selection and data transmission in cooperative … · selection and data transmission in...

SELECTION AND DATA TRANSMISSION IN COOPERATIVE SYSTEMS K.Sakthivel

1, S.Anitha

2

Assistant Professor 1 2

Department of EEE, BIST, BIHER, Bharath University, Chennai.

[email protected]

Abstract—A common and practical paradigm in

cooperativecommunications is the use of a dynamically selected

‘best’ relay to decode and forward information from a source to a

destination. Such a system consists of two core phases: a relay

selection phase, in which the system expends resources to select the

best relay, and a data transmission phase, in which it uses the

selected relay to forward data to the destination. In this paper, we

study and optimize the trade-off between the selection and data

transmission phase durations. We derive closed-form expressions for

the overall throughput of a non-adaptive system that includes the

selection phase overhead, and then optimize the selection and data

transmission phase durations. Corresponding results are also

derived for an adaptive system in which the relays can vary their

transmission rates. Our results show that the optimal selection phase

overhead can be significant even for fast selection algorithms.

I. INTRODUCTION

Relay-based multi-hop cooperation, in which a source node

transfers information to the destination with the help of a relay

selected from the available nodes has attracted considerable

at-tension in the literature [1]–[4]. The relay is selected

depending on its instantaneous channel gains on the basis of a

real-valued locally known metric that is a function of the

relay-destination (RD) channel gain or the source-relay (SR)

channel gain or both, depending on the cooperation protocol.

Relay selection has been shown to help the system exploit the

spatial diversity afforded by having geographically spaced

multiple relays. It improves the symbol error probability [3] or

increases the data transmission rate [5]. In general, the extent

and nature of the benefits from selection depends on both the

selection criteria and the cooperation scheme [6]–[11]. After the source broadcasts its data, these systems typically use

two phases to complete the transmission to the destination: (i) a relay selection phase, in which the ‘best’ relay with the

highest metric is chosen by a selection mechanism, and (ii) a data

transmission phase, in which data is transmitted to thedestination

by the selected relay. The selection phase is needed because the

source does not know a priori which relay is the best one.

Furthermore, since the metric is a function of local

The work of the first two authors was partially supported by a research project sponsored by Boeing-ANRC.

Channel gains, each relay knows only its metric, and not that of the others.

In most papers, the selection is assumed to be perfect and

instantaneous. In effect, it is assumed to incur no time or

energy overhead. However, in practice, the system does need

to expend time and energy during the selection phase to find

the best relay. The simulations in [12], [13], which modeled

several practical aspects of a contention-based se-lection

process, indicate that the relative time and energy spent in the

relay selection phase can be considerable. This overhead

clearly depends on the selection mechanism. For example, in a

centralized polling mechanism, the overhead for selection

increases linearly with the number of available relays. In [12],

a source uses overhead handshaking messages to exhaustively

track the rate that each candidate relay can support. The

selection phase overhead can be reduced by using distributed

mechanisms based on back-off timers [14] or time-slotted

splitting algorithms [15]–[17]. The selection phase cannot always be perfect. For example,

a practical system may terminate the selection phase after

some time even when the best relay has not been selected.

This leads to an outage during the subsequent data

transmission phase. While increasing the selection phase

duration reduces this outage probability, it does so at the

expense of the overall throughput due to the less time

available for data transmission. Thus, the two phases affect

each other, and cannot be optimized in isolation. This paper conducts a comprehensive system-level analysis

and optimization that considers the trade-offs between the two

phases. Such a modeling and joint optimization has received

limited attention in the literature [11]–[13], [18]. For example,

[18] considers outage and throughput, but not the selection

phase overhead. We consider a generic system-level model

that explicitly models the two phases and develop analytical

expressions for the overall system throughput. We first

analyze a non-adaptive system in which the data rates and

time intervals for the phases are fixed, and then an adaptive

system in which the selected relay adapts its transmission rate

to improve overall throughput. The optimal trade-off between

the two phases is different for these two systems. To be able to make precise system-level quantitative state-

ments, a choice needs to be made about the mechanism used

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 5101-5110ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

5101

for selection. To this end, we consider the splitting algorithm for

relay selection [19-23] given its remarkable speed and scalability.

