English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

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. Copyright 2006 ACM

Solving the single server semi-Markov queue with matrix exponential kernel matrices for interarrivals and services