Busy period, virtual waiting time and number of customers in Gδ∣Mϰ∣1∣B system

In this article, we determine the integral transforms of several two-boundary functionals for a difference of a compound Poisson process and a compound renewal process. Another part of the article is devoted to studying the above-mentioned process reflected at its infimum. We use the results obtained to study a G ^δ ∣M ^ϰ ∣1∣B system with batch arrivals and finite buffer in the case when δ˜ge(λ). We derive the distributions of the main characteristics of the queuing system, such as the busy period, the time of the first loss of a customer, the number of customers in the system, the virtual waiting time in transient and stationary regimes. The advantage is that these results are given in a closed form, namely, in terms of the resolvent sequences of the process.