iosr-Jm   Volume-7 ~ Issue-1

Abstract: Queuing is the common activity of customers or people to avail the desired service, which could be processed or distributed one at a time. Bank ATMs would avoid losing their customers due to a long wait on the line. The bank initially provides one ATM in every branch. But, one ATM would not serve a purpose when customers withdraw to use ATM and try to use other bank ATM. Thus the service time needs to be improved to maintain the customers. This paper shows that the queuing theory used to solve this problem. We obtain the data from a bank ATM in a city. We then derive the arrival rate, service rate, utilization rate, waiting time in the queue and the average number of customers in the queue based on the data using Little's theorem and M/M/I queuing model. The arrival rate at a bank ATM on Sunday during banking time is 1 customer per minute (cpm) while the service rate is 1.50 cpm. The average number of customer in the ATM is 2 and the utilization period is 0.70. We conclude the paper by discussing the benefits of performing queuing analysis to a busy ATM.

Keywords: Bank ATM, Little's theorem, M/M/I queuing model, Queue, Waiting lines.

[1] N. K. Tiwari & Shishir K. Shandilya, Oprations Research. Third Edition, ISBN 978-81-203-2966-9. Eastern Economy Edition, 2009.

[2] Nita H. Shah, Ravi M. Gor, Hardik Soni, Operations Research. 4th Edition, ISBN 978-81- 203-3128-0. Eastern Economy Edition, 2010.

[3] K. Sanjay, Bose, "An Introduction to queuing system", Springer, 2002.

[4] J. D. C. Little, "A Proof for the Queuing Formula: ", Operations Research, vol. 9(3), 1961, pp. 383-387, doi: 10.2307/167570

[5] M. Laguna and J. Marklund, Business Process Modeling, Simulation and Dsign. ISBN 0-13-091519-X. Pearson Prentice Hall, 2005.

Abstract: Let M be a semiprime -ring satisfying a certain assumption. Then we prove that every Jordan left higher k-centralizer on M is a left higher k-centralizer on M. We also prove that every Jordan higher kcentralizer of a 2-torsion free semiprime -ring M satisfying a certain assumption is a higher k-centralizer.

Keywords: Semiprime -ring, left higher centralizer, higher k-centralizer, Jordan higher k-centralizer𝜏)-centralizr

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Vol.6, No.21, 2012.

Abstract: Let 0 ( ) n j i j p z a z    be a polynomial of degree n and p(z) be its derivative, then Zygmund [9] proved that     1 1 2 0 2 '( ) | ( ) | , 1 0 | | r r i r i r p e d n p e d r           In this paper we shall obtain similar type of inequalities in reverse order for the polynomials having r fold zeros at origin and rest of the zeros in | z |  k , k  1. Mathematics Subject Classification (2010): 30A10, 30C15, 30C10

Key words: Polynomials, Zeros, Polar derivative, Inequality

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[5] V.K. Jain, Integral inequalit ies for polynomials having a zero of order m at the origin, Glasnik Matematicki 37(57) (2002), 83-88.
[6] N.A. Rather, Extremal Properties and Location of the Zeros of Polynomials, Ph.D. Thesis, University of Kashmir, 1998.
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[8] A.E. Taylor, Introduction to Functional Analysis, John Wiley and Sons, Inc., New York, 1958.
[9] Zygmund, A remark on conjugate series, Proc. London Math. Soc. 34 (1932), 392-400.

Abstract: The effects of variable Fluid Properties like variation of permeability, porosity, thermal conductivity and magnetic field on Mixed Convection Heat transfer from Vertical Heated Plate Embedded in a Sparsely Packed Porous Medium have been approached numerically. The boundary layer flow in the porous medium is governed by Lapwood – Forchheimer – Brinkman extended Darcy model and the Lorentz force. The natures of these equations are highly non-linear and coupled each other. The non-linear differential equations are non-dimensionalised using the non-dimensional parameter involving Grashoff number Gr, Prandtl number Pr, Hartmann number M, Eckert number E and so on. Similarity transformations are employed and the resulting ordinary differential equations are solved numerically by using shooting algorithm with Runge – Kutta and Newton – Raphson method to obtain velocity and temperature distributions. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in decreasing the flow field, whereas its influence is reversed on the rate of heat transfer for all values of permeability considered. The effect of Magnetic field is diminution with velocity of the fluid flow. Further, the obtained results under the two limiting conditions were found to be in good agreement with the existing results.

Keywords: Heat transfer, MHD, Newtonian fluid, porous medium, similarity solution.

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