Stationary waiting time distribution in queueing system with negative customers and bunker for ousted customers under FIRST–FIFO–FIFO service discipline

Consideration is given to the single server queueing system with Poisson input flows of ordinary and negative customers. An arriving ordinary customer occupies one place in an infinite buffer. Negative customer upon arrival pushes out one ordinary customer from the queue in the buffer to another queue (bunker) and leaves the system. Customers from bunker are served with relative priority. Service times of customers from buffer and bunker are both exponentially distributed but with different rates. It is assumed that negative customer always pushes out the first customer in the queue in the buffer and after service completion the first customer in the queue in the buffer enters server or, if buffer is empty, the first customer in the queue in the bunker. Stationary waiting time distribution of an arriving ordinary customer in terms of Laplace–Stieltjes transform is obtained.