Fundamental probability characteristics of the queueing system \(\text{G}^{\kappa}|\text{G}|1\) (Q2755163)

This article deals with different probability characteristics of the queueing system \(\text{G}^{\kappa}|\text{G}|1\) with a group inflow of requests. Under the condition that the queueing system begins its evolution from the canonical initial state (a group of requests of random volume \(\kappa\) enters the free system at the initial time \(t=0\)) the authors obtain the distribution of the main characteristics of the queueing system \(\text{G}^{\kappa}|\text{G}|1\) such as: the length of queue in the transition and stationary regimes of functioning of the system; the number of requests serving by the system on the interval \([0,t]\), including a request on the serving device at time \(t\); the number of requests entered in the queueing system on the interval \([0,t]\); the virtual waiting time for service for the first request of a group, entered in the queueing system at time \(t\geq 0\); the entering flow of requests and outgoing flow of queueing requests; the ~total down time of the system on the interval \([0,t]\).