The Impact of Edge Effects on the Performance of MAC Protocols in Ad Hoc Networks With Fading Flavio Fabbri∗, Mariam Kaynia†, and Roberto Verdone∗ ∗ Wireless

† Dept.

Communication Laboratory, DEIS, University of Bologna, Bologna, Italy of Electronics and Telecommunications, Norwegian Univ. of Science and Technology, Trondheim, Norway Emails: [email protected], [email protected], [email protected]

Abstract—In this paper, the impact of edge effects on the performance of MAC protocols is evaluated. We consider a network where packets are distributed in finite space according to a 2-D PPP, while packets arrive in time according to a 1-D PPP. Each transmitter communicates with its own receiver a fixed distance away using either the ALOHA or CSMA protocol. The metric used for analysis is outage probability, which is the probability that the measured SINR falls below a predefined threshold for the duration of a packet. Approximate analytical expressions are derived for the outage probability of the different MAC protocols assuming a fading channel. Compared to unbounded regions, ALOHA and CSMA are shown to yield lower outage probabilities in finite regions, since the boundedness can be regarded as spatial filtering. Furthermore, the benefit seems to be greater for small outage probabilities, i.e., in the region of practical interest.

I. I NTRODUCTION Wireless Ad Hoc Networks are of great interest because of the very many applications they make possible (e.g., environmental sensing, military communications, emergency [1]), as they do not require complex and costly infrastructure and they are self-configuring and adaptable to changes in the network topology. Such networks are sometimes deployed on very large regions (e.g., forests) by randomly dropping nodes, or they can instead be placed in bounded areas, such as buildings [2]. Once a network is operated, the nodes communicate with each other and route information along by sharing a common wireless medium. Therefore, interference is often an issue since a receiver may be disturbed by those transmitters which do not have the desired packet, but are concurrently active. In particular, when the signal to interference plus noise ratio (SINR) is below a given threshold, correct reception of packets cannot be guaranteed. Several Medium Access Control (MAC) strategies have been proposed to overcome this and are essentially based on either randomizing the transmission instants (e.g., ALOHA [3]) or postponing transmission in case too much interference is sensed (e.g., CSMA [4]). However, interference is intuitively related to the network topology (i.e, number of nodes and their positions). In fact, given a fixed nodes density, different sizes of the deployment region give rise to different interference profiles, that cannot be evaluated by the models that are based on infinite networks. This work was supported by the COST2100 action.

In this paper we propose an analytical framework for computing the probability of outage in a network scenario where nodes are randomly distributed on a finite domain according to a 2-D Poisson point process (PPP), each transmitter generates packets at random time instants according to a Poisson process and send them to its designed receiver. The model accounts for different types of MAC protocols and includes the effects of the finiteness of the deployment region (edge effects). The objective of our analysis is to evaluate the impact of edge effects on the outage probability. We carry out the computation by assuming a Rayleigh fading channel. Our main finding is that both ALOHA and CSMA-like protocols perform better in bounded regions, as the edge effect may be regarded as spatial filtering. Also, the benefit is greater for small outage probabilities, i.e., in the region of practical interest. Some previous work addressed the mathematical characterization of multiple access schemes, especially carrier sensing in its standardized evolution [5]. A great effort has been put into characterizing the performance of wireless ad hoc networks and what role interference plays on it [6]. The edge effect due to the finiteness of deployment region has been initially considered in [7]. In [8] the specific case of a square domain is analyzed in detail. However, the two latter works only focus on connectivity, while no hint is given on its implications on performance at MAC layer. The physical nature of fading phenomenon is investigated in [9] and its impact on the performance of wireless sensor networks is addressed. Once again, the analysis is mainly concerned on connectivity and routing aspects. Finally, a large amount of research has been devoted to the performance of MAC protocols in infinite networks in non-fading [10] and fading environments [11]. This paper is organized as follows. In Section II, the system model is presented. In Section III, we compute the outage probability for different MAC protocols. Numerical results are reported and commented in Section IV and final remarks and conclusions are presented in Section V. II. S YSTEM M ODEL Our system model considers an ad hoc network where transmitter nodes are located on a finite 2-D plane according to a homogeneous Poisson point process (PPP) with spatial density λs [nodes/m2]. Each transmitter has packets arriving in time according to an independent 1-D PPP with density λt

