In this paper we consider the two-user broadcast channel with security constraints. We assume that one of the receivers has a secrecy constraint; i.e., its packets need to be kept secret from the other receiver. The receiver with secrecy constraint has full-duplex capability to transmit a jamming signal to increase its secrecy. We derive the average delay per packet and provide simulation and numerical results, where we compare different performance metrics for the cases when the legitimate receiver performs successive decoding and when both receivers treat interference as noise.