In this paper, an NxN input-buffered crosspoint packet switch which selects a Head of the Line, HOL, packet in contention randomly is analyzed with a new approach. The approach is based on both a Markov chain representation of the input buffer and the probability that a HOL packet is successfully served. The probability as a function of N is derived, and it makes it possible to express the average packet delay and the average number of packets in the buffer as a function of N. The contention resolution policy based on the occupancy of the input buffer is also presented and analyzed with this same approach and the relationship between two selection policies is analyzed in terms of the occupancy of the input buffer.