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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we provide a novel matrix-analytic approach for studyingdoubly exponential solutions of randomized load balancing models (also known assupermarket models) with Markovian arrival processes (MAPs) and phase-type (PH)service times. We describe the supermarket model as a system of differentialvector equations by means of density dependent jump Markov processes, andobtain a closed-form solution with a doubly exponential structure to the fixedpoint of the system of differential vector equations. Based on this, we showthat the fixed point can be decomposed into the product of two factorsinflecting arrival information and service information, and further find thatthe doubly exponential solution to the fixed point is not always unique formore general supermarket models. Furthermore, we analyze the exponentialconvergence of the current location of the supermarket model to its fixedpoint, and apply the Kurtz Theorem to study density dependent jump Markovprocess given in the supermarket model with MAPs and PH service times, whichleads to the Lipschitz condition under which the fraction measure of thesupermarket model weakly converges the system of differential vector equations.This paper gains a new understanding of how workload probing can help in loadbalancing jobs with non-Poisson arrivals and non-exponential service times.

Doubly Exponential Solution for Randomized Load Balancing Models with Markovian Arrival Processes and PH Service Times