Random packing of an interval

At each stage of the packing of a closed interval K , a random number of random open intervals (the packing objects) are placed in that part of K which is as yet unoccupied. No overlapping between the packing objects is allowed. The packing prescription is such that the packing process terminates after at most a finite number of stages. Attention is focused on the final configuration, K = K – + G , where G is a random open subset of K , and is that part of K which is eventually occupied by packing objects, while K – , a random closed subset of K , is that part of K which remains unoccupied.