Explicit formulae and convergence rate for the system M α /G/1/N as N→∞

The paper deals with the system M ^α /G/1/N with a finite number of waiting places in which arrivals can occur in a group. The number of customers in the line and the virtual waiting time are studied both in the transient and in the stationary regime. Special attention is paid to the stationary distributions of these functionals as N→∞. The number of customers lost during a busy period is considered as well.