Time-dependent behaviour of an alternating service queue

TL;DR

This paper analyzes a model of an alternating service queue, deriving explicit formulas for its time-dependent waiting times, correlations, and cycle length distribution, and compares these results to Lindley's recursion.

Contribution

It provides the first explicit expressions for the time-dependent behavior of an alternating service queue modeled by a Lindley-type equation.

Findings

Explicit formulas for waiting-time distribution over time

Correlation between consecutive waiting times derived

Distribution of cycle length obtained

Abstract

We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit expressions for its time-dependent waiting-time distribution, the correlation between waiting times, and the distribution of the cycle length. Since our model is closely related to Lindley's recursion, we compare our results to those derived for Lindley's recursion.