self-stabilizing end-to-end communication in bounded capacity, omitting, duplicating and non-fifo...

Self-Stabilizing End-to-End Communication

in Bounded Capacity, Omitting, Duplicating and non-FIFO

Dynamic NetworksShlomi Dolev1, Ariel Hanemann1, Elad M. Schiller2, and

Shantanu Sharma1

1 Department of Computer Science, Ben-Gurion University of the Negev, Israel

2 Department of Computer Science and Engineering, Chalmers University of Technology, Sweden

14th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2012)

Toronto, Canada (1-4 October 2012)

Outline

• Introduction

• Problem Specification

• The Algorithm

• Key Features

• Conclusion

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• End-to-end communication is an essential task in communicating systems

• Intromission of errors in message transmission is common

• Dynamic networks have a greater chance of having errors, like, omission, duplication, reordering, than conventional networks

• Network has known capacity constant, which is an upper bound on number of packets in the network

Introduction

S R

Omission of packets

S R

Duplication by the sender

S R

Duplication by the channel

S R

Reorder

S R

capacity of the channel

S R

capacity packets

capacity of the “channel”

• Self-Stabilization

– A self-stabilizing system is a system that can automatically recover following the occurrence of transient faults

– e.g.-token based mutual exclusion algorithm

Introduction

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Outline

• Introduction


• The Algorithm

• Key Features

• Conclusion

Problem Specification

• Design an algorithm for a bounded capacity non-FIFO network which– Guarantee exactly one copy of packet delivery

– Tolerate corruption, omission, duplication of messages by the “channel” and the sender

– Deliver messages in the same order they were sent

– Applied to topological independent network

– Employed to any starting configuration

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Problem Specification

• Why new end-to-end communication protocol?– TCP is not self-stabilizing

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Outline

• Introduction


• The Algorithm

• Key Features

• Conclusion

The Algorithm-Motivation

• Dolev et al* has presented self-stabilizing data link algorithm for reliable FIFO packet delivery over bounded non-FIFO and non-duplicating channel

• The sender sends a message infinitely often until it gets ‘3capacity + 2‘ identical acknowledgements

• The receiver delivers a message when it gets identical ‘capacity + 1‘ messages

Shlomi Dolev, Swan Dubois, Maria Potop-Butucaru, and Sébastien Tixeuil. Stabilizing data-link over non-fifo channels with optimal fault-resilience. Inf. Process. Lett., 111(18):912–920, 2011.

*

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S R

Alternating bitab = 0

Now, the receiver delivers the message m only onceand changes last_delivered = 0

Last delivered alternating bit

last_delivered = 1

m, 0

ack(m, 0)

1st message

2ed message

3rd message

capacity+1message

mm

m

m

1

2

capacity

capacity+1

3capacity+1

3capacity+2

Acknowledgments

Messages

capacity messages

The channel may contain capacity (or zero) messages in the channel from sender to receiver

Hence, the sender sends capacity +1 messages to the receiver.

capacity messages

The channel may contain capacity (or zero) messages in the channel from receiver to sender

Hence, the sender waits 3capacity+2 acknowledgement messages

capacity acks for message in the channel from sender to receivercapacity+1 acks for the message sent by sendercapacity acks for message in the channel from receiver to sender1 ack for bad initialization

m, 0 m, 0

ack(m, 0)ack(m, 0)ack(m, 0)

Last delivered alternating bit

last_delivered = 0

But, the sender sends message until it gets 3capacity+2 acknowledgements. However, the receiver acknowledges all incoming message but do not store (due to same last_delivered=0)

m, 0

ack(m, 0)

m, 0

ack(m, 0)

Now, the sender fetches new message, changes alternating bit to 1 and repeat the whole process

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• Disadvantages Dolev et al*:– Explicit synchronization of the sender and the

receiver

– One packet delivery requires lots of packet flow overburden network

– Does not consider duplication by the channel

Shlomi Dolev, Swan Dubois, Maria Potop-Butucaru, and Sébastien Tixeuil. Stabilizing data-link over non-fifo channels with optimal fault-resilience. Inf. Process. Lett., 111(18):912–920, 2011.

