Chapter 14 Asynchronous Network Model by Mikhail Nesterenko “Distributed Algorithms” by Nancy A. Lynch

Outline processes channels –reliable –with failures send/receive system broadcast system multicast system

Processes system consists of an N-node directed graph G=(V,E), each node has in-neighbors and out-neighbors a process P i is associated with every node – modeled as an arbitrary I/O automaton with the following restrictions: –a process communicates with an external user through input and output actions (“user interface”) –outputs send(m) i,j where j is an out-neighbor, inputs receive(m) j,i –faults: stopping – stop i input actions that permanently disables all tasks of P i Byzantine – replaces P i with an I/O automaton with the same external interface

Channels is associated with every directed edge of the graph external interface: send(m) i,j, receive(m) i,j channel is usually specified using mixed strategy –safety properties are given as an automaton –liveness properties – using special liveness axioms complete channel – traces of the basic automaton satisfying liveness axioms in general the channel I/O automaton can be arbitrary specific kinds of interest –reliable FIFO channel – defined in Chapter 8 (called universal reliable FIFO channel) –reliable reordering channel –channel with failures

Reliable Reordering Channel liveness defined using the following axiom If at any point in  and for any m  M we have m  in-transit, then at some later point in , a receive(m) event occurs allows delivery of all messages exactly once but does not preserve order mixed strategy –safety defined using the automaton

Channels with Failures failures considered – message loss and duplication infinite number of failures – no liveness guarantees (cf. all messages are lost) restrictions on failures –strong loss limitation – if there are infinitely many sends of a certain message then there are infinitely many receives of this message –weak loss limitation – if there are infinitely many sends then there infinitely many receives –finite duplication – each message is duplicated only finitely many times channel types –lossy FIFO channel: reliable FIFO + channel loss + one of the loss limitations –lossy reordering channel: reliable reordering + channel loss + duplication + loss and finite duplication limitations

Properties of Asynchronous Send/Receive Systems partial order defined on events: event  depends on preceding event  if  and  are on the same process  is the receive and  is the send of the same message  and  are transitively related by rules 1. and 2. 1 in the sense discussed in Chapter 8

Complexity Measures communication complexity – number of messages that was sent or received (or number of bits per message) time complexity –l – upper bond on time between successive chances for each task (of each process) to perform a step –for universal reliable FIFO channel: d – upper bound of delivery time of the oldest message sometimes – the bound on the delivery time of each message (what’s the difference?) time bound can be extended to other channel types

Broadcast Systems consists of a set of processes and a single broadcast channel processes – each process output bcast(m) and input receive(m) j,i only one type of broadcast channel is considered – universal reliable broadcast channel delivers every message to every process (including the sender) in FIFO order for each particular pair of processes –there is a separate “channel” (queue) between each pair of processes reliable broadcast system has reordering of events property similar to send/receive system complexity –communication – either number of broadcasts or receives –time – same as for send/receive systems

Multicast Systems more general than broadcast and send/receive system allows to send a (single) message to a subset of processes in the system mcast(m) i,I – send a message from process P i to a subset of processes I consists of a set of processes and a single multicast channel reliable multicast channel delivers every message to every process (including the sender) in FIFO order for each particular pair of processes (separate queue for each pair) –special case – multicast where only broadcast+point-to-point (unicast) communication allowed and FIFO preserved