Akar, NailSohraby, K.2016-02-082016-02-082006http://hdl.handle.net/11693/27165Date of Conference: 11-13 October 2006Conference Name: 1st International Conference on Performance Evaluation Methodolgies and Tools, VALUETOOLS 2006Markov 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.EnglishLindley equationMarkov renewal processesMatrix exponential distributionOrdered schur decompositionMarkov processesMatrix algebraQuality of serviceQueueing networksConference Paper10.1145/1190095.1190109