A Specific $M\mathrm{\mid }G\mathrm{\mid }\mathrm{\infty }$ Queue System Busy Period and Busy Cycle Distributions and Parameters

Solving a Riccati equation, induced by the study of the transient behaviour of the MGInf queue system, a collection of service times distributions is determined. For the MGInf queue, which service time distribution is a member of that collection, the busy period and busy cycle probabilistic studies are performed. In extra, the properties of that distributions collection are deduced and presented.