On An Exact Solution Of The Rate Matrix Of Quasi-Birth-Death Process With Small Number Of Phase
@inproceedings{Murthy2017OnAE, title={On An Exact Solution Of The Rate Matrix Of Quasi-Birth-Death Process With Small Number Of Phase}, author={Garimella Rama Murthy and Alexander S. Rumyantsev}, booktitle={European Conference on Modelling and Simulation}, year={2017} }
A new method of obtaining exact solution for the rate matrix R in the Matrix-Analytic method in case of the phase state of dimension two is proposed. The method is based on symbolic solution of the determinental polynomial equation, and obtaining a linear matrix equation for the unknown rate matrix R by Cayley–Hamilton theorem. The method is applied to analyze the EnergyPerformance tradeoff of an Internet-of-Things device. A new randomized regime switching scheme is proposed, which, as it is…
8 Citations
On an exact solution of the rate matrix of G∕M∕1-type Markov process with small number of phases
- Mathematics, Computer ScienceJournal of Parallel and Distributed Computing
- 2018
Efficient Algorithms for Computation of Equilibrium/Transient Probability Distribution of Finite Markov Chains: Potential Lower Bound on Computational Complexity
- Computer Science, Mathematics
- 2018
Efficient algorithms for computation of equilibrium as well as transient probability distribution of arbitrary finite state space Continuous / Discrete Time Markov Chains are proposed to solve structured systems of linear equations efficiently.
Matrix Quadratic Equations: Algebraic Geometry
- Mathematics
- 2019
In this research paper, we consider matrix quadratic equations in which the coefficient matrices as well as unknown matrix are 2 x 2 matrices. It is shown that linear algebraic techniques enable…
Efficient Redundancy Techniques in Cloud and Desktop Grid Systems using MAP/G/c-type Queues
- Computer Science
- 2018
Three variations of Fork-Join systems in the context of a multi-server queueing system with a versatile point process for the arrivals are considered, considering phase type distributions as well as shifted exponential and Weibull for replication policies.
G/M/1-type Markov Chain Model of Spread Spectrum ( CDMA ) Cognitive Radio Wireless Networks
- Business
- 2018
A G/M/1-type Markov Chain model ( with two states at each level ) of CDMA Cognitive Radio based wireless networks is developed and the equilibrium as well as transient performance evaluation of such networks is carried out efficiently.
Efficient Computation of Equilibrium/Transient Probability Distribution of Arbitrary Finite State Space Continuous Time Markov Chains
- Mathematics
- 2020
In this research paper, efficient algorithms for computation of equilibrium as well as transient probability distribution of arbitrary finite state space Continuous / Discrete Time Markov Chains are…
Steady-State and Transient Analysis of a Single Channel Cognitive Radio Model with Impatience and Balking
- Computer Science
- 2020
Evaluating a Single-Server Queue with Asynchronous Speed Scaling
- Computer ScienceMMB
- 2018
The approach is based on a simple client-server-type application run on a single linux-operated laptop, equipped with standard frequency scaling tools, and explicit analytical results are obtained by means of Matrix-Analytic method.
References
SHOWING 1-10 OF 35 REFERENCES
On an exact solution of the rate matrix of G∕M∕1-type Markov process with small number of phases
- Mathematics, Computer ScienceJournal of Parallel and Distributed Computing
- 2018
Equilibrium analysis of skip free markov chains: nonlinear matrix equations
- Mathematics
- 1991
Nonlinear matrix equations of the form where Fi, i=0, 1,2 ... ,m are known nxn nonnegative sub-matrices of a state transition matrix arise ubiquitously in the analysis of various stochastic models…
An efficient method to compute the rate matrix for retrial queues with large number of servers
- Computer Science, MathematicsAppl. Math. Lett.
- 2010
Spectral analysis of M/G/1 and G/M/1 type Markov chains
- MathematicsAdvances in Applied Probability
- 1996
When analyzing the equilibrium behavior of M/G/1 type Markov chains by transform methods, restrictive hypotheses are often made to avoid technical problems that arise in applying results from complex…
Transient and equilibrium analysis of computer networks: finite memory and matrix geometric recursions
- Computer Science
- 1991
The state space expansion technique can be utilized to arrive at a finite memory recursion for the equilibrium and transient behavior of M/G/1-type Markov processes, and various performance measures of interest in the overload control of these networks are defined.
Introduction to Matrix Analytic Methods in Stochastic Modeling
- MathematicsASA-SIAM Series on Statistics and Applied Mathematics
- 1999
This chapter discusses quasi-Birth-and-Death Processes, a large number of which are based on the Markovian Point Processes and the Matrix-Geometric Distribution, as well as algorithms for the Rate Matrix.
Spectral Expansion Solution for a Class of Markov Models: Application and Comparison with the Matrix-Geometric Method
- MathematicsPerform. Evaluation
- 1995
Solving matrix polynomial equations arising in queueing problems
- Mathematics, Computer Science
- 2002
Matrix-geometric solutions in stochastic models - an algorithmic approach
- Education
- 1982
This book is the product of a close collaboration between two mathematicians and an engineer and has been helpful in pinpointing the problems which engineering students encounter in books written by mathematicians.
COMPUTATIONAL ASPECTS FOR STEADY STATE ANALYSIS OF QBD PROCESSES
- Mathematics
- 2000
A comparative framework is adopted and implemented to evaluate the capability of some chosen methods (spectral expansion, matrix geometric and its enhanced versions) in both finite and infinite cases.