[packets/sec/node]. Upon the formation of each packet, it is transmitted with a constant power ρ to its intended receiver, which is assumed to be positioned (with random orientation) a fixed distance R away. Assuming each packet has a fixed duration, T , at each time instant the density of transmitters that have received a packet in the last T seconds is λ = T λs λt . In order to address the problem of edge effect in space, we devote our attention to a 2-dimensional square region, D, of side L and consider only those nodes that fall inside it as part of the study. The origin of our coordinates system is placed in the center of the square. For the sake of the analysis carried out in the next sections, we propose a tessellation of such a domain featuring eight subregions, as shown in Fig. 1. The advantage of this lies in allowing us to switch to polar coordinates very easily, owing to the decomposition of the surface into sectors of annuli. Specifically, given whatever position (x, y) inside the square, only a fraction of the surface of a circle of radius r centered in (x, y) lies in D. Such fraction is θi (r)/π when r1,i ≤ r ≤ r2,i , with r1,i , r2,i and θi (r) defined in Tables I and II, respectively [8]. For the channel model, we consider deterministic path loss attenuation effects (with exponent α > 2) and fading effects. Each receiver potentially sees interference from all transmitters, and these independent interference powers are added to ρR−α h00 P , the channel noise η , resulting in SINR = −α η+

i

ρr

i

h0i

where ri is the distance between the node under observation (this could be either the transmitter or receiver of the packet we are considering) and the i-th interfering transmitter. hij are fading coefficients drawn from the random variable Hij . H00 represents the fading effects between the receiver under observation and its designated transmitter. If the received SINR falls below the required SINR threshold β either at the start or at any time during a packet transmission, the packet is received in outage with probability Pout . That is,   ρR−α h00 Pout = Pr <β . (1) P −α η+

i ρri

h0i

The packet transmissions occur according to either ALOHA or CSMA. In the ALOHA protocol, packets are transmitted to their intended destinations regardless of the channel conditions. CSMA protocol, instead, performs channel sensing at the beginning of the packet and the packet is then sent only if the measured SINR is large enough. Otherwise it is backed off. Since retransmissions are not accounted for in our model, each backoff is equivalent to dropping the packet, which is then considered to be in outage. In the following, we denote the transmitter-receiver pair under observation as TX0 -RX0 , and the interfering transmitterreceiver pairs as TXi -RXi , i > 0. III. D ERIVATION

OF THE

O UTAGE P ROBABILITY

The evaluation of outage probability consists of solving Equation (1) in the specific case of the square domain D. However, the consideration of all interfering contributions in the denominator of (1) turns out to be unpractical. For this

(-L/2, L/2)

(L/2, L/2)

(x,y) y

1 2 3

x 4

5 6 7 8

(-L/2, -L/2)

Fig. 1.

(L/2, -L/2)

Tessellation of D into eight subregions.

reason we focus on the probability of having single interferers, denoted as dominant [11], whose received interference power alone is strong enough to results in the outage of RX0 . Results will prove this assumption to be reasonable. A. The ALOHA Protocol We consider two versions of the ALOHA protocol, namely slotted and unslotted ALOHA. 1) Slotted ALOHA: In slotted ALOHA, TXs start their transmissions at the beginning of the next time slot after each packet has been formed, regardless of the channel conditions. The division of time into slots prevents partial overlap of packets, something that is expected to decrease the outage probability compared to unslotted systems. However, slotted systems require synchronization, which can be costly and introduce delays in the system. The outage probability of slotted ALOHA within a bounded network of size L × L is given by the following theorem. Theorem 1: The outage probability of slotted ALOHA can be approximated as h i P˜out (Slotted ALOHA) = Ex,y 1 − e−µ(x,y) Z L/2Z x 8 1−e−µ(x,y) dydx, (2) = 2 L

0

0

with µ(x, y) =

8 Z X i=1

r2,i

r1,i

2θi (r) λ r

ζβ dr ζ β + R−α r α

(3)

and ζ = E[Hij ], ∀i, j . Proof of Theorem 1: RX0 is in outage if there is at least one interferer for the duration, T , of its transmission. Consider the expected number, µ(x, y), of dominant interferers when RX0 is in (x, y). We have ZZ µ(x, y) = =

λ Pr(TXi causes outage for RX0 |(r, θ)) r dr dθ

ZZD

D

  ρR−α h00 λ Eh00 ,h0i Pr −α η + ρr

h0i





r dr dθ.