While the time taken by the splitting algorithm to select the best

node depends on the specific realizations of their metrics, on

average it can find the best node within 2.47 slots even when an

asymptotically large number of nodes contend. Even for such an

efficient algorithm, the time overhead of the selection phase often

turns out to be considerable. Our analysis shows that the optimal

selection phase duration is often at least a factor of two or more

than the above average in order to ensure a sufficiently large

probability of success in selecting the best relay[24-29]. Thus,

our analysis shows that a joint design is also desirable in systems

that use other selection mechanisms. The paper is organized as follows. The system model is set

up in Sec. II. The analysis is developed in Sec. III. The design

implications are brought out in Sec. IV, and are followed by

our conclusions in Sec. V.

II. SYSTEM MODEL

Figure 1 shows a schematic of the cooperative relay network that we consider. It contains one source node, one

destination node, and n decode-and-forward relays. The channels from the source to the relays as well as from the relays to the destination are assumed to be frequency flat

channels that undergo independent fading. Thus, for relay i,

the source to relay (SR) channel power gain, hsi, and the relay

to destination (RD) channel power gain, hid, are independent and identical exponentially distributed random variables with the same mean[30-35].

We focus on the identically distributed case in this paper

due to space constraints. The analysis can be generalized to

handle the case of non-identical SR and RD channels [19]. We

assume, without loss of generality (w.l.o.g.), the fading

powers means are all normalized to 1. We assume a block

fading channel model in which the channel gains remain

constant over the selection and data transmission phases

(described below). In practice[36-39], the system can operate

over time-varying channels and thus have to live with partially

(though not fully) outdated metrics after selection. Modeling

the time-varying nature of the channels and its impact on the

overall system performance, and then optimizing the selection

mechanism’s parameters is an interesting avenue for future

work. The noise at each receiving node is additive white

Gaussian with zero mean and unit variance[40-45]. For

analytical tractability, we shall assume that the direct source

to destination link is weak, as is typically the case [6], [20].1

We now describe the cooperation protocol for the baseline non-adaptive system. The adaptive system is discussed next.

1) SR Data Transmission Phase: The source broadcastsBbits in Td time units and all the relays listen. The fading-averaged SNR at a relay’s receiver is ρs. To relate B, hsi, and ρs, we use the ideal Shannon capacity formula,and assume that a relay i can decode the source’s

1The reader is referred to [21] for an analysis that

includes the S-D link. The papers discusses why doing so makes the analysis more involved.

hs1 R1

h1d

S R2 D

hsn hnd

Rn

Fig. 1. A cooperative system consisting of a source (S), a destination (D), and n relays, from which the best relay is selected chosen.

transmission only if

2 B

− 1

B ≤ W Tdlog2(1 + hsiρs), i.e., hsi> W Td

γsr ,

ρs

(1)

where W is bandwidth in Hz. Practical coding ineffi-ciencies can also be easily incorporated along the lines of [22], [23].

2) Relay Selection Phase: The relays contend for a

durationof Tc slots, each of duration tslot. The selection criterion and algorithm is explained below in Sections II-A and II-B.

3) RD Data Transmission Phase: At the end of the relayselection phase, the selected relay, if any, transmits

data to the destination for Td time units (using the same modulation and coding as the source). The destination decodes the message if hjd>2

B

1 /ρr γrd,

W Td

where j is the selected relay_and ρr

−is

_the fading-

averaged SNR at the destination. We say an outage occurs if the destination cannot receive

source’s message successfully. All time durations such as Td – and consequently B itself – are normalized w.l.o.g. with respect to a

contention slot’s duration tslot. A. Relay Selection Criterion

The goal of the selection algorithm is to select the relay with the highest RD channel gain [20]. Each relay knows its RD channel gain but not that of others. Furthermore, only those relays that decode the source’s message and have an RD channel gain large enough to support transmission to the destination participate in the selection process. Other relays settheir metrics to 0 and do not contend, as this wastes energywithout improving throughput. Formally, the local

