Delay models for contention trees in closed populations

In this paper we consider some models for contention resolution in cable networks, in case the contention pertains to requests from a finite population of stations and is carried out by means of contention trees. More specifically, we study a number of variants of the standard machine repair model, that differ in the service order at the repair facility. Considered service orders are first come first served, random order of service, and gated random order of service. For these variants, we study the sojourn time at the repair facility. In the case of the free access protocol for contention trees, the first two moments of the access delay in contention are accurately represented by those of the sojourn time at the repair facility under random order of service. In the case of the blocked access protocol, gated random order of service is shown to be more appropriate.