(4)

TX0

Assuming Rayleigh fading, channel coefficients are exponentially distributed, i.e., fH0i (h0i ) = ζe−ζ h0i . Therefore, taking the expectation in (4) yields after rearranging    ρR−α h00 <β P (r) = Eh00 ,h0i Pr −α η + ρr



ζβ , ζ β + (r/R)α

(5)

with µ(x, y) as in (3). Proof of Theorem 2: This proof is similar to that of Theorem 1, with the only difference that in the unslotted case, we have to consider all packet arrivals during (−T, T ]. That is, the continuity of packet transmissions in time gives rise to partial overlap of packets, resulting in an additional packet period to be considered. Note that the number of packet arrivals (and hence, the amount of interference) in (−T, 0] is independent from that in (0, T ], and this is why the only difference between Eqs. (2) and (6) is the factor 2 in the exponent of the exp(·)-expression. B. The CSMA Protocol Two variants of CSMA are considered, denoted as CSMATX and CSMARX 1 , respectively. In the former, the sensing operation is performed at the transmitter. In the latter, instead, the receiver senses the channel and inform the transmitter whether the channel is free or not. We assume this can happen over an orthogonal control channel. the same notation as in [10], [11]

RX0 (x,y) ri

y

h0i

where we have assumed path loss and fading are the main sources of signal degradation and consequently set the noise to zero. Equation (5) shows the dependence of outage probability upon the network key parameters. When the ratio of interfererand transmitter-receiver distances is large, P (r) approaches zero. However, once the channel characteristics are fixed, the rate of decay is influenced by the required SINR. Now, defining the integration limits, (4) becomes (3). The dependence upon x, y is in r1,i , r2,i and θi (r) (refer to Tables I and II). Finally, by exploiting Poissonianity of nodes and packets, we get the outage probability as 1 − e−µ(x,y) which results, after averaging, in (2). Note that we only consider the lower half of the first quadrant of Fig. 1 in the integration of (2), without loss of generality, because of symmetry. 2) Unslotted ALOHA: In unslotted ALOHA, communication is continuous in time, something that allows for partial overlap of packets. No channel sensing or backoffs are performed, meaning that packets are transmitted as soon as they are formed. The outage probability of unslotted ALOHA is given in the following theorem. Theorem 2: An approximated expression for the outage probability of unslotted ALOHA is obtained as h i (6) P˜out (Unslotted ALOHA) = Ex,y 1 − e−2µ(x,y) ,

1 following

(x0,y0) R

x

R RXi

TXi

Fig. 2. Setup for derivation of the outage probability of CSMATX and CSMARX .

1) CSMA with Transmitter Sensing: CSMATX is the conventional CSMA protocol, in which the transmitter senses its own channel upon each packet arrival and estimates the SINR at its receiver. Based on this estimated SINR, the transmitter makes the backoff decision. If the channel is sensed idle, the transmission is initiated; Otherwise, the packet is dropped and counted to be in outage. The outage probability of CSMATX is given by the following theorem. Theorem 3: The total outage probability of CSMATX is approximated by: n P˜out (CSMATX ) = Ex,y,φ P˜b (x0 , y0 ) + P˜b (x, y)e−µd (x,y) h i  −µ (x,y) + 1−e

d

1 − P˜b (x0 , y0 )

− P˜b (x0 , y0 )P˜b (x, y)e−µd (x,y)

o

with x0 = x + R cos φ, y0 = y + R sin φ (see Fig. 2) and   8 Z r2 X 2,i

µd (x, y) =

i=1

r2 1,i

2 ζ β λ r θi (r) ζ β + R−α r α

1−

ζβ ζ β + R−α r α

(7)

dr.