metric, μi, based on which a relay i contends is

μi=_

0, h

si < γ

sr or hid< γrd

. (2)

hid

, otherwise

The complementary cumulative distribution function (CCDF)

of the metric μi is denoted by Fc(μ) = Pr (μi≥μ). B. Relay Selection Algorithm

The splitting-based selection algorithm only requires that the

CCDF and n is known to all relays. It proceeds as follows [15],

[17]. At the beginning of a slot k, each relay

International Journal of Pure and Applied Mathematics Special Issue

5102

locally computes two thresholds HL(k) and HH(k), and the destination. One implication of this is that no relay

transmits if its metric μ satisfies HL(k)< μ < HH(k). At the will get selected after _nFc(γrd)_ initial idle slots.

end of each slot, the source broadcasts one of three outcomes • The slot duration of the splitting algorithm depends on

to all the relays: (i) idle when no relay transmitted, (ii) success the transmission protocol. Each slot needs to allow for

when exactly one relay transmitted, or (iii) collision when two transmissions – one by the nodes and the other by

multiple relays transmitted and collided.2 The relays update the sink – and necessary gaps, as required, between these

their thresholds for the next slot accordingly. two transmissions. For example, in 802.11 systems, each

Formally, the algorithm is specified as follows. Let Hmin(k) slot’s duration can easily exceed 100 μsec [24].

denote the largest value of the metric known up to slot k C. Adaptive System

above which the best metric surely lies. And, let split (a, b)

F −1 Fc(a)+Fc(b) . This split function ensures that, on aver- Since the relay knows its channel gain to the destination, it

2

c

can reduce its transmission duration by adapting its transmit

only half the relays involved in the last collision transmit

age, _ _

rate to log2(1 +ρrhid). The relay’s transmit SNR, ρr , is

in the next slot. It can be easily shown that

e−(γsr+

μ),

μ ≥ γrd

kept the same as for the non-adaptive system. In addition, the

system wastes no time in the RD phase in case the selection

Fc(μ) = e−(γsr+γrd), 0 < μ < γrd. (3) phase results in an outage.

1, μ = 0 It must be noted that other forms of adaptation are certainly

In the first slot, the variables are initialized as follows: possible if the system design allows it. For example, the relay

HL(1) = max(γrd, F −1 (1/n)),HH (1) =

∞ , and Hmin(1) = can adjust its transmit power instead of rate to minimize energy

consumed. Furthermore, in some systems, even the selection

th c

0. In the (k + 1) slot, the variables are updated based on the phase can terminated as soon as a success is fed back by

outcome as follows:

the source or when it becomes obvious (after _nFc(γrd)_ idle

1) If feedback (of the kth

slot) is an idle and no col-

lisions have occurred thus far, then HH(k+ 1) = slots) that no success is possible. These adaptations and others

are not analyzed in this paper due to space constraints, and

HL(k), Hmin(k + 1) = 0, and HL(k + 1) =

are addressed in detail in [19].

max(γrd, F

−1(

i+1 )).

c n

HH(k + 1) =

2) If feedback is a collision, then III. ANALYSIS

HH(k), Hmin(k + 1) = HL(k), andHL(k + 1) = We first analyze the throughput of the non-adaptive system

3) split (HL(k), HH(k)). and then that of the adaptive system.

If feedback is an idle and a collision has occurred in the A. Non-Adaptive System

past, then HH(k+1) =HL(k), Hmin(k+1) =Hmin(k),

and HL(k+ 1) = split (Hmin(k), HH(k)). The destination can successfully decode only when all the

The reader is referred to [15], [17] for a detailed explanation following three conditions are satisfied: (i) There is at least

of the above steps. We shall call the durations of the algorithm one relay that has decoded the message from the source,

before and after the first non-idle slot as the idle and collision (ii) Among the relays that have decoded the source message,

phases, respectively. During idle phase, the algorithm ensures at least one of them has a good enough link to the destination,

that only one node, on average, transmits in each slot. Once and (iii) The selection phase can select the best relay within

collision happens, the nodes are split in subsequent slots until Tcslots. In our set up, the above conditions together are

success happens. equivalent to the condition that the selection phase terminates

The splitting algorithm is fast because it ensures that one successfully withinTcslots.

node, on average, transmits in each of the idle slots, regardless The throughput, η, for the non-adaptive system is therefore

of the number of nodes in the system. Furthermore, in the η = BPs(Tc)

(4)

event of a collision, it is very likely that only two nodes have ,

collided. These are then separated quickly by successively 2Td + Tc

where Ps(Tc) is the probability that the selection phase

splitting the interval.

