cpsc 689: discrete algorithms for mobile and wireless systems

CPSC 689: Discrete Algorithms for Mobile and Wireless Systems

Spring 2009

Prof. Jennifer Welch

Discrete Algs for Mobile Wireless Sys 2

Lecture 30 Topic:

Virtual Node Layers Sources:

Dolev, Gilbert, Lynch, Shvartsman, Welch. Geoquorums. Dolev, Gilbert, Lynch, Schiller, Shvartsman, Welch. Virtual Mobile Nodes. Chockler, Gilbert. Virtual Infrastructure for collision-prone wireless networks. Gilbert PhD thesis. Virtual Infrastructure for wireless ad hoc networks. Brown, Gilbert, Lynch, Newport, Nolte, Spindel. The Virtual Node Layer: A

programming abstraction for wireless sensor networks. Dolev, Gilbert, Lahiani, Lynch, Nolte. Timed virtual stationary automata. Dolev, Lahiani, Lynch, Nolte. Self-stabilizing mobile node location

management and message routing. Gilbert, Lynch, Mitra, Nolte. Self-stabilizing mobile robot formations with

virtual nodes. Nolte PhD thesis. Virtual stationary automata for mobile networks. MIT 6.885 Fall 2008 slides


Overview Platform: Mobile computers with sensors, actuators, wireless

communication. People, robots, vehicles, could use this hardware to:

Establish ad hoc networks. Coordinate in running applications:

Collect and process data Produce models of the environment Plan activities, disseminate plans

Examples: Rescue workers in disaster areas Soldiers in battle Robots exploring a novel location Cars on highway

But application design for MANETs is very hard, because the networks change unpredictably.


To simplify application design: Virtual Node Layer, consisting of:

Virtual Nodes, Client Nodes, and A Local Broadcast service.

Virtual Nodes: Simple abstract machines. Better behaved than physical nodes,

e.g., stationary, fail less often. Fail by stopping, recover by restarting

in initial state. Client Nodes similar to physical nodes. Makes it easier to write applications.

Application

Virtual Node Layer


Virtual Node Layer


Virtual Node layer


Route message to a designated geographical

region

Geographical routing (Geocast)


Gather, aggregate,

analyze, and distribute data.

Data management


Coordinate activities of robots, people, vehicles

in a region.

Region coordination


Geoquorums

Goal: Implement atomic Read/Write memory in MANETs.

Read Write


Geoquorums Uses a Virtual Object Layer:

Passive Virtual Objects, at fixed, normally-populated geographical locations.

Client Nodes, which can access the VOs directly.

Emulate the VO Layer over the MANET, using Replicated State Machine algorithm and a standard geographical routing algorithm.

Implement Read/Write memory over the VO layer, using a quorum-based algorithm.

Atomic Memory

Virtual Object Layer


Virtual Mobile Nodes

New kind of Virtual Node: Active agent, not just a passive object. Moves according to a pre-planned trajectory.

Applications: Pick up, deliver messages. Highway control: VMN can

notify cars about hazards ahead, ambulance approach from behind.


An ambulance is coming.Get out of the left lane.

Traffic jam ahead. Slow down.Consider another route.

High Tech Highway


Emulating Virtual Mobile Nodes

Replicated State Machines. Similar to emulation of Virtual Objects. It’s all relative:

is the same as:


Virtual Stationary Nodes

Simplest and most important special case of Virtual Mobile Nodes---no motion!

New VSN model, with more control over timing. Leader-based implementation. Self-stabilizing.


Application: Point-to-point message routing in MANETs

Geographical routing over VSN layer. Mobile client location service.

Keeps track of locations of Client Nodes. Each Client Node has home location VSNs, which keep

track of its current VN region. Determined by hash function from Client Node id.

Client Node sends its physical location to its home locations, using geographical routing.

Requester sends location queries to home locations, also using geographical routing.

Point-to-point message routing between Client Nodes. Based on geographical routing and location service.


Application: Motion Coordination

Use VSNs to coordinate motion of Client Nodes: VSN can gather, analyze information about its local

region, exchange information with neighboring VSNs, plan motion of CNs.

CNs can use advice from nearby VSNs to determine their motion.

Examples: Robot motion coordination Highway control, using computers on board the cars. Air-traffic control


Robot Motion Coordination

Given a curve, and a set of Client Nodes (robots) at arbitrary locations, move the Client Nodes so that they are (nearly) all on the curve, and (approximately) evenly spaced.

