We present an analytical model for the access during the Service Periods (SP) of the IEEE 802.11ad Hybrid Medium Access Control protocol. As a performance measure of this protocol, we derive the worst case and average delay faced by the SP packets. We show that as the arrival rate of the SP packets increases, the delay increases linearly till a point, beyond which it grows exponentially. Further, we extend the model to variable length of beacon interval, and random allocation of SPs to the nodes. We show how a network designer can do optimal allocation of the SP and the CBAP duration to achieve a tradeoff between SP delay and CBAP throughput. We further extend our analysis for the case of heterogeneous system. Our analytical results are compared with simulation and the results show a good match. © 2015 IEEE.