On conditional ASTA: a sample-path approach

Muhammad El-Taha, Department of Mathematics and Statistics, University of Southern Maine

Abstract

In this paper finite-time and infinite-time sample-path analogues of the joint and conditional covariance formulas, and joint and conditional ASTA are proved under minimal requirements. We apply sample-path ASTA and conditional ASTA to give simple proofs of extensions of well-known formulas in G / G / c / K queueing systems, and provide additional insight into the job observer property in networks of queues. Our proofs are intuitively appealing and elementary. The approach taken in this paper reveals that the essential issues related to ASTA are elementary, and the relations among limiting averages follow immediately from the definitions, assuming the limits exist.