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Superstabilizing Protocols for Dynamic Distributed Systems
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Title: Superstabilizing Protocols for Dynamic Distributed Systems
1
Superstabilizing Protocols for Dynamic
Distributed Systems
- Authors Shlomi Dolev, Ted Herman
- Presented by Vikas Motwani
- CSE 291 Wireless Sensor Networks
- June 3rd 2003
2
Outline
- Self-Stabilization
- Dynamic Systems
- Superstabilization
- Update Protocol
- Superstabilizer
- Warm Legitimacy
- Conclusion/Relation to Sensor Networks
3
Self-Stabilization
- Most General Technique enabling a system to
tolerate arbitrary transient faults
self-stabilization - Protocol is Self-Stabilizing if, in response to a
transient fault, it converges to a legitimate
state in finite time. - Evaluated by Efficiency of Convergence time of
convergence to a legitimate state following a
transient fault - Largely ignores behavior of protocols between
transient fault and restoration to legitimate
state, Main concern recovery from transient
fault and convergence to legitimate state
4
Dynamic Systems
- A system where communication links and processors
may fail and recover during normal operation - Protocols for dynamic systems designed to contend
with such failures and recoveries without global
reinitialization - However, these protocols consider only global
states that are reachable from a predefined
initial state under a constrained sequence of
failures and failures are handled with as few
adjustments as possible. - Makes guarantees about the behavior of the system
between fault and restoration to legitimate state
5
A Dynamic System representation
- Graph representation processorsnodes and
linksedges - Processors may communicate only with neighbors
- Processors communicate using registers, and
application of model to message passing system
intended - Associated with each processor code, local
variables, program counter, shared register, list
of neighbors - Local processor variables variables used for
computations and field image variables (refers to
fields of registers)
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Superstabilization
- Combine benefits of both self-stabilizing and
dynamic protocols - Protocol is super-stabilizing if
- It is self-stabilizing, and,
- When it starts in a legitimate state and a
topology change occurs, a passage predicate must
hold and continue to hold until the protocol
reaches a legitimate state, hence accounting for
protocol behavior during transition - Specified with respect to a class to topology
changes more stable than self-stabilization as
system maintains stability with respect to
passage predicate even when disturbed by topology
change - Motivation topology change is usually detected,
if not, self stabilization is a fallback
mechanism to deal with the change
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Terminologies
- Computation 1-step sequence of global system
states - Fair computation computation that is finite or
contains infinitely many steps of each
non-crashed processor - Suppose P is a predicate with some system
property, a legitimacy predicate L is specified
with respect to P to determine whether or not
the property of interest holds - L also specifies permissible values of all
register fields, program counters and local
variables so P remains invariably true in a
computation - Interrupt statement statement concerned with
adjusting to topology change - Trajectory sequence of global states in which
each segment is either a fair computation or a
sequence of topology change events (removal or
addition of a single component)
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Superstabilization Paradigm
- Specifies a class ? of topology change events
- Definition A protocol P is superstabilizing with
respect to ? if and only if P is
self-stabilizing, and for every trajectory ?
beginning at a legitimate state and containing a
single topology change event of type ?, the
passage predicate holds for every local state ? ?
