Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Data networks
On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
Signals & systems (2nd ed.)
Exact aggregate solutions for M/G/1-type Markov processes
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
The BMAP/G/1 QUEUE: A Tutorial
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times
Queueing Systems: Theory and Applications
Performance of correlated queues: the impact of correlated service and inter-arrival times
Performance Evaluation - Internet performance symposium (IPS 2002)
Computational Analysis of Stationary Waiting-Time Distributions of GIX/R/1 and GIX/D/1 Queues
Probability in the Engineering and Informational Sciences
A spectral approach to compute performance measures in a correlated single server queue
ACM SIGMETRICS Performance Evaluation Review - Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)
On Queues with Markov Modulated Service Rates
Queueing Systems: Theory and Applications
Solving the ME/ME/1 queue with state-space methods and the matrix sign function
Performance Evaluation
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Queueing Theory: A Linear Algebraic Approach
Queueing Theory: A Linear Algebraic Approach
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Markov renewal processes with matrix-exponential semi-Markov kernels provide a generic tool for modeling auto-correlated interarrival and service times in queueing systems. In this paper, we study the steady-state actual waiting time distribution in an infinite capacity single-server semi-Markov queue with the auto-correlation in interarrival and service times modeled by Markov renewal processes with matrix-exponential kernels. Our approach is based on the equivalence between the waiting time distribution of this semi-Markov queue and the output of a linear feedback interconnection system. The unknown parameters of the latter system need to be determined through the solution of a SDC (Spectral-Divide-and-Conquer) problem for which we propose to use the ordered Schur decomposition. This approach leads us to a completely matrix-analytical algorithm to calculate the steady-state waiting time which has a matrix-exponential distribution. Besides its unifying structure, the proposed algorithm is easy to implement and is computationally efficient and stable. We validate the effectiveness and the generality of the proposed approach through numerical examples.