Stationary waiting time in a queueing system with inverse service order and generalized probabilistic priority

The paper considers a single-server queueing system with a buffer of infinite capacity. Customers arrive according to a Poisson process. Service discipline is LIFO (Last In, First Out) with generalized probabilistic priority. It is assumed that at any instant, the remaining service time of each customer present in the system is known. Upon arrival of a new customer, its service time is compared with the remaining service time of the customer in service. As a result of the comparison, one of the following occurs: both customers leave the system; one customer leaves the system and the other occupies the server; and both customers stay in the system (one of the two occupies the server). These actions are governed by probabilistic functions. Whenever a customer remains in the system, it acquires a new (random) service time. The paper proposes the methods for calculating customer's sojourn time distribution and busy period (in terms of Laplace–Stieltjes transform) and several performance characteristics.