E.g., perimeter of hazardous waste area.


VN

VN

VN

VN

VN

VN

Virtual Node Approach Divide region into zones, one VN per zone. VN coordinates Client Nodes in its zone. Directs motion of CNs in its zone:

Towards the curve. On the curve, to even out spacing.

Communicates with neighboring VNs, sends “extra” clients to neighboring zones.

CN

CN


Virtual Traffic Light (VTL)

For an intersection without a real traffic light.

Computers in cars can emulate a VN, programmed to be a traffic light.

Any policy desired, e.g., 30 sec in each direction.

Cars just see “red” or “green”, on local displays.

VTL dies when no cars are around. But then we don’t need a traffic

light.


Virtual Air-Traffic Controllers (VATCs)

Aircraft in regions of airspace without ground-based controllers, e.g., the ocean.

Need algorithm for arbitrating access to regions.

Use VATCs, emulated by computers on the aircraft.

VATC behaves like human ATC, e.g.: Keeps track of aircraft in local region. Tells neighboring ATCs when it’s OK to

hand off an aircraft. Tells aircraft how to move within the local

region. VATCs compatible with current ATC system.


Virtual Node Layers in Unreliable MANETs

Nice theoretical results…but: They all assume reliable communication. Real MANETs have lost messages, collisions:

How to cope with message losses? Three approaches:

1. Mask communication failures, using Contention Manager, Collision Detector services.

2. Implement VNs that have weaker semantics.3. Self-stabilization.


1. Masking Communication Failures

Contention Manager: Gives “active/passive” advice to each node, at each round. Eventually, advises one node per round to be “active”. Implemented by backoff protocols.

Collision Detector: Notifies receiver that it might have missed a message, because of a

collision (). Completeness: Situations when must be delivered.

When some message is lost, or When half or more are lost, or When a majority are lost, or When all are lost.

Accuracy: Situations when may be delivered. Accurate: When some message is lost, or Eventually Accurate


Virtual Node Layers for Networks with Message Losses

Mobile network model: Message collisions, losses Contention manager Collision detector

New algorithm to emulate VN layer over unreliable MANET layer.

Uses consensus-like strategy. Application: Tracking


2. Weaker Semantics A simple reactive VN layer

Simple timing-independent state machines, which react to the arrival of a message by changing state and producing some new messages to send.

With message losses, VNs have an additional failure mode: Can jump to some other “sensible” state---one

that would result from receiving some subset of the messages that have been sent.


3. Self-Stabilization Mobile networks are subject to unpredictable failures,

changes. Try as we might to mask problems, sometimes, things will

go wrong. Self-Stabilization: No matter what state the system winds

up in, it will gravitate back (quickly) to normal behavior. A standard notion for traditional distributed algorithms:

[Dijkstra’s famous paper, 74] [Dolev’s book, 00]


Self-Stabilizing Algorithms for Mobile Networks

Problems for which Lynch's group has SS solutions using VN layers: Communication:

Geographical broadcast: Broadcast a message to everyone in the vicinity of a specified geographic location.

Point-to-point message communication: Allow clients to send messages to nodes with specified ids, wherever they are in the network.

Robot motion coordination: Arrange robots along a known curve in the 2-

dimensional plane, approximately evenly spaced.

[Tina Nolte PhD thesis, completed October, 2008]


Some Details

Geoquorums [Dolev, Gilbert, Lynch, Shvartsman, Welch 03,

04] [Gilbert PhD thesis 07]


GeoQuorums

Virtual Object layer definition Client Nodes Virtual Object automata CNs invoke operations on

Virtual Objects from anywhere in the network, receive responses.

No other communication mechanism

Emulation algorithm


Virtual Object Layer Definition Client Nodes

(Untimed) I/O automata Move arbitrarily Fail/recover Frequent geo-updates:

Real time Current location

Unique identifiers Have outputs that are invocations of operations on the

VOs, inputs that are responses. Virtual Object automata


Virtual Object Layer Definition

Client Nodes Virtual Object automata

Atomic Object I/O Automata: Internal copy of object data

+ input buffers for requests + output buffers for responses.

[Lynch, Distributed Algorithms, Chapter 13]

Fail/recover. Associated with

predetermined locations in space.