Comments: terminates successfully. The denominator in (4) is the total

time, including selection phase, taken by the source and relays

• Note that the formulation above differs slightly from the

to transmit B bits (normalized with respect to tslot).

original algorithm proposed in [15]. During idle phase,

To determine Ps(Tc), we first state an intermediate result

we introduce the max(.) function to prevent relays with

about the selection algorithm’s behavior.

metrics below γrd from transmitting. This is done, since

Lemma 1:The probability,p(a, b), that exactlybslots are transmission from such relays only results in wastage

required to resolve a collision involving a relays is

of energy without increasing throughput as they have

either not decoded the source’s message or do not have 1 a a

a strong enough RD channel to forward the message to p(a, b) =

_

p(a, b − 1) + i=2 i_

p(i, b −1)_

, ∀ a, b >1,

2a

2The sink can determine these outcomes based, for example, on the strength

where p(a,1) =a/2a, ∀a >1, and p(1, b) = 0.

(5)

of the received power, which is measurable by many receivers today [16].


5103

.


5104

Proof: The proof is given in Appendix A.

The main result on the probability of success now follows.

Theorem 1:The probability of successful data transfer is min(Tc,r)

i

_

n−1

r

1

Ps(Tc) =

−

+I{Tc>r}n_

α−

_

(1−α)n−1

i=1 n n

min(Tc −1,r)n n 1 k i n−k Tc−i

_

_

+ i=1k=2k_

1 −

j=1 p(k, j)

n n

n n

_

_α

r k Tc−r −1

+I{T

c

>r+1} k=2k −

_

(1−α)n−k

p(k, j),

j=1

where, T(x, y;k), 0≤x < y, is the average time required for data transmission when the relay with the highest metric is selected

from among k relays all of whose metrics lie in the interval

(Fc−1

(y), Fc−1

(x)). It is given by

T (x, y; k) = B ke−kγ

sr k−1 (

−

1)j k −1 log(2)

W (y − x)k

j=0

j _

×(yeγsr )

k−1 −j_

ψ1 j+ 1, log(1 +

ρrF

c−1(y

) )

ρr _

− ψ

1j+ 1,log(1 +

ρrF

c−1

(x))

_, (9)

ρr _

and ψ1(a, u) = u t exp _ t +

1 −

a _ dt.

∞ 1 et

Proof: The proof is given in Appendix C.

We specify the intervals limits in T(., .;k) in terms of Fc−1

(.)

as it helps simplify the notation. This is valid as Fc−1

(.) is a

one-to-one monotonic mapping for continuous distributions.

IV. RESULTS AND SYSTEM DESIGN IMPLICATIONS

We study the system-level tradeoffs using both the analytical

B. Adaptive System results derived in Sec. III and Monte Carlo simulations with

105samples. The parameter values chosen are:ρs = ρr =

In this system, a relay can now adapt its transmission rate.

6 dB, andB = W Td log2(1 + 100.6

), which implies that a

Equivalently, it adapts its transmission duration – subject to a relay or destination can decode successfully if its instantaneous

cap of Tmax, which is a system parameter. A relay contends

received SNR is at least 6 dB.

only if it can transmit the information to the destination within For the non-adaptive system, Figure 2 shows that the prob- Tmax,i.e., it contends when its RD channel gain exceeds the

ability of successful selection, Ps(Tc), increases as the total

adp

B

2 W T

max −1.

number of available relays (n), or the selection phase duration

threshold γrd ρr

The new throughput (normalized with respect to tslot ) then ( Tc ) increases. For large T , P s (T c ) saturates at 1 − (1 − α)

n.

nc

equals BPs(Tc)

This is because (1−α) is the probability that an outage

η =

,

(7) occurs because none of the n available relays contend in the

Td+ Tc+ Tadp selection phase. Notice also that the analytical and simulation

where Tadp is the average RD transmission phase duration. results match very well.