(8) P˜b (x, y) is the probability that the node in (x, y) is in outage at the start of the packet. Therefore P˜b (x0 , y0 ) expresses the

backoff probability for the CSMATX case. This probability can be approximated as  −µ(x,y) 1−PbI P˜b (x, y) = 1 − e , (9) with PbI derived numerically by the expression  I PbI = 1 − e

−µ(0,0) 1−Pb

,

(10)

or expressed in closed form in terms of the Lambert function, W0 (·), as PbI = 1 −

∞ W0 (µ0 ) 1 X (−n)n−1 n =1− µ0 , µ0 µ0 n!

(11)

n=1

with µ(x, y) given by (3) and µ0 = µ(0, 0). Proof of Theorem 3: In CSMATX , outage occurs if one or more of the following events occur: 1) the transmitter backs off; 2) once a transmission is initiated, the received SINR falls below β at the start of the packet; and 3) the received SINR falls below β during transmission. The probability that TX0 located in (x0 , y0 ) backs off, P˜b (x0 , y0 ), depends on how many other transmitters are generating interference, i.e., how many of them do not back off

and can consequently cause TX0 to back off. We assume their number is still Poisson distributed. However, the backoff probability of each interferer depends on its own position as well as on the positions and backoff probabilities of all the other nodes in a chain fashion. In order to make another simplifying assumption, we denote by a constant, PbI , the backoff probability of all the interferers independently of their positions. Equation (9) is motivated by the two latter assumptions. We then compute PbI as if all interferers were placed in the origin (10). Note that, with respect to CSMATX , P˜b (x0 , y0 ) is the approximate backoff probability, while P˜b (x, y) is simply the approximate probability that the SINR measured by RX0 is below threshold at the start of a packet. To find the probability that a packet goes into outage during its transmission, consider all active dominant interferers on the plane (i.e., all interferers that started their transmission during the last T s, and that can alone cause outage for the current packet). This random variable has expectation (recall (5)) ZZ µd (x, y) =

λ·Pr(TXi activated|(r, θ))

D

· Pr(TXi causes outage for RX0 |TXi active at (r, θ)) · rZZ dr dθ

=

λ·Pr(TXi activated|(r, θ))·P (r) r dr dθ.

(12)

D

Now, Pr(TXi activated|(r, θ)) depends on the interference measured by TXi , which should be below a certain threshold. Assuming I) that TXi suffers from the interference received by TX0 only and II) that the distance TXi -TX0 is approximately the same as TXi -RX0 , we simply have Pr(TXi activated|(r, θ)) ≈ 1 − P (r). The latter approximation makes sense because it is very likely that two neighboring links both interfere with each other’s transmissions. By exploiting Poissonianity, we get the outage probability during transmission as 1 − e−µd (x,y) . Finally, computing the union of the three events yields (after rearrangement) Eq. (7), where x, y are averaged over D and φ on the interval [0, 2π]. 2) CSMA with Receiver Sensing: In CSMARX , the receiver senses the channel upon arrival and informs its transmitter over an orthogonal control channel whether or not to back off from transmission. Theorem 4: The total outage probability of CSMARX is given by n h io P˜out (CSMARX ) = Ex,y P˜b (x, y)+[1− P˜b (x, y)] 1−e−µd (x,y) ,

(13)

where µd (x, y) is given by (8) and P˜b (x, y) by (9). Proof of Theorem 4: In CSMARX , a packet is considered to be in outage if the SINR measured by RX0 is less than β either at the start of the packet or at some point during its transmission, i.e., P˜out (CSMARX ) = Pr [SINR < β at t = 0 ∪ SINR < β at some t ∈ (0, T ]]. Now Pr [SINR < β at t = 0] is the actual backoff probability and is approximated by P˜b (x, y). The other term is the

