A Queueing System with Negative Claims, InfiniteBuffer and Finite Bunker for Superseded Claims

Study is performed of the queuing system with Poisson incoming flows of ordinary and negative claims. For ordinary claims, there is an infinite-capacity buffer. The arriving negative claim knocks out an ordinary claim queued in the buffer and moves it to a finite-capacity buffer of superseded claims (bunker). If upon the knock out of the ordinary claim bunker is full, knocked out claim is lost. If the buffer is empty, then the negative claim discharges the system without affecting it. After servicing the current claim, the server receives a claim from the buffer or, if the buffer is empty, the bunker. The claims arriving from both the buffer and bunker are served exponentially with the same parameter.
Expressions for the stationary joint probability distribution of number of claims in buffer and bunker and for main probabilistic characteristics of the system were obtained.

queueing system, negative claim, bunker