*

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S2E2C Algorithm

• S2E2C (Self-Stabilizing End-to-End Communication) Algorithm

– Overcomes all the cons of Dolev et al (presented previously)

– Sends n messages (packets) infinitely often instead of one message at a time

– Consider the duplication by the channel

– Message to packet transformation

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S R

Alternating Index AltIndexs= 1 LastDeliveredIndexr = 0

Now, the receiver selects majority of the message s and deliver it

Packet_set

1,0,m1,1,m

(2,2,m) (1,2,m)

1,n-1,m

(1, 0, m)

(1, 0, m)

(1, 1, m)(1, 1, m)

(1, 1, m)

(0, 2, m)

(1, 2, m)

2,2,d3

1,capacity,m

(2, 3, m)

(1, 3,m)(1,3,m) (2,3,m)

(1, capacity, m)(1, capacity+1, m)

1,capacity+1,m

(1, n-1, m)m

Correct messages

S2E2C Algorithm

(1, capacity, m)2,3,m

1,2,m1,3,m

After the delivery of the correct messages, the receiver acknowledges the sender.

Alternating Index

Label Data

(2, 2, m)

(1, 0, m)

Transmission of messages from the sender to the receiver.

Capacity

• With only one message

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The Algorithm-The Idea

• Distinct Labels with each outgoing packets– prevent duplication and guarantee in-order delivery of

messages as they were sent

• Alternating index 0, 1 or 2– avoids explicit synchronization between the sender and the

receiver

• The receiver accumulates packets of ‘n‘ distinct labels with identical alternating index before the delivery of messages

• The sender waits for capacity+1 distinct labels acknowledgements before the next fetch

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S R


Now, the receiver selects n distinct labels which have identical alternating index except LastDeliveredIndex.

ACK_set

01

Packet_set

1,0,d1

1,1,d2

(2,2,d3) (1,2,d3)

1,n-1,dn-1

(1, 0, d1)

(1, 0, d 1)

(1, 1, d2)(1, 1, d2)

(1, 1, d 2)

(0, 2, d 3)

(1, 2, d3)

2,2,d3

1,capacity,dc

(2, 3, d 4)

(1, 3, d4)(1,3,d4) (2,3,d4)

(1, capacity, dc)(1, capacity+1, dc+1)

1,capacity+1,dc+1

(1, n-1, dn-1)

1st message

2edmessage

3rd message

plth message

Messages with errors

1st message

2edmessage

3rd message

plth message

Correct messages

0, 11 , 1capacity, 1

S2E2C Algorithm

capacity

(1, capacity, dc)2,3,d4

1,2,d3

1,3,d4

After the delivery of the correct messages, the receiver acknowledges the sender.

Alternating Index

Label Data

(2, 2, d 3)

(1, 0, d 1)

Transmission of messages from the sender to the receiver.Transmission of acknowledgements from the receiver to the sender.

Capacity

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1st message

2ed message

3rd message

plth message

ml

The sender fetches pl messages of ml length

The Algorithm at Sender

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1st message

2ed message

3rd message

plth message

ml

1st bit 2ed bit 3rd bit mlth bit

Error Correcting Encoding

Error Correcting Bits

n > ml

AltIndexlbl

1st Packet2ed Packet

3rd Packet nth Pacet


The sender appends redundant bits to each pl message which results in message length n (n>ml)

Consider all the bits of each pl messages

ai ai ai ai ai ai1 2 3 ml n-1 n

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• The transmitting packet has the form ofai, lbl, dat

ai is alternating indexlbl is labelsdat is data which is formed by ith bit of all messages

• The sender waits for capacity + 1 distinct label acknowledgements before next fetch

• The sender changes its alternating index x to x+1 mod 3, at every fetch

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The Algorithm at Receiver

• The receiver collects packets of n distinct labels which have alternating index different from last delivered index

– capacity distinct labels may be from the channel

– n – capacity distinct label packets must be from the sender

• The receiver forms messages form all incoming packets

ith message is formed by the ith bit of every packet

ai ai ai ai ai1 2 3 ml n-1 n

ai

The Algorithm at Receiver

• After delivery of the message– Resets data structure– changes LastDeliveredIndex to the value of delivered

message alternating index

• The receiver acknowledges the sender with ’capacity + 1’ distinct labels and the value of LastDeliveredIndex

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Outline

• Introduction


• The Algorithm

• Key Features

• Conclusion

Key Features

• Handles capacity corruptions in the messages

• Does one time delivery of message with handling of omission and reorder, i.e., simulate reliable FIFO message delivery over the non-FIFO network

