On recurrence and availability factor for single--server system with general arrivals

TL;DR

This paper investigates the recurrence and ergodic properties of a single-server queueing system with variable arrival and service rates, linking convergence to stationarity with reliability theory insights.

Contribution

It establishes recurrence and ergodic properties for such queueing systems with general arrival and service intensities, providing a new theoretical framework.

Findings

Proves recurrence and ergodicity under variable intensities

Links convergence to stationarity with reliability concepts

Provides conditions for system stability

Abstract

Recurrence and ergodic properties are established for a single--server queueing system with variable intensities of arrivals and service. Convergence to stationarity is also interpreted in terms of reliability theory.