Bounding Availability of Repairable Systems
IEEE Transactions on Computers
Computing bounds on steady state availability of repairable computer systems
Journal of the ACM (JACM)
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Bound Computation of Dependability and Performance Measures
IEEE Transactions on Computers
Output models of MAP/PH/1(/K) queues for an efficient network decomposition
Performance Evaluation
IEEE Transactions on Computers
A joint moments based analysis of networks of MAP/MAP/1 queues
Performance Evaluation
Lumping and reversed processes in cooperating automata
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Product-forms in batch networks: Approximation and asymptotics
Performance Evaluation
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In this paper, we propose a new approach to compute bounds on stationary measures of queueing systems with an input process described by a Markovian Arrival Process (MAP) and a sequence of stations with Phase Type (PH) service time distributions. Such queueing systems cannot be solved exactly since they have an infinite state space in several natural dimensions. Based on earlier work on the computation of bounds for specific classes of infinite Markov chains, the paper presents a new approach specifically tailored to the analysis of the mentioned class of queueing networks. By increasing the size of the state space of the aggregated Markov chain to be solved for bound computation, bounds can be made arbitrarily tight, but practical limits come up due to the computational complexity. However, we show by means of several examples that tight bounds can be derived with low effort for a large set of queueing systems in the mentioned class.