probability that RX0 does not require TX0 to back off and that the channel becomes busy during transmission, which is explained in the proof of Theorem 3. IV. N UMERICAL R ESULTS AND D ISCUSSIONS In order to validate our framework, we designed a simulator environment where nodes and packet arrivals are generated as explained in the system model section. The aim of the comparison is to estimate the relevance of the approximations in the derivation of the model. The most significant of them is that we consider only the dominant interferers. For the following plots, we set R = 1 meter, ρ = 1 mW, the pathloss exponent α = 3 and the target SINR β = 1. In Fig. 3 the outage probability is reported as a function of λ for the four different MAC protocols considered. Both simulation and analytical curves are plotted and the comparison shows a good agreement. The same figure also compares the performance of the protocols. Slotted ALOHA exhibits the lowest outage probability because partial overlap of packets is avoided, even though at the cost of synchronizing the network. The performance of conventional CSMA (i.e., CSMATX ) appears to be even worse than that of Unslotted ALOHA in the left region of the plot. This is due to the fact that we count backoff as outage. However, for large packet densities, the number of nodes backing off is large enough and thus the amount of interference experienced by a single link is reduced compared to the case where all transmitters access the channel. As a consequence, CSMATX outperforms Unslotted ALOHA in saturation conditions. When the sensing operation is performed at the receiver, the impact of hidden and exposed terminal problems [4] is reduced. This makes CSMARX the most reliable among the unslotted protocols. Once the model is validated, we show the edge effect in Fig. 4, where the probability of outage in a bounded region is plotted as a function of the square side L, for fixed values of the density λ = 0.01, 0.1 [packets/m2 ]. It is possible to see the rate of decrease in the outage probability when the deployment region gets smaller. For example, for λ = 0.1, when L ranges from 200 to 3.3 meters, the relative decrease in the outage probability is 40% for Unslotted ALOHA and of almost 50% for CSMA and for slotted ALOHA. When λ = 0.01, the situation is of more interest to practical applications, since the outage probability is in the order of 10%. In this region, the relative outage probability decrease due to edge effect is above 50%. In summary, making the domain area smaller reduces the number of transmitters, that is, of potential interferers for a given transmitter-receiver pair. Moreover, the model also shows that the interference contribution is location dependent. Since nodes are distributed on a finite domain, a receiver located exactly in the corner of D should intuitively experience lower interference with respect to another one located in the center. In fact, if we take, e.g., Slotted ALOHA with L = 3.3 m and evaluate the ratio of the expected number of dominant interferers in the corner over that in the center, µ(L/2, L/2)/µ(0, 0), we obtain about 0.4, as expected.

Probability of Outage

10

10

0

TABLE I B OUNDARY VALUES FOR r IN THE EIGHT SUBREGIONS

−1

Region

Range: r1,i ≤ r ≤ r2,i

1

0≤r≤ L −x 2 L −x≤r≤ L −y 2 2

2

10

10

−2

Simulated OP of Sl. ALOHA Analytical OP of Sl. ALOHA Simulated OP of Unsl. ALOHA Analytical OP of Unsl. ALOHA Simulated OP of CSMA−RX Analytical OP of CSMA−RX Simulated OP of CSMA−TX Analytical OP of CSMA−TX

−3

10

−4

10

−3

−2

10 10 2 Density, λ [packets/m ]

−1

10

0

3

L −y≤r≤ 2

4

p

Fig. 3. Probability of outage (OP) for the different MAC protocols in a Rayleigh fading environment, as a function of node density (analytical and simulated results).

Probability of Outage

3

0.3

4 OP of Slotted ALOHA OP of Unslotted ALOHA OP of CSMA−RX OP of CSMA−TX

λ=0.1

0.2 λ=0.01

5 6 7

0.1

8 0

1

10 Side of deployment region, L [m]

AND

2 2 −x) +( L +y ) (L 2 2

2 2 −x) +( L +y ) ≤r≤ L +x (L 2 2 2

L +x≤r≤ 2

p

p

2 2 +x) +( L −y ) (L 2 2

2 2 +x) +( L −y ) ≤r≤ (L 2 2

p

2 2 +x) +( L +y ) (L 2 2

IN THE EIGHT SUBREGIONS

θi (r) π L π +arcsin 2 −x 2 r L L π +arcsin 2 −x −arccos 2 −y 2 r r L L π + 1 (arcsin 2 −x −arccos 2 −y ) 2 2 r r L L L π −arccos 2 +y + 1 (arcsin 2 −x −arccos 2 −y ) 2 r 2 r r L L π − 1 (arccos 2 +y +arccos 2 −y ) 2 2 r r L L L 1 (arcsin 2 −y +arcsin 2 +y )−arccos 2 +x 2 r r r L L 1 (arcsin 2 +y −arccos 2 +x ) 2 r r

2

10

Fig. 4. Probability of outage (OP) for the different MAC protocols in a Rayleigh fading environment, as a function of the square side L (analytical results). Ellipses group the curves for different values of λ.

