Instability of LRTF multiclass queueing networks

Abstract

We provide an example of a strictly subcritical multiclass queueing network which is unstable under the longest remaining time first (LRTF) service discipline. It is a reentrant line with two servers and four customer classes, Poisson arrivals and deterministic service times. Our instability proof can be generalized to a class of light-tailed stochastic model primitives, including independent, identically distributed exponential service times. A similar example of an unstable deterministic, strictly subcritical LRTF network is also given. Our arguments work for any service discipline such that there are no departures from any network station during its busy period.