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

Consideration is given to $M|G|1$ type queueing system. Inverse service order with generalized probabilistic priority is implemented in the system. It is assumed that at any instant, the remaining service time of each customer residing in the system is known. Upon arrival of a new customer, the system finds out its service time and compares it with the remaining service time of the currently served customer. The result of this comparison leads to one of the cases: one of them enters the server and another occupies the first place in the queue; one of them leaves the system and another enters the server; or both leave the system. In each case when customer remains in the system, its remaining service time may be updated. An analytical method that allows computing stationary performance characteristics related to the number of customers in the system is presented. Numerical examples based on the developed mathematical relations are provided.