  This paper develops a detailed quantitative model which uses the Drake
equation and an assumption of an average maximum radio broadcasting distance by
an communicative civilization to derive a minimum civilization density for
contact between two civilizations to be probable in a given volume of space
under certain conditions, the amount of time it would take for a first contact,
and whether reciprocal contact is possible. Results show that under certain
assumptions, a galaxy can be teeming with civilizations yet not have a
guarantee of communication between any of them given either short lifetimes or
small maximum distances for communication.
