Modeling and study a general vacation queuing system with impatience customers

TL;DR

This paper models a general vacation queueing system with impatient customers, providing conditions for stationarity, solving integral equations for Poisson arrivals, and analyzing the tail behavior of waiting times.

Contribution

It introduces a comprehensive model for vacation queues with impatience, deriving new conditions and solutions for the stationary workload and waiting time distributions.

Findings

Stationary workload existence condition established.

Integral equation solved for Poisson arrivals.

Relationship between waiting time tail and service time tail derived.

Abstract

In this paper we models and studies a general vacation queueing model with impatient customers. We first propose a sufficient condition for the existence of the stationary workload process. We then give an integral equation for the independent and identically distributed case. This integral equation is solved when customers arrive according to a Poisson Point process. A relationship between the tail of the waiting time distribution and the tail of service distribution is also given.