i-manager Publications

Performance Evaluation of Homogeneous Parallel Processor System of Markov Modeled Queue

C S Reddy,*, Prasad K.R**, Mamatha . E***, Sathish A****

*Assistant Professor, RGM Engineering College, Nandyal.

**Professor, BOS, S. V. University, Tirupati.

***Syamaladevi Institute of Science and Technology, Nandyal.

**** Associate Professor, RGM Engineering College, Nandyal.

Periodicity:October - December'2008
DOI : https://doi.org/10.26634/jse.3.2.250

Abstract

The high expectation of performance and availability for communication systems has presented great challenges in the modeling and design of fault tolerant wireless systems. The proper modeling methodology to study the degradation of such systems is so-called performability modeling. In this paper, an overview of approaches for the construction and the solution of performability model spectral approximation method is given. In the existing exact solutions for Markovmodulated queues are computationally intensive and prone to numerical problems when the number of states of the Markovian environment becomes large. To address this problem, a simple technique, spectral approximation method is proposed. It uses the dominant eigenvalue of the characteristic matrix polynomial, together with the associated left eigenvector. This approximation is shown to be asymptotically exact in heavy arrival.

Keywords

Unbounded queues, QBD process, Mean queue length, Markov processes, Exponential distribution

How to Cite this Article?

C S Reddy, Prasad K.R, Mamatha E and Sathish A (2008). Performance Evaluation of Homogeneous Parallel Processor System of Markov Modeled Queue. i-manager’s Journal on Software Engineering, 3(2), 58-65. https://doi.org/10.26634/jse.3.2.250

References

[1]. Wallace, V. L., The Solution of Quasi Birth and Death Processes arising from Multiple Access Computer Systems, Ph.D Thesis, University of Michigan, 1969.

[2]. Evans, R. V., Geometric Distribution in some Two- Dimensional Queueing Systems, Operations Research, 15 (1967), pp. 830-846.

[4]. Bini.D., Meini. B., “On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems”, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 906-926.

[5]. Gail,H. R., Hantler, S. L., B.A. Taylor, Spectral analysis of M/G/1 and G/M/1 type Markov chains, Adv. Appl. Prob. 28 (1996) 114-165.

[6]. I. Mitrani, R. Chakka, “Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method”, Perform. Eval. 23 (3) (1995) 241-260.

[7]. Chakka, R. Mitrani, I., “A Numerical Solution Method for Multiprocessor Systems with General Breakdowns and Repairs”, Proceedings of 6th Int. Conf. on Performance Tools and Techniques, pp. 289-304, September, 1992.

[8]. Ciardo, G. Smirni, E., “Etaqa: An Efficient Technique for the Analysis of QBD-Processes by Aggregation”, Performance Evaluation, 3637 (1999), pp. 71-93.

[9]. Hung, T. Tran and Tien, V. DO., “Computational aspects for study state analysis of QBD processes”,Periodica Polytechnica Ser. El. Eng. Vol. 44, No. 2, pp. 179- 200 (2000).

[10]. Chakka, R., “Performance and Reliability Modeling of Computing System Using Spectral Expansion”, University of Newcastle upon Tyne, Ph.D Thesis, 1995.

[11]. Chandra Sekhar Reddy, C., Prasad, K. R., “Analysis and per formance evaluation of homogeneous multiprocessor system of Markov modulated queues”, st Proceedings of 1 Int. Conf. on RF and Signal Processing systems, pp-5-10, February 2008.

[12]. Kuo-Hsiung Wang, Li Ping Wang, Gang Chen, JauChuan Ke, “Comparative analysis for the N policy M/G/1 queuing system with removable and reliable server”, Mathematical Methods of Operations Research 61(2005), pp 505-520.

[13]. Chandra Sekhar Reddy, C., Prasad K. R., “Performability modeling of identical multiprocessor system with remodeling and restarting delay”, Journal of computer science, 2 (2008) pp. 755-762.

[14]. Dhanunjaya, S. Trivedi K.S., Logothetis, D., Performance modeling of wireless networks with generally distributed handoff interarrival times, Computer Communications 26 (2003), pp. 1747-1755.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.