If others jump to the queue front, how long I will wait?

TL;DR

This paper models waiting times in queues considering the impact of intruders who jump ahead, highlighting the importance of contextual inference due to limited observational data.

Contribution

It introduces two queue models that incorporate intruder behavior, emphasizing the need for inference from context when data is scarce.

Findings

Intruder jumps significantly increase expected waiting times.

Contextual inference can improve wait time estimations.

Limited data makes direct evaluation challenging.

Abstract

Two models of a queue are proposed: a human queue and two lines of vehicles before a narrowing. In both models, a queuer tries to evaluate his waiting time, taking into account the delay caused by intruders who jump to the queue front. As the collected statistics of such events is very limited, the evaluation can give very long times. The results provide an example, when direct observations should be supplemented by an inference from the context.