Virtual Object Layer Emulation Physical network

assumptions: Physical mobile nodes

(Untimed) I/O automata Move arbitrarily,

fail/recoverGeo-updates: time,

location.Unique identifiers

Communication: Reliable local broadcast service, within each VO region.


Summary: Geoquorums VO Layer consists of Client Nodes + Virtual Objects, where

any client can access any object. Provides relatively stable, persistent data objects, in badly-

behaved mobile network.

Assumes Physical Layer, just Physical Nodes + reliable local broadcast.

Emulation uses: Standard GeoCast algorithm. A highly redundant replicated state machine strategy to

emulate each VO. Depends on reliability of local broadcast.


Some More Details

Virtual Stationary Nodes [Gilbert PhD thesis 07] [Dolev, Gilbert, Lynch, Schiller, Shvartsman,

Welch 04]


Virtual Stationary Nodes

VSN Layer definition Client Nodes VSN automata Local broadcast communication

Differences from VO Layer: VSNs are active agents, not just

passive objects. Broadcast communication, not

invocation/response. Local communication only.


VSN Layer Definition

Client Nodes: Essentially as before (Untimed) I/O automata Move arbitrarily Fail/recover Geo-updates Unique identifiers

VSN automata: Active agents, not passive objects (Untimed) I/O automata Associated with predetermined locations in space. Fail/recover Geo-updates (time) Unique identifiers

Local broadcast communication service VCast: CN to nearby CNs VN to/from CNs in its region. VN to neighboring VNs.


VSN Layer Emulation Physical network

assumptions: As before. Physical mobile nodes

(Untimed) I/O automata Move arbitrarily,

fail/recoverGeo-updatesUnique identifiers

Communication: Reliable local broadcast service, within each VSN region.


Summary: VSN Layers VSN Layer: Client Nodes + Virtual Stationary Nodes +

local broadcast communication service. Provides a relatively stable, reliable, static overlay network. Many applications.

Physical Layer: Physical Nodes + reliable local broadcast. Emulation uses highly redundant replicated state machine

strategy to emulate each VSN. Depends on reliability of local broadcast.


Some More Details

Virtual Mobile Nodes [Gilbert PhD thesis 07] [Dolev, Gilbert, Lynch, Schiller, Shvartsman,

Welch 04]


Virtual Mobile Nodes

VMN Layer definition Client Nodes VMN automata Local broadcast communication

Main difference from VSN Layer: The VMNs move, according to predetermined, globally

known trajectories.


VMN Layer Definition

Client Nodes: As for VSN Layer VMN automata: Active agents

(Untimed) I/O automata Associated with predetermined trajectories in space. Fail/recover Geo-updates Unique identifiers

Local broadcast communication service VCast: CN to nearby CNs VMN to/from nearby CNs VMN to nearby VMNs.


Virtual Mobile Node (VMN) Notion of a virtual node

Can perform general computation Moves in a controllable pattern, e.g.

Sweep the plane in a regular pattern Pseudorandom walk

Implement on top of physical nodes that move in unpredictable/uncontrollable ways

How? A VMN is replicated at a set of physical nodes that changes as the nodes move in and out of the VMN’s path.


Physical Network Assumptions

Physical mobile nodes (Untimed) I/O automata Move arbitrarily,

fail/recover Geo-updates Unique identifiers

Communication: Reliable local broadcast

service.


More on Communication

Physical mobile nodes communicate using a physical broadcast service.

Simplifying assumptions: Every node that remains within distance Rphys

of sender receives the message Upper bound d on delivery time

Strong abstraction of wireless broadcast with a small number of retries.


VMN Abstraction A VMN has some local state (its code is provided

by application designer) A VMN communicates with other entities, called

clients; a client can be a physical mobile node or other VMN

Communication is through a virtual broadcast service, similar to the physical one:

radius Rvirt

Might repeat, reorder msgs even if physical bcast does not


Simple Idea to Simulate a VMN Use an “agent”, a dynamic process that jumps from

physical node to physical node in the direction specified by the VMN path

Generalization of, e.g., Nath & Nicolescu, where moving entity is an arbitrary process instead of a message

Drawback: not robust if current host fails or next part of VMN path is not populated by a physical node.

Our solution: Use replication.


Replicating a VMN Define the mobile point to be circular region of

radius Rmp that moves on the VMN path: at time t, the center of the mobile point is the position of the VMN

Every physical node that is within the mobile point’s current region replicates the state of the VMN and participates in the simulation protocol.

