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Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

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290 L. Hughes, K. Shumon, and Y. Zhang2aExpected zoneDr1r2C2bD2bC2c(a) An ellipse(b) Transmission areaFig. 3. Fixedpathlengthshapes.4 TransmissionAreawithFixedPathLengthAs well as mak<strong>in</strong>g the transmission area with a limit<strong>in</strong>g angle, the area can alsobe determ<strong>in</strong>ed from the path length. S<strong>in</strong>ce nodes with a fixed path length forman ellipse, the second CARP algorithm uses an ellipse as the transmission area.In Fig. 3(a), the current and dest<strong>in</strong>ation nodes are two foci of an ellipse; thedistance between these two nodes is 2c. The major axis of the ellipse is 2a andthe m<strong>in</strong>or axis of ellipse is 2b.The follow<strong>in</strong>g equations are of <strong>in</strong>terest:r 1 + r 2 =2a (2)b 2 + c 2 = a 2 (3)All the nodes located on the ellipse boundary have the same path length 2a,as shown <strong>in</strong> equation 2, while nodes located <strong>in</strong>side the ellipse have a shorter pathlength. These nodes are <strong>in</strong>side the transmission area.An expected zone is def<strong>in</strong>ed as the overlapp<strong>in</strong>g area of a circle (centred atthe dest<strong>in</strong>ation) and the ellipse as shown <strong>in</strong> Fig. 3(b).The transmission area <strong>in</strong>formation for this algorithm is the current nodeaddress (x c ,y c ).4.1 Transmission Area Creation SubsystemThe parameters a, b and c determ<strong>in</strong>e the shape of the ellipse; however s<strong>in</strong>ce theyare correlated as illustrated <strong>in</strong> equation 3, if any two of them are known, thethird can be calculated.The value of a is related to the radius of the expected zone, r, andthedistance between the source and the dest<strong>in</strong>ation, 2c. S<strong>in</strong>ce the positions of thecurrent and dest<strong>in</strong>ation nodes are assumed to be fixed at the transmission of thepacket, a is determ<strong>in</strong>ed from the radius of the expected zone, r, which is relatedto the speed of the dest<strong>in</strong>ation [7].An ellipse <strong>in</strong> a sparse network has a larger value of b than that <strong>in</strong> a densenetwork to <strong>in</strong>clude more nodes <strong>in</strong> the area. Fig. 3(b) shows the transmission areawith different values of b <strong>in</strong> networks with different densities.When an <strong>in</strong>termediate node forwards the packet, it substitutes the currentnode co-ord<strong>in</strong>ates with its own to create the transmission area for the next hop.

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