While increasing Tc improves the probability of successful

The probability of successful selection, Ps(Tc), above is again

given by (6) with γrd simply replaced by γ adp 3 Finally, the selection, it also increases the overall time of the three phases.

.

rd

This important trade-off between the overall system through-

average RD transmission phase duration, Tadp, is then given

put and Tc is shown in Figure 3. For small Tc, increasing Tc

by the following result.

improves throughput since the probability of outage decreases.

Theorem 2:When the RD data transmission duration is

However, for larger Tc, the throughput starts decreasing as

adapted, its average equals

Ps(Tc)saturates. The results show that the optimal value for

min(Tc,r) i

_

n−1 i − 1

i

the selection phase duration depends on both n and Td. For

Tadp =

1

; 1

T ,

example, for Td= 13, Tc= 4 and 5 are optimal for n= 6 and

− n

i=1 n n _ 15, respectively. Whereas, forTd = 100, the optimal values

min(Tc−1,r) n 1

k n k Tc

− i of Tc increase to 7 and 8 for n= 6 and 15, respectively.

+ n 1 i

_

− T

i − 1 , i ; k p(k, j) Furthermore, the throughput increases as the number of relays

− n

i=1 k=2k_

n_ n n

_j=1 increases or as the data transmission duration increases. The

where I{x} is an indicator function that equals 1 if condition x is true and is 0 otherwise, α = Fc(γrd),

and r =_nα_−1.

Proof: The proof is given in Appendix B.

The above result can be understood as follows. Its first two terms correspond to the first non-idle slot being a success. The third and the

fourth term correspond to the first non-idle slot (ith

slot) being a

collision among k >1 relays that is resolved in the remaining Tc−i slots.

(6)


5105

transm

issio

n

1

0.9

0.8

data

0.7

in

success

0.6

0.5

Analysis: n=6

of

Pro

ba

bili

ty

Simulation: n=6

0.4 Analysis: n=15

Simulation: n=15

1 2 3 4 5 6 7 8 9 10

Tc

Fig. 2. Probability of successful data transfer as a function of selection phase

duration (Tc) and number of relays (n) for the non-adaptive system.

1

n=15, Analysis

0.9

Td=100 n=15,

Simulation

Td=13

0.8

Th

rou

gh

pu

t

0.7 n=6,

Td=100

0.6

0.5 n=6,

Td=13

0.4 2 3 4 5 6 7 8 9 10 1

Tc

Fig. 3. Non-adaptive system: Trade-off between overall throughput, normal-ized with respect to W , and selection phase duration for different numbers of

relays (n) and for different source data transmission durations, Td, normalized

with respect to tslot. n = 15and Td= 100, the maximum throughput of 1.202of the adaptive system is 22% more than its non-adaptive counterpart. The optimal selection duration shrinks for the adaptive case. For

example, at Td= 13, Tc= 3 and 4 are throughput optimal for n= 6 and 15, respectively. As in the non-adaptive system, the optimum

selection duration increases as Td increases. As Figures 3 and 4

suggest, the throughput is a concave function of Tc. Thus, fast convex optimization techniques can be used to determine

optimum Tc. The optimal Tctypically lies between2and9(slots),

with the exact valuedepending on Td.

V. CONCLUSIONS

We analyzed the system-level interactions and trade-off

between the relay selection and data transmission phases of a

cooperative relay system. To this end, we developed analytical

expressions for the probability of successful selection and the

average system throughput. We saw that even with a fast

splitting-based selection algorithm, the relative overhead

1.3

n=15,

1.2 Td=100

1.1 n=15, Analysis

Simulation

Thro

ugh

put

Td=13

1

0.9 n=6,

0.8 Td=100 n=6,

0.7 Td=13

0.6

0.5 5 T

1 2 3 4 6 7 8 9 10

c

Fig. 4. Adaptive system: Trade-off between overall throughput, normalized with respect to W , and selection phase duration for different numbers of

relays (n) and different source data transmission durations, Td, normalized

with respect to tslot, for Tmax=Td. of the selection phase was non-negligible. In general, the relative

overhead of the selection phase decreased as the source

transmission duration increased. Also, the overhead increased as

the number of available relays increased. We also saw that the

optimal system parameter settings for the adaptive and non-

adaptive systems are different. The optimum selection phase

duration value was lower for the rate adaptive system. The results

in this paper show that the time devoted to the selection phase

must be carefully chosen in order to maximize the overall system

throughput. Future work includes optimizing the energy-

efficiency of the systems as well.

