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
Performance of Computer Communication Systems: A Model-Based Approach
Performance of Computer Communication Systems: A Model-Based Approach
The PH/PH/1 queue at epochs of queue size change
Queueing Systems: Theory and Applications
The BMAP/G/1 QUEUE: A Tutorial
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Inverse Free Parallel Spectral Divide and Conquer Algorithms for
Inverse Free Parallel Spectral Divide and Conquer Algorithms for
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)
System-theoretical algorithmic solution to waiting times in semi-Markov queues
Performance Evaluation
| Hi-index | 0.00 |
Markov renewal processes with semi-Markov kernel matrices that have matrix-exponential representations form a superset of the well-known phase-type renewal process, Markovian arrival process, and the recently introduced rational arrival process. In this paper, we study the steady-state waiting time distribution in an infinite capacity single server queue with the auto-correlation in interarrival and service times modeled with this general Markov renewal process. Our method relies on the algebraic equivalence between this waiting time distribution and the output of a feedback control system certain parameters of which are to be determined through the solution of a well known numerical linear algebra problem, namely the SDC (Spectral-Divide-and-Conquer) problem. We provide an algorithmic solution to the SDC problem and in turn obtain a simple matrix exponential representation for the waiting time distribution using the ordered Schur decomposition that is known to have numerically stable and efficient implementations in various computing platforms.