V. C ONCLUSION

p

TABLE II B OUNDARY VALUES FOR THE ANGLE θ

2

0.4

p

7

1

0.5

L +y≤r≤ 2

6

Region

0.6

2 2 −x) +( L −y ) (L 2 2

2 2 −x) +( L −y ) ≤r≤ L +y (L 2 2 2

5

8

p

F UTURE W ORK

We proposed an analytical framework for evaluating the outage probability of different MAC protocols with consideration of edge effect. For a given packet density, the impact of enlarging the domain area is that of raising the number of transmitters, that is, of potential interferers for an arbitrary transmitter-receiver pair. This has been shown to have a great impact and further highlights the importance of considering boundedness of real networks. In real settings, traffic pattern, besides network geometry, also plays a role on outage probability. However, the aim here has been to show the effect of boundedness on widely used MAC protocols, assuming homogeneous traffic characteristics. Practical implications include the possibility of deploying a greater density of nodes in indoor networks than predicted by previous models, due to the presence of walls and obstacles. As future work, we intend to relax the assumption of fixed transmitter-receiver distance. R EFERENCES [1] C.-Y. Chong and S. P. Kumar, “Sensor networks: evolution, opportunities, and challenges”, Proceedings of the IEEE, vol. 91, no. 8, pp. 1247–1256, Aug. 2003.

[2] I. F. Akyildiz and W. Su and Y. Sankarasubramaniam and E. Cayirci, “Wireless sensor networks: a survey”, Computer Networks, vol. 38, no. 4, pp. 393–422, 2002. [3] N. Abramson, “THE ALOHA SYSTEM: another alternative for computer communications”, AFIPS ’70 (Fall): Proceedings of the November 17-19, 1970, fall joint computer conference, pp. 281–285, 1970. [4] L. Kleinrock and F. A. Tobagi, “Packet switching in radio channels: Part 1-carrier sense multiple access modes and their throughput-delay characteristics”, IEEE Trans. on Comm., vol.23(12), pp.1400–1416, 1975. [5] G. Bianchi, “Performance analysis of the IEEE 802.11 distributed coordinated function”, IEEE JSAC, 18(3):535547, March 2000. [6] P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks”, IEEE Trans. on Information Theory, vol. 46, no. 2, pp. 388–404, March 2000. [7] C. Bettstetter and J. Zangl, “How to achieve a connected ad hoc network with homogeneous range assignment: an analytical study with consideration of border effects”, 4th International Workshop on Mobile and Wireless Communications Network, 2002, pp. 125–129, Sep 2002. [8] F. Fabbri and R. Verdone, “A Statistical Model for the Connectivity of Nodes in a Multi-Sink Wireless Sensor Network Over a Bounded Region”, IEEE European Wireless (EW2008), pp. 1–6, 22–25 June 2008. [9] D. Puccinelli and M. Haenggi, “Multipath fading in wireless sensor networks: measurements and interpretation”, IWCMC ’06: int. conference on Wireless communications and mobile computing, pp. 1039–1044, Vancouver, British Columbia, Canada, 2006. [10] M. Kaynia and N. Jindal, “Performance of ALOHA and CSMA in spatially distributed wireless networks”, Proc. IEEE International Conf. on Communications (ICC), pp. 1108–1112, Beijing, China, May 2008. [11] M. Kaynia, G. E. Øien, and N. Jindal, “Impact of Fading on the Performance of ALOHA and CSMA”, Proc. IEEE International Workshop on Signal Processing Advances for Wireless Communications (SPAWC), pp. 394-398, June 2009.

The Impact of Edge Effects on the Performance of MAC ...

∗Wireless Communication Laboratory, DEIS, University of Bologna, Bologna, Italy. †Dept. of Electronics and Telecommunications, Norwegian Univ. of Science and Technology, Trondheim, Norway. Emails: [email protected], mariam.[email protected], [email protected]. Abstract—In this paper, the impact of ...

154KB Sizes 0 Downloads 240 Views

Recommend Documents

The Impact of Edge Effects on the Performance of MAC ...
characterizing the performance of wireless ad hoc networks and what role interference plays on it [6]. The edge effect due to the finiteness of deployment region ...

