Tail asymptotics for a random sign Lindley recursion

TL;DR

This paper analyzes the tail behavior of a generalized Lindley recursion in queuing systems with dependent times, providing precise asymptotics across different cases and comparing with existing models.

Contribution

It derives exact tail asymptotics for a generalized Lindley recursion, extending understanding beyond classical Lindley's recursion and related systems.

Findings

Identifies three distinct tail asymptotic regimes.

Provides precise asymptotic formulas for each case.

Compares new results with classical Lindley and alternating service systems.

Abstract

We investigate the tail behaviour of the steady state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queuing systems with dependent interarrival and service times, and includes alternating service systems and carousel storage systems as special cases. We obtain precise tail asymptotics in three qualitatively different cases, and compare these with existing results for Lindley's recursion and for alternating service systems.