iosr-Jm   Volume-12 ~ Issue-1 ~ Jan-Feb 2016

Abstract: Queue is the study of traffic behavior near a certain section where demand exceeds available capacity. Queue can be seen in many situations, boarding a bus, train or plane traffic signal etc. Mobility is an in dispensable activity of our daily lives and traffic congestion is one popular approach to mobility. In this paper we discuss the Markovian modelling of vehicular traffic congestion in Nagercoil junction and Marthandam junction at kanayakumari district. Queuing theory analytic methodologies, simulation and Chi- square distribution are applied and parameters such as average arrival rate and service rate are calculated based on the data obtained at the Marthandam and Nagercoil junctions on daily basis for six days in a week. Keywords: Queuing system, Poisson process, Markov process, Chi - square distribution, exponential distribution

[1]. Dr.S.P Gupta &Dr.M.P Gupta, Business Statistics, Sultan Chand & Sons, New Delhi.
[2]. Mehdi, J (2003) Stochastic Models in Queuing theory, second Edition, Esevier, Berlin.
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[4]. Kendall D.G.Stochastic process occurring in the theory of queuing analysis by the method of the imbedded Markov chain. The Annals of Mathematical statistics 1953. 24(3).
[5]. Irene K.V.A Simulation approach to the design of the single – server Queuing system. Department of mathematics and statistics, University of Cape coast 2008.
[6]. Gerlough D.C and Schuhl A. Use of Poisson distribution in High Way Traffic and the probability theory .Applied to distribution of vehicles on Two – lane High way. New York, Columbia University press 1955.
[7]. Agbonia F.O. Road traffic Congestion and the quest for effective transportation Proceedings of the National Conference of Nigerian society of Engineers in Calaba 2011.

Abstract: Numerical methods have been formulated for the numerical approximation of real two dimensional integrals. The truncation error associated with the methods has been analyzed using the Taylors' series expansion. The methods have been verified by considering standard examples.

Keywords: Approximation rules, Degree of precision, Taylors' series expansion.

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Abstract:The groups of much attention for which the Diffie - Hellman problem may be hard and used securely are the multiplicative group * p F , (Z/nZ)* and the group of rational points on an elliptic curve over a finite field. These groups involve large key sizes or expensive arithmetic operations. In this paper we consider the group of Lucas sequences and describe the generalization of discrete log problem to the group of Lucas sequences and adapt the baby-step giant-step algorithm to the generalization. For the computations we implement fast computing methods proposed by Smith.
Key word: Discrete Log Problem, Lucas Sequences, Public Key Cryptography.

[1]. W. Diffie and M.E. Hellman, "New directions in cryptography", IEEE Trans. Inform. Theory, IT-22(6):644-654, 1976.
[2]. T. ElGamal, "A public key cryptosystem and a signature scheme based on discrete logarithms", IEEE Trans. Inform. Theory,
31(4):469-472, 1985.
[3]. Marc Gysin, "The Discrete Logarithm Problem for Lucas Sequences and a New Class of Weak RSA Moduli", The University of
Wollongong, NSW 2522.
[4]. Peter J. Smith and Michael J.J. Lennon, "A New Public Key System", LUC Partners, Auckland UniServices Ltd, The University of
Auckland, Private Bag 92019m Auckland, New Zealand.
[5]. B.Ravitheja, "RSA-Like Cryptosystem based on the Lucas Sequence", dissertation, 2015.

Abstract: In this paper, the three-point distribution functions for simultaneous velocity, temperature and concentration fields in dusty fluids turbulent flow undergoing a first order reaction have been studied. The various properties of constructed distribution functions have been discussed. From beginning to end of the study, the transport equation for three-point distribution function undergoing a first order reaction has been obtained. The resulting equation is compared with the previous equation which related to the distribution function by many authors and the closure difficulty is to be removed as in the case of ordinary turbulence.

Keywords: Magnetic Temperature, Concentration, Three-point distribution functions, MHD turbulent flow, First Order Reactant..

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