Today, we witness an explosion in wireless networks that are accessed by high-performance mobile devices running a wide variety of demanding applications. The IEEE 802.11ad is a standard targeted at meeting these design requirements. Analytical modeling and performance evaluation is a crucial step needed for the evolution of any standard. In this paper, we model the service periods (SPs) of the IEEE 802.11ad hybrid medium access control as a special case of periodically gated queueing system (PGQS) with Bernoulli scheduling. We first state and prove some basic theorems related to the probability generating functions of the PGQS. Using these results, we derive the average delay and the delay variations (jitter) of packets belonging to SP of IEEE 802.11ad. We show that as the arrival rates increases, the delay increases linearly until the critical arrival rate, and beyond that, it becomes unbounded. Further, a practical scheme for the admission control mechanism of 802.11ad is also presented. To validate the model, analytical results are compared with simulation results. © 2019 John Wiley & Sons, Ltd.