On {\em BASTA} for Discrete-Time Queues

TL;DR

This paper proves that BASTA/ASTA properties hold in discrete-time queues regardless of scheduling rules, clarifying their applicability beyond traditional assumptions.

Contribution

It establishes that BASTA/ASTA principles are valid in discrete-time queues under any scheduling rule, extending the theoretical understanding.

Findings

BASTA/ASTA hold regardless of scheduling rules

Clarifies the conditions under which BASTA/ASTA are valid

Extends classical queueing theory results

Abstract

We address the issue of Bernoulli/Geometric arrivals see time-averages, {\em BASTA}, in discrete-time queues when using a variety of scheduling rules. It is well-known that {\em BASTA}/{\em ASTA} holds in the framework of a discrete-time process with an imbedded arrival process without regard to scheduling rules. However, when scheduling rules are invoked, it is not always clear whether arrivals see time averages as asserted by the general theory. We resolve this issue so that {\em BASTA}/{\em ASTA} holds regardless of the scheduling rule at play.