Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Turning back time in Markovian process algebra
Theoretical Computer Science
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
A programming language
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Response time distributions and network perturbation into product-form
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
A general result for deriving product-form solutions in markovian models
Proceedings of the first joint WOSP/SIPEW international conference on Performance engineering
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Queueing systems with Poisson arrival processes and Hypo-exponential service time distribution have been widely studied in literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, matrix-analytic method may be applied. Let πnk be the steady-state probability of observing the k-th stage of service busy and n customers in the queue, with 1 ≤ k ≤ K, and K the number of stages, and let πn = (πn1,..., πnK). Then, it is well-known that there exists a rate matrix R such that πn+1 = πnR. In this paper we give a symbolic expression for such a matrix R. Then, we exploit this result in order to address the problem of approximating a M/HypoK/1 queue by a model with initial perturbations which yields a product-form stationary distribution. We show that the result on the rate matrix allows us to specify the approximations for more general models than those that have been previously considered in literature and with higher accuracy.