A system and method for minimizing latency for direct group communications, such as push-to-talk (PTT) calls, among a group of wireless telecommunication devices on a wireless telecommunication network. The wireless telecommunication device selectively requests and then receives an open dedicated broadcast channel for an outgoing communication, which can include a group communication stream to a communication server that receives and creates a group communication to all wireless telecommunication devices of the designated group. The wireless telecommunication device selectively receives a broadcast channel based upon a predetermined probability, and assigns a greater probability of receiving an open broadcast channel for requests to transmit group communication streams than for requests to open a broadcast channel that are not for a group communication.