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In this paper, a new analogue of blossom based on post quantum calculus is introduced. The post quantum blossom has been adapted for developing identities and algorithms for Bernstein bases and B$\acute{e}$zier curves. By applying the post quantum blossom, various new identities and formulae expressing the monomials in terms of the post quantun Bernstein basis functions and a post quantun variant of Marsden's identity are investigated. For each post quantum B$\acute{e}$zier curves of degree $m,$ a collection of $m!$ new, affine invariant, recursive evaluation algorithms are derived., Comment: 13 pages, 4 figures, name of two more authors who contributed in revised form added, slight change in title of the paper

In this paper, we use the blending functions of Bernstein polynomials with shifted knots for construction of Bezier curves and surfaces. We study the nature of degree elevation and degree reduction for Bezier Bernstein functions with shifted knots. Parametric curves are represented using these modified Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We get Bezier curve defined on [0, 1] when we set the parameter \alpha=\beta to the value 0. We also present a de Casteljau algorithm to compute Bernstein Bezier curves and surfaces with shifted knots. The new curves have some properties similar to Bezier curves. Furthermore, some fundamental properties for Bernstein Bezier curves and surfaces are discussed., Comment: 11 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1507.04110

In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier curves based on (p,q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) \in [0, 1] \times [0, 1] depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. Furthermore, some fundamental properties for (p,q)-Bernstein Bezier curves are discussed. We get q-Bezier curves and surfaces for (u, v) \in [0, 1] \times [0, 1] when we set the parameter p1 = p2 = 1., Comment: 16 pages, 7 figures, basis function revised. arXiv admin note: substantial text overlap with arXiv:1505.01810

In this paper, performance evaluation of Newton-Raphson and Conjugate Gradient method has been studied in comparison to Steepest Decent method for coverage and connectivity control in backbone based wireless networks. In order to design such wireless networks, the main challenge is to ensure network requirements such as network coverage and connectivity. To optimize coverage and connectivity, backbone nodes will be repositioned by the use of mobility control based on above mentioned methods. Thus the network get self organized which autonomously achieve energy minimizing configuration. Furthermore by simulation using MATLAB R2010a, methods are compared on the basis of optimized cost, number of iterations and elapsed time i.e. total time taken to execute the algorithm., Comment: 15 pages, 16 figures

In this paper, we use the blending functions of Lupa\c{s} type (rational) $(p,q)$-Bernstein operators based on $(p,q)$-integers for construction of Lupa\c{s} $(p,q)$-B$\acute{e}$zier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupa\c{s} $(p,q)$-B$\acute{e}$zier Bernstein functions. Parametric curves are represented using Lupa\c{s} $(p,q)$-Bernstein basis. We introduce affine de Casteljau algorithm for Lupa\c{s} type $(p,q)$-Bernstein B$\acute{e}$zier curves. The new curves have some properties similar to $q$-B$\acute{e}$zier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain $(u, v) \in [0, 1] \times [0, 1] $ depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. We get $q$-B$\acute{e}$zier surfaces for $(u, v) \in [0, 1] \times [0, 1] $ when we set the parameter $p_1=p_2=1.$ In comparison to $q$-B$\acute{e}$zier curves and surfaces based on Lupa\c{s} $q$-Bernstein polynomials, our generalization gives us more flexibility in controlling the shapes of curves and surfaces. We also show that the $(p,q)$-analogue of Lupa\c{s} Bernstein operator sequence $L^{n}_{p_n,q_n}(f,x)$ converges uniformly to $f(x)\in C[0,1]$ if and only if $00$ fixed and $p \neq 1,$ the sequence $L^{n}_{p,q}(f,x)$ converges uniformly to $f(x)~ \in C[0,1]$ if and only if $f(x)=ax+b$ for some $a, b \in \mathbb{R}.$, Comment: 24 pages, 9 figures, $(p,q)$-lupas operator and limit $(p,q)$-lupas operators and their property introduced, typo corrected

In this paper, we have analyzed the effect of node mobility on the performance of AOMDV multipath routing protocol. This routing protocol in ad hoc network has been analyzed with random way point mobility model only. This is not sufficient to evaluate the behavior of a routing protocol. Therefore, in this paper, we have considered Random waypoint, Random Direction and Probabilistic Random Walk mobility Model for performance analysis of AOMDV protocol. The result reveals that packet delivery ratio decreases with the increasing node mobility for all mobility models. Also, average end-to-end delay is also vary with varying node speed, initially upto 20 nodes in all mobility models delay is minimum., Comment: 9 pages, 6 figures, International Journal of Wireless & Mobile Networks (IJWMN) Vol. 6, No. 3, June 2014

In this paper, performance analysis of Location Aided Routing (LAR) protocol in different city scenarios has been done. The mobility model considered is Manhattan model. This mobility model used to emulate the movement pattern of nodes i.e., vehicles on streets defined by maps. Our objective is to provide a qualitative analysis of the LAR protocol in different city scenarios in Vehicular Ad hoc Networks. We have considered three different city scenarios for the analysis of the protocol. The simulation work has been conducted using the Glomosim 2.03 simulator. The results show that LAR1 protocol achieves maximum packet delivery ratio is 99.68 % and maximum average end-to-end delay is 7.319969 ms when the network is sparsely populated. Further, for densely populated network maximum achieved packet delivery ratio is 87.58% and average end-to-end delay is 0.017684 ms.

Vehicular Ad-hoc Networks (VANETs) is attracting considerable attention from the research community and the automotive industry to improve the services of Intelligent Transportation System (ITS). As today's transportation system faces serious challenges in terms of road safety, efficiency, and environmental friendliness, the idea of so called "ITS" has emerged. Due to the expensive cost of deployment and complexity of implementing such a system in real world, research in VANET relies on simulation. This paper attempts to evaluate the performance of VANET in a realistic environment. The paper contributes by generating a real world road Map of JNU using existing Google Earth and GIS tools. Traffic data from a limited region of road Map is collected to capture the realistic mobility. In this work, the entire region has been divided into various smaller routes. The realistic mobility model used here considers the driver's route choice at the run time. It also studies the clustering effect caused by traffic lights used at the intersection to regulate traffic movement at different directions. Finally, the performance of the VANET is evaluated in terms of average delivery ratio, packet loss, and router drop as statistical measures for driver route choice with traffic light scenario. This experiment has provided insight into the performance of vehicular traffic communication for a small realistic scenario.

Geocasting is a special variant of multicasting, where data packet or message is transmitted to a predefined geographical location i.e., known as geocast region. The applications of geocasting in VANET are to disseminate information like, collision warning, advertising, alerts message, etc. In this paper, we have proposed a model for highway scenario where the highway is divided into number of cells. The intersection area between two successive cells is computed to find the number of common nodes. Therefore, probabilistic analysis of the nodes present and void occurrence in the intersection area is carried out. Further, we have defined different forwarding zones to restrict the number of participated nodes for data delivery. Number of nodes present and void occurrence in the different forwarding zones have also been analysed based on various node density in the network to determine the successful delivery of data. Our analytical results show that in a densely populated network, data can be transmitted with low radio transmission range. In a densely populated network smaller forwarding zones will be selected for data delivery.