APPENDIX A. Proof of Lemma 1

The probability that i relays, among the a that collided, transmit in

the next slot equals _a

i

_/2

a. Thus p(a, b) =a/2

a for b= 1. When b >1,

the following three cases arise: (i) The next slot is idle: The

probability that the collision among a relays is resolved in b −1slots is

p(a, b −1); (ii) i (i >1)relays collide in the next slot: The probability that

it is resolved in exactly b−1 remaining slots is p(i, b−1); (iii) The next

slot is a success: Since the collision is already resolved, the

probability that it is resolved in exactly b slots is 0. B. Proof of Theorem 1

For i ≤ r

, the probability that the first non-idle slot is the ith

n 1 k 1 −

i n−k

slot and k≥1 relays transmit in it is

. k n n

The i= (r+ 1) case is slightly different. From (2), relays

_ _ _ _ _ _

whose RD channel gains are below ar set their metrics to be 0. This occurs

with probability 1−α, where α=Fc(ar). Now, the probability that the first non-

idle slot is (r+ 1)th

slot with k relays involved in it is the probability that k relays have their metric between F

−1 r and ar , and the remaining

c n

n − k relayskhave metric Therefore, this probability equals 0. _ _

_ n _ _ r _ (1 −α)

n−k . No non-idle slot can occur after the

k α−th n

(r + 1) slot. If k relays are involved in the collision in the


5106

ith

slot, the probability that the collision is resolved in the

remaining Tc−i slots is Tc−i p(k, j).

j=1

Depending on Tc and r_,the following two cases occur:

1) Tc ≤ r: Successfulthdata transfer a

occurs if in the

first non-idle slot (i slot): (i) success occurs,

which happens with probability n 1 1 − i , or 1 n n

(ii) k 2 relays collide, which happens with probability

n ≥k 1 − i n − k _ _ _ _ _ _

1

_ _ _

, and are resolved in Tc−i slots. k n n

Thus ,

_ _ _

Tc

1 −

i

_

n−1

Ps(

Tc) =i=1

n

Tc−1 n n 1 k i n−k Tc−i

+ i=1 k=2 k _

_

1 −

_

j=1 p(k, j).

n n

2) Tc> r: Successful data transfer occurs if during the firstnon-idle slot (i≤r+ 1):

(i) a success occurs, or (ii) if resolved in

Tc− i s lots .

k ≥2relays collide and this isth

If a collision occurs in the (r+1) slot, the interval that

needs to be split has a probability mass α−nr since only

relays with non-zero metrics contend. The expression for

Ps(Tc)becomes n−1

r i r

_

Ps(

Tc) =i=11−

+n_

α−

_

(1−α)n−1

n n

rn n 1 k i n−k Tc−i

+ i=1 k=2 k _

_

1 −

_

j=1 p(k, j)

n n

n k_ _

α −n_ k (1 −α)

n−k Tc−r −1 p(k, j).

+ k=2 j=1

n r

Equation (6) compactly expresses the above two results using

the indicator function I{.}. C. Proof of Theorem 2

First, we derive the expression for T(x, y;k). Given that a metric lies in (Fc−1

(y), Fc−1

(x)), its

probability distribution function (PDF) isf1(t) =

e−γsre−tand its cumulative

y−x distribution function is F

1(t) =

e−γsr(e

γsry−e−t

). Using y−x

order statistics [25], the average total transmit time required

when k relays have their metrics in the above interval and the one with the highest metric is selected is B Fc

−1(x)

1

T (x, y; k) = _

Fc−1(y) kf1(t)F1(t)k−1

dt,

W log2(1 + ρrt)

B F −1(x)

ke−kγ

sre−t(e

γsry e−

t)

k−1

c

=

_

−

dt.

