To achieve these goals three time out periods are defined when heart beat sending is required. Additionally, we define an interval to model the latency in the underlying transport. These should be defined to cover common cases (e.g. 95th-percentile):
* ACK_GRACE_INTERVAL: When <math>\Pi^S_i</math> a receives a non-empty message it needs to inform the group about the transcript update no later than ACK_GRACE_INTERVAL time. Therefore if <math>\Pi^S_i</math> f <math>U_i</math> does not send a message ACK_GRACE_INTERVAL seconds after receiving a non empty message,<math>\Pi^S_i</math> will send a heartbeat.
* REKEY_GRACE_INTERVAL, to ensure in session forward secrecy, the protocolrequires that each <math>U_i</math> updates their DH ephemeral key as well as group key. After a session is established or it was rekeyed, each<math>\Pi^S_i</math> needs to send its new DH ephemeral key no later thanREKEY_GRACE_INTERVAL. Therefore if <math>\Pi^S_i</math> has not sent any message by thatperiod of time, it issues an empty message. Similarly after receivingall ephemeral keys from all participants, <math>\Pi^S_i</math> needs to send itssecret for computation of new key no later than REKEY_GRACE_INTERVAL.
* BROADCAST_LATENCY: Modelling the amount of time which a message takes to reach the server and broadcast to the other clients. It should be based on the transport considered.