? - Adjustment Measure maximum number of processors
having different states in a state-space, ranging
over the minimal collection of variables and
fields upon which P depends, taken over all
states derived from a legitimate state and a
topology change event. small adjustment measure
few adjustments are necessary in response to a
topology change
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Evaluating Superstabilization Protocols
- Cycle a minimal sequence of steps in a
computation so that an iteration of the protocol
at processor p executes the program for p from
the first to the last statement - Time complexity measured in rounds 1st round
terminates at 1st state at which p has completed
at least one cycle, round i1 terminates when p
has completed at least one cycle after round i - Stabilization time maximum number of rounds it
takes the protocol to reach a legitimate state
from an arbitrary state - Superstabilization time maximum number of rounds
it takes for the protocol starting from an
arbitrary legitimate state, followed by an
arbitrary ?-change event to again reach a
legitimate state
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General Superstabilization
- General method takes a self-stabilizing protocol
P and outputs a protocol Ps that is both
self-stabilizing and super-stabilizing - Done by modifying P and superimposing a new
component called the superstabilizer - Superstabilizer uses as a tool, a
self-stabilizing update protocol
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Update Protocol
- Suppose that every processor has a field image
xp the update problem is to broadcast xp to all
processors - Topology update when the field xp contains all
local information about ps links and network
characteristics - In addition, let each processor have a field ep
which contains three tuples ltq,u,kgt where q is
processor identifier, u is same type as xp, k is
distance between p and the processor named in 1st
component
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Update Protocol Implementation
- For the update protocol, Distance-stable state
any state for which - Each processor p has exactly one tuple in its ep
field for every processor q in the network,
reachable by some path from p - ep contains no other tuples
- Each computation that starts in such a state
preserves the above two conditions
13
SuperStabilizer
- A tool used in transforming a given
self-stabilizing protocol P into a
superstabilizing protocol Ps. - Function F determines a new legitimate state from
a previously legitimate state perturbed by a
topology change E - Superstabilizer makes use of F by assembling the
image of a global state from local snapshots,
followed by disseminating F(global state) to all
processors so a new legitimate state is reached - Superstabilizer hides E from any processor in a
way that no user of protocol P can observe a
state inconsistent with current topology by
making global transition between legitimate
states for different topologies effectively atomic
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Characteristics
- Superstabilizer has 2 components
- Modified Update Protocol
- Interrupt statement
- P is modified as follows
- Each action of P is guarded by a Boolean freezep
so that when freezep holds, no action of P is
enabled at processor p and PC remains static - All freeze fields false in absence of topology
changes - Step scheduling arranged so that a cycle of
superstabilizer is inserted before each read step
of P, so any news of topology changes is
processed by superstabilizer before P at each
processor - Superstabilizer also specifies an interrupt
section for the protocol Ps so that topology
changes incident on processor p are handled by
the superstabilizer at p
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Superstabilizing Protocol
- Combination of superstabilizer and modified
protocol P results in superstabilizing protocol
Ps - Legitimate state for Ps is any state in which
- Variables, fields and program counter with
respect to P satisfy LP - Update protocol component is in legitimate
state(all e fields have accurate tuples) - Each freeze variable is false
- Each computation that starts in such a state
preserves the above conditions
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Warm Legitimacy
- Passage protocol defined in terms of freeze
fields. - For any state ?, warm? set of processors with
freeze fields false - ? is warm legitimate if there exists a state ?
and topology T. ? where ? is LP, such that
?warm ?warm (? is warm-legitimate if it is
in a legitimate state with respect to some
topology) when we disregard any processor with
freezep true - Passage protocol for the general method the
protocol state is warm-legitimate - Pseudo-variable snapp collection of all local
variables, shared fields and program counter of P
for processor p - When topology change occurs, P is frozen at all
processors, snap value is recorded, a snap value
for the new topology is computed, and each frozen
processor is assigned the new snap value and then
unfrozen
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Interrupt statement
- In response to a topology change E incident on a
processor p, the program counter of protocol Ps
is reset to the first statement of the
superstabilizer, the neighborhood Np is adjusted
to reflect E, and the write operation is
atomically executed. - This operation halts P by setting freezep to true
18
Conclusion/Relation to Sensor Networks
- Sensor Networks Dynamic environment with high
probability of failures and need to stabilize to
an equilibrium state - Ability of a self-stabilizing system to recover
from transient failures is based on the
assumption that the failures do not continue to
occur safe assumption? - Global state vs. local state?
- What kind of predicates would we want to
apply/enforce/check for? - Can we predict/decide a class of failures that we
could account for?
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