Sample-path stability conditions for multiserver input-output processes
type: Item
instance of: scholarly article
title: Sample-path stability conditions for multiserver input-output processes
zbMATH Open document ID: 0812.60089
DOI: 10.1155/S1048953394000353
author: Muhammad El-Taha
author: Shaler jun. Stidham
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1995-02-13T00:00:00Z
full work available at URL: https://eudml.org/doc/47151
review text: Summary: We extend our studies of sample-path stability to multiserver input- output processes with conditional output rates that may depend on the state of the system and other auxiliary processes. Our results include processes with countable as well as uncountable state spaces. We establish rate stability conditions for busy period durations as well as the input during busy periods. In addition, stability conditions for multiserver queues with possibly heterogeneous servers are given for the workload, attained service, and queue length process. The stability conditions can be checked from parameters of primary processes, and thus can be verified a priori. Under the rate stability conditions, we provide table versions of Little's formula for single server as well as multiserver queues. Our approach leads to extensions of previously known results. Since our results are valid pathwise, non-stationary as well as stationary processes are covered.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60K99
zbMATH DE Number: 722524
zbMATH Keywords: sample-path stability
zbMATH Keywords: multiserver input-output processes
zbMATH Keywords: stability conditions
zbMATH Keywords: Little's formula
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 722524