$M\mathrm{\mid }G\mathrm{\mid }\mathrm{\infty }$ Queue Busy Cycle Renewal Function

We present formulas to compute the busy cycle renewal function for the $M\mathrm{\mid }G\mathrm{\mid }\mathrm{\infty }$ queue and exemplify for some service time distributions. The busy cycle renewal function value in t is the number of busy periods that begin in the interval from 0 till $t$. This number is of crucial importance in practical applications of $M\mathrm{\mid }G\mathrm{\mid }\mathrm{\infty }$ queue.