Effects of sample size on the performance of ... -
area under the receiver operating characteristic curve (AUC). With decreasing ..... balances errors of commission (Anderson et al., 2002); (11) LIVES: based on ...

Evaluating the Impact of Reactivity on the Performance ...
interactive process to design systems more suited to user ... user clicks on a link or requests a Web page during its ses- sion. ...... Tpc-w e-commerce benchmark.

On the Impact of Arousals on the Performance of Sleep and ... - Philips
Jul 7, 2013 - Electrical Engineering, Eindhoven University of Technology, Den Dolech. 2, 5612 AZ ... J. Foussier is with the Philips Chair for Medical Information ..... [6] J. Paquet, A. Kawinska, and J. Carrier, “Wake detection capacity of.

On the Impact of Arousals on the Performance of Sleep and ... - Philips
Jul 7, 2013 - techniques such as the analysis of the values in neighboring epochs [3] ..... Analysis Software (ADAS),” Physiology & Behavior, vol. 65, no. 4,.

On the Impact of a Single Edge on the Network Coding ...
California Institute of Technology [email protected]. Abstract—In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes.

Evaluating the Impact of Reactivity on the Performance of Web ... - Core
Bursts mimic the typical browser behavior where a click causes the browser to first request the selected Web object and then its embedded objects. A session ...

Peer Effects, Teacher Incentives, and the Impact of ...
This finding is consis- tent with the hypothesis that teachers are tailoring instruction to class composition, although this could also be mechanically true in any successful intervention. Rigorous evidence on the effect of tracking on learning of st

impact of performance appraisal on employee productivity pdf ...
There was a problem previewing this document. Retrying... Download ... impact of performance appraisal on employee productivity pdf. impact of performance ...

Effects of direction on saccadic performance in relation ...
Received: 27 September 2002 / Accepted: 26 February 2003 / Published online: 25 April 2003 ... good indicators of lateral preferences in these tasks. Other oculomotor tasks ... programming and execution of saccadic eye movements has been studied both

Effects of direction on saccadic performance in relation ...
Apr 25, 2003 - visual stimulus presentation and the onset of the response results in the reduction of ... The data presented in this study stem from the ASPIS ... appear on an imaginary horizontal line either at the center of the screen or at a ...

Impact of Power Control on the Performance of Ad Hoc ...
control (MAC) protocol such ,as time division multiple access. (TDMA), and a ..... receiver of more than one transmission at any time slot, a d ii) a node is not ...

Impact of Delay Variability on LEDBAT Performance
throughput for applications when no other traffic exists. A competing ...... change) USING 20 SEED NUMBERS. LEDBAT Throughput (Kb/s). ∆dave path (ms) tave.

The Impact of the Lyapunov Number on the ... - Semantic Scholar
results can be used to choose the chaotic generator more suitable for applications on chaotic digital communica- .... faster is its split from other neighboring orbits [10]. This intuitively suggests that the larger the Lyapunov number, the easier sh

On-The-Edge-Of-The-Auspicious-GENDER-AND ...
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. On-The-Edge-Of-The-Auspicious-GENDER-AND-CASTE-IN-NEPAL.pdf. On-The-Edge-Of-The-Auspicious-GENDER-AND-CASTE-

The Effects of The Inflation Targeting on the Current Account
how the current account behaves after a country adopts inflation targeting. Moreover, I account for global shocks such as US growth rate, global real interest rate ...

At the Very Edge of a Storm: The Impact of a Distant ...
Jun 21, 2017 - employment and access to clean water and sanitation. .... consumption expenditure required for daily calorie energy intake per person that is ...

IMPACT OF SALINITY ON THE GROWTH OF Avicennia ...
osmotic pressure of 4.3166 MPa against ostomatic pressures of their surrounding water of 0.9968 ..... Mangrove regeneration and management. Mimeograph.

On the Impact of Kernel Approximation on Learning ... - CiteSeerX
The size of modern day learning problems found in com- puter vision, natural ... tion 2 introduces the problem of kernel stability and gives a kernel stability ...

On the Impact of Kernel Approximation on ... - Research at Google
termine the degree of approximation that can be tolerated in the estimation of the kernel matrix. Our analysis is general and applies to arbitrary approximations of ...