Stationary characteristics of $M/G/2/\infty$ queue with identical servers, LIFO service, and resampling policy

Consideration is given to the $M/G/2/\infty$ queue with identical servers, LIFO (last in, first out) service discipline and one special case of the generalized probabilistic priority policy called resampling. The latter implies that a customer arriving to the nonidle system assigns independently new remaining service time to each customer currently in service. The new customer itself either enters a free server, if there is any, or occupies a place in the queue. Remaining service times are assumed to be independent identically distributed random variables with the known general absolute continuous distribution. Under the assumption that the stationary regime exists, the main performance characteristics of the system, including the joint stationary distribution of the total number of customers in the system and the remaining service times of customers in service, are derived.