W Fc−1

(y) log2(1 + ρrt)(y−x)k

Expanding the integrand as a binomial series and further simplifying yields (9).

Given that the first non-idle slot is the ith

slot and k relays are involved

in it, the average time required is T_i−

n1

,ni;k

_, if i≤r, and T

_n

r, α;k

_, if i=r+

1. The probability of this event can be derived from the proof of Theorem

1. Combining the above results leads to the desired expression.

REFERENCES

1. Nimal, R.J.G.R., Hussain, J.H., Effect of deep

cryogenic treatment on EN24 steel, International

Journal of Pure and Applied Mathematics, V-

116, I-17 Special Issue, PP-113-116, 2017

2. Parameswari, D., Khanaa, V., Deploying

lamport clocks and linked lists, International

Journal of Pharmacy and Technology, V-8, I-3,

PP-17039-17044, 2016

3. Parameswari, D., Khanaa, V., Case for massive

multiplayer online role-playing games,

International Journal of Pharmacy and

Technology, V-8, I-3, PP-17404-17409, 2016

4. Parameswari, D., Khanaa, V., Deconstructing

model checking with hueddot, International


PP-17370-17375, 2016

5. Parameswari, D., Khanaa, V., The effect of self-

learning epistemologies on theory, International


PP-17314-17320, 2016

6. Pavithra, J., Peter, M., GowthamAashirwad, K.,

A study on business process in IT and systems

through extranet, International Journal of Pure

and Applied Mathematics, V-116, I-19 Special

Issue, PP-571-576, 2017

7. Pavithra, J., Ramamoorthy, R., Satyapira Das,

S., A report on evaluating the effectiveness of

working capital management in googolsoft

technologies, Chennai, International Journal of

Pure and Applied Mathematics, V-116, I-14

Special Issue, PP-129-132, 2017

8. Pavithra, J., Thooyamani, K.P., A cram on

consumer behaviour on Mahindra two wheelers

in Chennai, International Journal of Pure and

Applied Mathematics, V-116, I-18 Special

Issue, PP-55-57, 2017

9. Pavithra, J., Thooyamani, K.P., Dkhar, K., A

study on the air freight customer satisfaction,

International Journal of Pure and Applied

Mathematics, V-116, I-14 Special Issue, PP-

179-184, 2017


study on the working capital management of

TVS credit services limited, International




study on the analysis of financial performance

with reference to Jeppiaar Cements Pvt Ltd,


5107



189-194, 2017

12. Peter, M., Dayakar, P., Gupta, C., A study on

employee motivation at Banalari World Cars

Pvt Ltd Shillong, International Journal of Pure


Issue, PP-291-294, 2017

13. Peter, M., Kausalya, R., A study on capital

budgeting with reference to signware

technologies, International Journal of Pure and


Issue, PP-71-74, 2017

14. Peter, M., Kausalya, R., Akash, R., A study on

career development with reference to

premheerasurgicals, International Journal of

Pure and Applied Mathematics, V-116, I-14


15. Peter, M., Kausalya, R., Mohanta, S., A study

on awareness about the cost reduction and

elimination of waste among employees in life

line multispeciality hospital, International



16. Peter, M., Srinivasan, V., Vignesh, A., A study

on working capital management at deccan

Finance Pvt Limited Chennai, International



17. Peter, M., Thooyamani, K.P., Srinivasan, V., A

study on performance of the commodity market

based on technicalanalysis, International Journal

of Pure and Applied Mathematics, V-116, I-18


18. Philomina, S., Karthik, B., Wi-Fi energy meter

implementation using embedded linux in ARM

9, Middle - East Journal of Scientific Research,

V-20, I-12, PP-2434-2438, 2014

19. Philomina, S., Subbulakshmi, K., Efficient

wireless message transfer system, International



20. Philomina, S., Subbulakshmi, K., Ignition

system for vechiles on the basis of GSM,



283-286, 2017

21. Philomina, S., Subbulakshmi, K., Avoidance of