• No explicit synchronization between the sender and the receiver

• No need of denotative reset operation at the sender and at the receiver

• Topological independence

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Key Features


• The intromission of error correcting bits is capable to prevent capacity errors or loss of capacity packets

• capacity corruption is equivalent to loss of distinct capacity labels packets

ai ai ai ai ai1 2 3 ml n-1 n

ai

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Key Features






Key Features

• Does one time delivery of message with handling of omission and reorder– The omission of packets is prevented by error

correcting bits

– The duplication of messages is done by either channel or the sender• The channel can duplicate up to capacity packets• The sender duplicates each packets infinity often

– Distinct labels ensures one time order delivery of all the messages

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Key Features






Key Features

• No explicit synchronization between the sender and the receiver– Synchronization of alternating index is necessary due to

arbitrary initialization

– If the sender and the receiver are having same alternating index, then the receiver does not deliver incoming messages. But, it acknowledges the sender by capacity + 1 distinct labels

– On reception of capacity + 1 distinct labels, the sender changes alternating index and fetches new messages

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Key Features

• No explicit synchronization between the sender and the receiver– Why alternating bit 0 and 1 is not useful in implicit

synchronization?

S R


ACK_set

0,0

1,0

capacity-1,0

Packet_set

Alternating Index AltIndexs= 1

1,0,*1,1,*1,2,*

capacity ,0

(0, 0, *)

1,n -2,*

(1,n-1,*)

1,n-1,*The receiver changes LastDeliveredIndexr to 1 and resets Packet_set

LastDeliveredIndexr = 1

0,0,*0,1,*

0,2,*

0,n -2,*Now, the sender sends packets with AltIndexs 0

(0, 1, *)(0, 2, *)(0, n-2, *)

The sender gets acknowledgement from the channel

capacity,0

Now, the sender resets and changes AltIndexs

0,1

0,11,1

capacity-1,1

The receiver acknowledges the sender

1,1Capacity-1,1

This situation is same as initial starting configuration, where the sender and the receiver are having alternting bit 0. Now, we are having alternating bit 1 at both the end

Such situation is successfully handled by alternating index 0, 1, 2

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Key Features

• No explicit synchronization between the sender and the receiver– Use of alternating index 0, 1 and 2

S R


ACK_set

0,1

1,1

capacity-1,1

Packet_set

Alternating Index AltIndexs= 2

0,0,*0,1,*0,2,*

capacity ,1

(1, 0, *)

0,n -2,*

(0,n-1,*)

0,n-1,*The receiver changes LastDeliveredIndexr to 0 and resets Packet_set

LastDeliveredIndexr = 0

1,0,*1,1,*

1,2,*

1,n -2,*1,n-1,*

Now, the sender sends packets with AltIndex 1

(1, 1, *)(1, 2, *)(1, n-2, *)

The sender gets acknowedgement from the channel

Capacity, 1

Now, the sender resets and changes AltIndex to 2The receiver gets packet form the channel

(1,n-1,*)

The receiver changes LastDeliveredIndexr to 1 and resets Packet_set

Now, the sender and the receiver are synchronized

0, 1

24

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Key Features






Key Features


– In arbitrary initialization, the sender and the receiver may have some garbage in its data structure then both do reset

– The reset process for garbage items is only required at arbitrary stages

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Key Features






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Outline

• Introduction


• The Algorithm

• Key Features

• Conclusion

Conclusion

• A self-stabilizing end-to-end communication algorithm

• Topological independent, fits for dynamic networks

• Implicit sender/receiver synchronization

• Simulate perfect FIFO behavior – in-order delivery, avoid omission, duplication by the sender, duplication by the channel - over non-FIFO networks

Interested audience may refer the paper with the same title for details and proofs.27of 27

Shlomi Dolev1, Ariel Hanemann1, Elad M. Schiller2, and Shantanu Sharma1

1 Department of Computer Science, Ben-Gurion University of the Negev, Israel

{dolev,hanemann,sharmas}@cs.bgu.ac.il2 Department of Computer Science and Engineering, Chalmers

University of Technology, [email protected]

Presentation is available at

http://www.cs.bgu.ac.il/~sharmas/publication.html



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