Each participating physical node keeps a copy of the VMN’s state.


Keeping Replicas Consistent Replicas are kept consistent by exchanging

messages concerning the actions to perform on the replicated state using a totally ordered (TO) broadcast service.

Use standard techniques to implement the TO-bcast: Each msg to be TO-sent has a unique timestamp (clock

time, sender id) Timestamped msg is sent using physical bcast After msg is received, it is not eligible to be delivered (by

the TO bcast service) until > d time after it was sent Deliver eligible msgs in timestamp order


Properties of TO-bcast

Assume Rphys > 2*Rmp + d*vmax. Then Msgs are TO-recv’d in the order sent,

breaking ties by sender id. If a physical node in the mobile point TO-

sends a msg, then every physical node that stays in the mobile point sufficiently long receives the message (exactly once).


VMN Simulation Based on Lamport’s replicated state machine

technique (1978), augmented to support joins, leaves, failure, recovery

One VMN simulation process per physical node Collection of simulation processes, physical bcast,

and TO-bcast together will simulate VMN and virtual bcast

Assumption: VMN’s path is fixed and known; thus so is mobile point’s.


Joining the Mobile Point

when physical node enters mobile point’s region: status := joining TO-send join request w/ timestamp when node TO-recv’s its own join request:

status := listening save subsequent msgs TO-recv’d in pending-actions

when an active node TO-recv’s new join request: TO-send response w/ its copy of VMN’s state

when listening node gets response: status := active set its copy of VMN’s state to that in msg start processing pending actions (more later)


While in the Mobile Point

Main task is to manage replica of VMN’s state.What can the VMN do? Receive a message from a client (via virtual bcast

service) TO-send msg to all replicas in mobile point when msg is TO-recv’d, enqueue on pending-actions

Initiate an internal or output action periodically check simulated state against state machine

transitions for VMN to see if an action is enabled. if so, TO-send a msg to all replicas in mobile point saying

to simulate this action. when msg is TO-recv’d, enqueue on pending-actions


While in the Mobile Point (cont’d)

To simulate transitions of the VMN: Periodically dequeue pending-actions If action has not already been simulated:

apply VMN’s transition function to current simulated state and this action

update simulated state if action is to send a msg to a client (and hasn’t

already been sent by another replica): send the msg via the physical bcast service


Leaving the Mobile Point

When physical node leaves the mobile point’s current region:

status := idle reinitialize copy of VMN’s state discard pending actions


Failure & Recovery

What if mobile point’s current region becomes depopulated by physical nodes? Current state of VMN is lost.

If no reponse to join request is received within d time:

Set copy of VMN’s state to failure-recovery state (as specified by designer of VMN)


Relationship between Virtual & Physical Broadcasting

Require Rphys > Rmp + Rvirt + 2*loc-update-interval*vmax When a client sends a msg to the VMN using virtual bcast:

– Client uses physical bcast to send msg to a physical node in the VMN’s mobile point (at time t)

– Physical node in the mobile point TO-sends the msg (by time t+d)

– Each physical node in the mobile point TO-recvs msg (by time t+2d+1)

When VMN sends a msg to a client using virtual bcast– At least one physical node in the mobile point TO-sends VMN’s

intent to do a send– Physical nodes receive and enqueue the message– At least one physical node sends the message via physical

bcast service (duplicates are possible)


Correctness of VMN Simulation

Formal proof uses timed I/O automata model. For each execution E of the simulating system,

show there exists a corresponding execution E’ of the virtual system.

Proof is by induction on the sequence of actions in E.

E

E’

“forward simulation relation”


Applications for VMNs Routing msgs: How to send a message to a specific node?

Would like to avoid tracking locations of all nodes flooding

Adapt idea of Chatzigiannakis et al.: Use a single VMN that repeatedly traverses the network

collecting and delivering msgs. Sender waits for VMN to come nearby and then sends to VMN Receiver waits for VMN to come nearby, then sends request for

any msgs destined for it, which VMN answers Use multiple VMNs to improve latency

Latency and space usage scale with number of VMNs and region size, not number of nodes


Applications for VMNs Routing a msg to a VMN: since VMN paths

are known, a third VMN shuttles between sender and destination VMNs carrying the message.