fire accident by wireless sensor network,



295-299, 2017

22. Pothumani, S., Anuradha, C., Monitoring

android mobiles in an industry, International



23. Pothumani, S., Anuradha, C., Decoy method on

various environments - A survey, International



24. Pothumani, S., Anuradha, C., Priya, N., Study

on apple iCloud, International Journal of Pure


Issue, PP-389-391, 2017

25. Pothumani, S., Hameed Hussain, J., A novel

economic framework for cloud and grid

computing, International Journal of Pure and


Issue, PP-5-8, 2017

26. Pothumani, S., Hameed Hussain, J., A novel

method to manage network requirements,


Mathematics, V-116, I-13 Special Issue, PP-9-

15, 2017

27. Pradeep, R., Vikram, C.J., Naveenchandra, P.,

Experimental evaluation and finite element

analysis of composite leaf spring for automotive

vehicle, Middle - East Journal of Scientific

Research, V-12, I-12, PP-1750-1753, 2012

28. Prakash, S., Jayalakshmi, V., Power quality

improvement using matrix converter,



98, 2017

29. Prakash, S., Jayalakshmi, V., Power quality

analysis & power system study in high

voltage systems, International Journal of Pure


Issue, PP-47-52, 2017

30. Prakash, S., Sherine, S., Control of BLDC motor

powered electric vehicle using indirect vector

control and sliding mode observer, International



31. Prakesh, S., Sherine, S., Forecasting

methodologies of solar resource and PV power

for smart grid energy management, International



32. Prasanna, D., Arulselvi, S., Decoupling

smalltalk from rpcs in access points,


5108


Mathematics, V-116, I-16 Special Issue, PP-1-4,

2017

33. Prasanna, D., Arulselvi, S., Exploring gigabit

switches and journaling file systems,



17, 2017

34. Prasanna, D., Arulselvi, S., Collaborative

configurations for wireless sensor networks

systems, International Journal of Pure and


Issue, PP-577-581, 2017

35. Priya, N., Anuradha, C., Kavitha, R., Li-Fi

science transmission of knowledge by way of

light, International Journal of Pure and Applied


290, 2017

36. Priya, N., Pothumani, S., Kavitha, R., Merging

of e-commerce and e-market-a novel approach,



316, 2017

37. Raj, R.M., Karthik, B., Effective demining

based on statistical modeling for detecting

thermal infrared, International Journal of Pure


Issue, PP-273-276, 2017

38. Raj, R.M., Karthik, B., Energy sag mitigation

for chopper, International Journal of Pure and


Issue, PP-267-270, 2017

39. Raj, R.M., Karthik, B., Efficient survey in

CDMA system on the basis of error revealing,



279-281, 2017

40. Rajasulochana, P., Krishnamoorthy, P., Ramesh

Babu, P., Datta, R., Innovative business

modeling towards sustainable E-Health

applications, International Journal of Pharmacy

and Technology, V-4, I-4, PP-4898-4904, 2012

41. Rama, A., Nalini, C., Shanthi, E., An iris based

authentication system by eye localization,

International Journal of Pharmacy and

Technology, V-8, I-4, PP-23973-23980, 2016

42. Rama, A., Nalini, C., Shanthi, E., Effective

collaborative target tracking in wireless sensor

networks, International Journal of Pharmacy and

Technology, V-8, I-4, PP-23981-23986, 2016

43. Ramamoorthy, R., Kanagasabai, V., Irshad

Khan, S., Budget and budgetary control,



189-191, 2017

44. Ramamoorthy, R., Kanagasabai, V., Jivandan,

S., A study on training and development process

at Vantec Logistics India Pvt Ltd, International


116, I-14 Special Issue, PP-201-207, 2017.

45. Pradeep, R., Vikram, C.J., Naveenchandran, P.,

Experimental evaluation and finite element

analysis of composite leaf spring for automotive

vehicle, Middle - East Journal of Scientific

Research, V-17, I-12, PP-1760-1763, 2013


5109

selection and data transmission in cooperative … · selection and data transmission in...

Documents