−1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Influence of α

Figure 5: C-ARQ performance vs. α

−2

−1

0.2

0.4

0.6

0.8

Optimum p

Figure 6: Optimum p

vs. α

tion of p

, without much impact on the throughput.

Because of the mobility of the user terminals,

many different combinations of p

and p

are pos-

sible. Figure 7 shows the computed p

∗

for differ-

ent settings of both parameters. In order to focus on

the performance improvement obtained with p

∗

com-

pared to p

= 1, Figure 8 plots the difference between

and R

, and Figure 9 depicts the difference be-

tween T

and T

. These ﬁgures show that, while

the retransmission rate is highly reduced, especially

in poor channel conditions, the throughput never de-

cays noticeable below the maximum. We can observe

that the proposed algorithm provides a good balance

between the two objectives pursued, even under dif-

ferent combinations of link qualities.

6 CONCLUSIONS

The analysis done in this paper shows that, in wire-

less networks with cooperative ARQ, a probabilistic

retransmission policy in the source node provides no-

table beneﬁts in terms of efﬁciency in the use of radio

resources, especially in situations of poor propagation

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

0.2

0.4

0.6

0.8

0.5

0.2

0.4

0.6

0.8

Optimum p

Figure 7: Optimum p

vs. p

and p

0.2

0.4

0.6

0.8

0.5

0.2

0.4

0.6

0.8

− R

Figure 8: R

− R

vs. p

and p

0.2

0.4

0.6

0.8

0.5

0.2

0.4

0.6

0.8

− T

Figure 9: T

− T

vs. p

and p

conditions in the direct link. The optimal retrans-

mission probability for the source node is obtained

by means of a multi-objective optimization technique,

known as global criterion method. It is shown that this

strategy reduces the retransmission rate of the source

node with a negligible reduction of the throughput.

This new concept breaks with the classical and

widely adopted policy of giving maximum priority

to retransmissions in wireless links. Consider, as an

example, the Radio Link Protocol of 3G access net-

works (H. Holma, 2004). As a consequence, the

results of this paper can be useful in the design of

scheduling mechanisms for cooperative wireless net-

works. The idea is to consider the computed re-

transmission probability, p

∗

, as a lower bound for the

amount of time-slots (i.e. bandwidth) reserved for

retransmissions at the base station. The rest of the

bandwidth can be assigned to other communication

processes whenever they have available data.

The model described can be extended to include

the concept of cooperation group deﬁned in (M. Dia-

nati, 2006). With this enhancement, the cooperation

involves an undeﬁned number of relays. Another fu-

ture line of research consists in the addition of Hybrid

ARQ features e.g. incremental redundancy and chase

combining, in the model.

ACKNOWLEDGEMENTS

This research has been supported by project grant

TEC2007-67966-01/TCM (CON-PARTE-1) and it

was also developed in the framework of Programa de

Ayudas a Grupos de Excelencia de la Regi´on de Mur-

cia, Fundaci´on Seneca, Agencia de Ciencia y Tec-

nolog´ıa de la RM (Plan Regional de Ciencia y Tec-

nolog´ıa 2007/2010)”.

REFERENCES

A. Nosratinia, e. a. (2004). Cooperative communication in

wireless networks. IEEE Communications Magazine,

42(10).

F. Fitzek, M. K. (2006). Cooperation in Wireless Networks:

Principles and Applications. Springer.

H. Holma, A. T. (2004). WCDMA for UMTS. Radio Access

for Third Generation Mobile Communications. Third

Edition. Wiley.

H. Holma, A. T. (2006). HSDPA/HSUPA for UMTS: High

Speed Radio Access for Mobile Communications. Wi-

ley.

I. Cerutti, A. Fumagalli, G. H. (2006). Saturation through-

put gain in ﬁxed multiplexing radio networks with

cooperative retransmission protocols. In IEEE Inter-

national Conference on Communications (ICC), vol-

ume 10. IEEE.

PROBABILISTIC RETRANSMISSION STRATEGY FOR SINGLE-RELAY COOPERATIVE ARQ

I. Cerutti, A. Fumagalli, P. G. (2007). Delay model of

single-relay cooperative arq protocols in slotted radio

networks with non-instantaneous feedback and pois-

son frame arrivals. In INFOCOM 2007. IEEE.

K. Doppler, e. a. (2007). On the integration of cooperative

relaying into the winner system concept. In 16th IST

Mobile and Wireless Communications Summit. IEEE.

L. Xiong, L. Libman, G. M. (2008). Optimal strategies for

cooperative mac-layer retransmission in wireless net-

works. In WCNC’08, IEEE Wireless Communications

and Networking Conference. IEEE.

M. Dianati, e. a. (2006). A node-cooperative arq scheme

for wireless ad hoc networks. IEEE Transactions on

Vehicular Technology, 55(3).

M. Zorzi, R. R. (1996). On the use of renewal theory in

the analysis of arq protocols. IEEE Transactions on

Communications, 44(9).

R. Pabst, e. a. (2004). Relay-based deployment concepts for

wireless and mobile broadband radio. IEEE Commu-

nications Magazine, 42(9).

Rao, S. (1996). Engineering Optimization: Theory and

Practice. Third Edtion. Wiley.

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