Instability of LAS multiclass queueing networks

We provide an example of a strictly subcritical multiclass queueing network which is unstable under the least attained service (LAS) service protocol. It is a reentrant line with two servers and six customer classes. The customer interarrival times in our system are bounded below and have finite exponential moments, while the corresponding service times are deterministic. As a special case, we obtain a deterministic, strictly subcritical unstable LAS network.