On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
A Queueing Model with Finite Waiting Room and Blocking
Journal of the ACM (JACM)
Probability and statistics with reliability, queuing and computer science applications
Probability and statistics with reliability, queuing and computer science applications
Simulation Modeling and Analysis
Simulation Modeling and Analysis
PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
Finite and Infinite QBD Chains: A Simple and Unifying Algorithmic Approach
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
Approximate solutions for heavily loaded Markov-modulated queues
Performance Evaluation - Performance 2005
Modelling and Performability Analysis of Network Memory Servers
ANSS '06 Proceedings of the 39th annual Symposium on Simulation
Modelling Network Memory Servers with Parallel Processors, Break-downs and Repairs
ANSS '07 Proceedings of the 40th Annual Simulation Symposium
Performance-Related Reliability Measures for Computing Systems
IEEE Transactions on Computers
On Evaluating the Performability of Degradable Computing Systems
IEEE Transactions on Computers
Proceedings of the 45th Annual Simulation Symposium
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Analytical solutions for two-dimensional Markov processes suffer from the state space explosion problem. Two stage tandem networks are effectively used for analytical modelling of various communication and computer systems which have tandem system behaviour. Performance evaluation of tandem systems with feedbacks can be handled with these models. However, because of the numerical difficulties caused by large state spaces, considering server failures and repairs at the second stage employing multiple servers has not been possible. The solution proposed in this paper is approximate with a high degree of accuracy. Using this approach, two stage open networks with multiple servers, break downs, and repairs at the second stage as well as feedback can be modelled as three-dimensional Markov processes and solved for performability measures. Results show that, unlike other approaches such as spectral expansion, the steady state solution is possible regardless of the number of servers employed.