Cognitive radio networks emerge as a promising solution for overcoming shortage and inefficient use of bandwidth resources by allowing secondary users (SUs) to access the primary users' (PUs) channel so long as they do not interfere with them. The dynamical spectrum availability makes SU's packet average delay one of the most important performance measures of a cognitive network. It is important to understand the nature of delay, as well as its dependence on PU behaviors. In this paper, we analytically model and analyze the dynamics of the spectrum availability and their impact on the SU's packet delay. The cognitive network is modeled as a discrete‐time queueing system. PU channel occupancy is modeled as a two‐state Markov chain. Our contribution in this paper is defining and characterizing the properties of the random process that describes the availability of the opportunistic resources. In addition, we apply the mean residual service time concept to achieve an analytical solution for the queueing delay. Moreover, inspired by the slotted Aloha system, we model the packet service mechanism and determine the manner in which it depends on the resource availability. The delay becomes unbounded if the spectrum availability dynamics are not carefully considered in network design. Copyright © 2015 John Wiley & Sons, Ltd.