Repeated random insertion into a priority queue
The average cost of inserting n elements into an initially empty heap is analyzed, under the assumption that the n! orders in which the n elements can be inserted are equally likely. It is proved that this average, expressed in number of exchanges per insertion, is bounded by a constant about 1.7645. © 1985.
Journal of Algorithms
Bollobás, B., & Simon, I. (1985). Repeated random insertion into a priority queue. Journal of Algorithms, 6 (4), 466-477. https://doi.org/10.1016/0196-6774(85)90028-8