In the polling mode in IEEE 802.16d/e, one of three modes: unicast, multicast and broadcast pollings, is used to reserve bandwidth for data transmission. In the unicast polling, the BS polls each individual MS to allow to transmit a bandwidth request packet, while in the multicast and broadcast pollings, the truncated binary exponential backoff (TBEB) mechanism is adopted as a contention resolution among mobile stations (MSs) in a multicast or broadcast group. This paper investigates the delay of bandwidth requests in the unicast, multicast and broadcast pollings, by deriving the delay distribution of the unicast polling and the TBEB by means of analytical methods. We consider an error-free channel as well as an error-prone channel with i.i.d. constant packet error rate per frame. Furthermore, we find the utilization of transmission opportunity to see efficiency of the bandwidth in the TBEB. Performance evaluations are provided to show that analytical results are wellmatched with simulations. By the numerical results, we can find the optimal parameters such as the initial backoff window size of the TBEB and the number of transmission opportunities (or slots) satisfying quality of service (QoS) requirement on delay and loss, and thus we can determine which scheme is better than others depending on the probability of a request arrival during one frame. Numerical examples address that the TBEB performs better than the unicast polling for light traffic loads and vice versa for heavy traffic loads. Also, it is shown that the multicast polling has better performance than the broadcast polling in the sense of shorter delay, lower loss probability and higher utilization of transmission opportunity.