Queuing system with negative customers, bunker and phase-type service time distribution

Consideration is given to queueing system with Poisson flows of ordinary and negative customers. Ordinary customer upon arrival occupies one place in a buffer. Negative customer upon arrival knocks out one ordinary customer from buffer into another queue (bunker) and leaves the system. If at the moment of negative customer's arrival buffer is empty, it leaves the system without causing any impact on it. After service completion customer from buffer goes to server and only if buffer is empty then the customer from bunker enters server. Service times of customers from both buffer and bunker have phase-type distribution of order g<infinity. Joint stationary probability distribution of number of customers in buffer, bunker and service phase is obtained for each of three cases: when capacities of buffer and bunker are both finite, when capacity of buffer is finite and of bunker is infinite, and vice versa.