The availability of peer-to-peer and other distributed systems depends not only on the system architecture but also on the availability characteristics of the hosts participating in the system. This paper constructs a model of remote host availability, derived from measurement studies of four host populations. It argues that hosts are incompletely partitioned into two behavioral classes, one in which they are cycled on/off periodically and one in which they are nominally kept on constantly. Within a class, logarithmic availability generally follows a uniform distribution; however, the underlying reason for this is not readily apparent.