In this paper, we derive the probability density function and cumulative distribution function of packet transmission time in a spectrum sharing system. In combination with the time-out characteristics of packets, we further study the outage probability and average transmission time under peak power interference constraint over Nakagami-m fading channel. Especially, we employ the M/G/1 queuing model to calculate the average waiting time of packets and average number of packets waiting in the queue of a secondary user. The numerical results show the importance of the peak interference power constraint on the delay of packets at the secondary user.