S D

M


Applications for VMNs Use VMNs to traverse the network and

collect sensor data, process it and answer queries

Differs from routing in that data may be aggregated, both regionally and temporally, as it is being collected


Applications for VMNs

Group communication services Dolev et al. (2002) showed how to

implement group communication services using a single mobile agent that performs a random walk

Use a robust VMN, instead of a fragile token, to collect and deliver group information


Applications for VMNsAtomic read-write memory: GeoQuorums algorithm (Dolev et al. 2003)

implements a virtual shared variable based on fixed-location densely populated regions, which maintain replicas of the data that are manipulated with quorum-based algorithms.

Instead, use VMNs to maintain the replicas of the shared variable: can adapt if densely populated areas move can move nearer to areas of the network that issue many

operations on the shared variable


Discussion

VMN abstraction can ease the task of designing algorithms for MANETs by providing programmable motion some robustness

Drawbacks: depends on a reliable and timely physical communication

service assumes a trusted environment expensive in terms of communication and power

consumption


Open Questions How to optimize for implementation?

Elect a temporary leader in the mobile point which would initiate all transitions on replicas

Keep replica state when leaving mobile point and get incremental updates on rejoining

Relax strong synchrony assumption using partially synchronous bcast algorithms (e.g., Lamport 1998, Bar-Joseph et al. 2002)

Develop a self-stabilizing simulation Determine paths of VMNs on the fly, e.g.,

Track a moving entity Avoid unpopulated areas

Generate new VMNs dynamically, e.g., A new VMN for each entity that enters a geographical area


Summary: VMN Layers

VMN Layer: Client Nodes + Virtual Mobile Nodes + local broadcast communication service.

Physical Layer: Physical Nodes + reliable local broadcast.

Emulation uses highly redundant replicated state machine strategy to emulate each VMN.

Depends on reliability of local broadcast.


Message Losses

All this work so far assumes that message delivery is reliable.

But what if it isn’t? (and in real mobile networks, it isn’t…)


More Details

Masking communication failures, using consensus and collision detectors. [Gilbert PhD thesis 07] [Chockler, Gilbert, Lynch PODC 08]


Masking Communication Failures Unreliable wireless broadcast model:

Synchronous rounds Physical Nodes: mobile, fail/recover, geo-update, identifiers. Local wireless broadcast:

Broadcast: Within radius R. Interference: Up to radius R’.

Message losses, collisions.

Assume additional services: Collision Detector Contention Manager

R R’


Eventual Collision-Freedom Eventually, if only one node in a local area broadcasts in a

round, then its message will be delivered. “Eventually” here replaces a probabilistic assumption.


Collision Detector

Complete: Detects if any message is lost.

Eventually accurate: Eventually no false positives.

Alice

Bob

CD

Bob either:• Gets both messages or• Detects a collision


Contention Manager

Reduces contention/collisions Example: Backoff protocol

Each node contends when it wants to broadcast. Contention manager issues advice to contending nodes:

active: It is safe for the node to broadcast. passive: The node should not broadcast.

Contention Manager Properties: Eventually non-interfering: Eventually, nearby nodes are not

advised to be active. Eventually regionally fair: Eventually, in any region, if some

node contends for sufficiently long, then some contending node is advised to be active for sufficiently long.


Emulating Virtual Infrastructure

Replicated State Machine, for each VN


Emulating a Virtual Node

Each participant is a replica. Replicas execute a

consistency protocol. Leader + backups Leader sends, receives

messages on behalf of the VN.

Join/leave protocol.


Consistency: First Attempt Use a fault-tolerant distributed consensus algorithm. For each virtual round:

Emulating nodes run a consensus algorithm, to agree on: Messages for VN to receive. Message for VN to send. VN state update.

Emulators update their own copies of the VN state. Leader sends message on behalf of the VN.

Problem: Consensus does not terminate until

collisions stop. Leads to unbounded-sized,

unsynchronized virtual rounds.


VN Layer Definition

Client Nodes, Virtual Nodes Communication:

CN-CN, CN-VN, VN-VN VN Layer messages may also be lost. Detect collisions when a message is lost (using VN

Layer Collision Detector). Synchronous rounds

Rounds are constant length

Discrete Algs for Mobile Wireless Sys 76CHAk4

Sequence of instances k1, k2, k3,… For each instance k:

Each node proposes an input. Each node receives a history output h, or .

