Research Article
Virtual Net: A Decentralized Architecture for Interaction in Mobile Virtual Worlds
| | Notations | Descriptions |
| | ri | Replica i |
| | rL | Group leader |
| | rc | Group leader candidate |
| | G | The set of group members |
| | R | The set of live replicas |
| | S | The set of senders |
| | epoch | The epoch number based on leader change |
| | cid | Configuration ID |
| | age | Age of a replica |
| | c | Cycle number c |
| | ∆t | Cycle length |
| | E / E(c) | The decided events / Decided events of c |
| | Qd | Delivery queue, containing the sorted events to be delivered to the application in sequence |
| | Qr | The received events |
| | Qp | The temporary buffer for event collection |
| | s | Sender s∈S |
| | Index(s) | The index of s in S sorted by sender ID |
| | Seq(e) | The sequence number of event e |
| | Sender(e) | The sender of event e |
| | e | Event e, in format of (Sender(e), Seq(e), Payload(e)) where Payload(e) denotes the payload of the event |
| | Seq(s, c) | The event sequence number of c from s |
| | e(s, j) | The event e of sequence number j from s. |
| | MinSeq(s, c) | The lowest sequence number of all undelivered events from s in c |
| | MaxSeq(s, c) | The sequence number of the last delivered non-empty event from s in c |
| | Consensus(c) | Return true if there is a consensus on the fly for c |
| | P | The set of cycles waiting consensus |
| | Z | The set of cycles in consensus |
| | LE | The flag of leader election |
| | GE | The flag of group reconfiguration |
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