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The discrete-time queueing system with inversive service order and probabilistic priority

This paper considers a queueing system Geo/G/1/∞ with inversive service order and probabilistic priority that is determined as follows. Upon arrival into the system of a new customer its length i is compared with the (remaining) length j of the customer in the device and with the probability of d(i, j), which depends only on i and j, a new arrival will occupy the server while pushing out a servicing customer to the first place in the queue, and with the supplemental probability d(i, j) = 1 - d(i, j), alternatively, a customer that was under service keeps on being served while the newly arrived one occupies the first position in the queue. The remaining queue shifts by one state. The main stationary characteristics of such system's behavior have been found.