Convergent History Agreement (CHA)

CHAk4

propose(x)

propose(y)

propose(z)

CHAk1

CHAk2

CHAk3

CHAk5

CHAk6

CHAk7

h1

h2

Discrete Algs for Mobile Wireless Sys 77CHAk4

A history is a sequence of proposals, one per instance, e.g.:

Validity: Each proposal for an instance k that appears in an output history is someone’s actual proposal for instance k.

Agreement: Any two output histories for instances k1 and k2, k1 ≤ k2, share a common k1-prefix.

Liveness: For some k, every output for any instance k’ k is an actual history (not ), in which all the elements for instances k,…k’ are actual proposals (not ).

CHA

CHAk1

CHAk2

CHAk3

CHAk5

CHAk6

CHAk7


Emulating a Series of Virtual Rounds Using CHA

CHA instance k: Proposals are for messages the VN should receive at round k. Returned histories indicate agreed-upon messages for VN to receive at

rounds ≤ k. At round k, each Physical Node i:

Broadcasts any Clienti messages, receives other Client messages. Decides which messages should be received by VN at round k, and

proposes them to CHA instance k. If CHA outputs , PNi doesn’t know what the VN receives, doesn’t emulate

the VN, but emulates Clienti detecting a collision. If CHA outputs a history:

Emulates the VN receiving the messages indicated in the history, through round k.

When appears in the history, emulate the VN receiving no messages but detecting a collision.

(If leader) Determines, broadcasts VN’s output messages for round k.


CHA Protocol, Instance k

Simplified version: version in the paper has optimizations to reduce communication.

Each node begins instance k with a proposal for the current instance, and a history through instance k-1.

Ballot := (history, proposal) Three rounds:

Round 1 [ballot]: If advice = active then broadcast(ballot)

Round 2 [veto1]: If collision occurred in round 1 then broadcast(veto)

Round 3 [veto2]: If collision occurred in round 2 then broadcast(veto)

• Generate new history through instance k:


Generate New History

Use colors: If green or yellow, use the (unique) history you received in round 1,

augmented with the associated proposal. If orange or red, use the history from your most recent green or yellow

round, augmented with s.

red

orange

yellow

green

ResultVeto 2Veto 1Ballot Accept

Reject


CHA output

red

orange

yellow

green

ResultVeto 2Veto 1Ballot

If round is green, then output your new history. If round is yellow, orange, or red, then output .


Analysis: Key Idea 1

For any instance k, the colors assigned by any two nodes differ by at most one shade.

If some node assigns green to instance k, then all nodes assign either green or yellow.

If some node “accepts the ballot” and outputs a history for instance k, then all nodes receive the ballot for instance k, and use it to define their new histories.

If some node assigns red to instance k, then all nodes assign either red or orange.

If some node “rejects the ballot” at instance k, then no node uses it to define its new history, and no node outputs a history at instance k.


Analysis: Key Idea 2

After the network, collision detector, and contention manager stabilize, eventually, every round is green.

When the underlying network is well-behaved, then ballots are received, and no vetoes are received.

Used to prove liveness properties for the emulated VN:

Eventual collision freedom. Eventual accuracy of the collision detector. Contention manager eventually well-behaved.


Emulating Entire VN Layer

Emulate each VN. Complications:

1. Must also emulate communication between VNs.2. VN emulators may interfere with each other, causing collisions.

Coping with the complications: Define static schedule for VN broadcasts:

Non-conflicting: Neighboring VNs are not scheduled at the same virtual round.

Fair: Every VN is scheduled periodically. Use schedule to avoid contention in VN emulation. Use 2 instances of CHA:

One for all the scheduled VNs. to agree on messages they broadcast and receive in virtual round k,

The other for unscheduled VNs, to agree on messages they receive in round k.


Summary: Masking Communication Failures

VN Layer: Client Nodes + Virtual Stationary Nodes + local broadcast communication service + collision detector + contention manager.

Physical Layer: Physical Nodes + unreliable local broadcast + collision detector + contention manager.

Emulation: Replicated state machine strategy, with leaders to

reduce communication. Convergent History Agreement (CHA) consensus

protocols for emulators of each VN to agree on messages sent and received.

Static scheduling, to emulate multiple VNs concurrently.


Summary: Masking Communication Failures

CHA emulation guarantees strong consistency semantics for emulated VN Layer.

Protocol is fairly heavyweight. Still could fail in practice: Depends on

reliable collision detection, various “eventual properties”.

cpsc 689: discrete algorithms for mobile and wireless systems

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