A discrete‐time queueing system with optional LCFS discipline

We consider a discrete‐time queueing system in which the arriving customers decide with a certain probability to be served under a LCFS‐PR discipline and with complementary probability to join the queue. The arrivals are assumed to be geometrical and the service times are arbitrarily distributed. The service times of the expelled customers are independent of their previous ones. We carry out an extensive analysis of the system developing recursive formulae and generating functions for the steady‐state distribution of the number of customers in the system and obtaining also recursive formulae and generating functions for the stationary distribution of the busy period and sojourn time as well as some performance measures.