Stationary characteristics of discrete-time $\mathrm{Geo}/G/1/\infty$ queue with batch arrivals and one queue skipping policy

Consideration is given to the discrete-time single-server system with one queue of infinite capacity and the geometric (Bernoulli) input flow. Customers are homogeneous, arrive in batches, and are served one by one in FIFO (first in, first out) manner. The sizes of arriving batches as well as the service times are assumed to be independent and identically distributed random variables with arbitrary discrete distributions. The queue skipping policy is implemented in the system: upon arrival of a batch, its size is compared with the current total number of customers in the system. If the size of the batch is larger than the system content, all customers residing in the system (including the one in server) are lost and the arrived batch enters the system; otherwise, the new batch leaves the system having no effect on it. Main stationary system performance characteristics, including those of the flow of lost customers, are obtained.