Program Execution Time, Program Execution Time, Reliability, and Queueing Analysis Reliability, and Queueing Analysis

in Mobile Environmentsin Mobile Environments

Chen XinyuChen Xinyu

2003-12-082003-12-08

Term PresentationTerm Presentation

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Wireless CORBA ArchitectureWireless CORBA Architecture

Cell

Access Bridge

Mobile Host

Static Host

Radio Link

Wired Link

Wired Network

Handoff: a mechanism for a Mobile Host to seamlessly

change a connection from one Access Bridge to another

Home Location Agent

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OutlineOutline

• Analysis of Program Execution Time Based Analysis of Program Execution Time Based on Various Checkpointing Strategieson Various Checkpointing Strategies

• Expected-Reliability AnalysisExpected-Reliability Analysis

• Analysis of Message Sojourn Time in Analysis of Message Sojourn Time in Access BridgeAccess Bridge

• Conclusions and Future WorkConclusions and Future Work

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Program Execution TimeProgram Execution Time

• MotivationMotivation• Previous workPrevious work

• program execution time with and without program execution time with and without checkpointing in the presence of failures on Static checkpointing in the presence of failures on Static Hosts with given time requirement without failuresHosts with given time requirement without failures

• Mobile EnvironmentsMobile Environments• Underlying message-passing mechanismUnderlying message-passing mechanism

• Interactions with other hostsInteractions with other hosts• Network communicationsNetwork communications• Discrete message exchangeDiscrete message exchange

• HandoffHandoff

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The Program’s Termination ConditionThe Program’s Termination Condition

• A program on a Mobile Host is A program on a Mobile Host is successfully terminated if it continuously successfully terminated if it continuously receives receives nn computational computational messagesmessages

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ObjectiveObjective

• To derive the cumulative distribution function To derive the cumulative distribution function of the program execution time on a Mobile of the program execution time on a Mobile Host and its expectation with message number Host and its expectation with message number nn in the advent of failures, handoffs, and in the advent of failures, handoffs, and checkpointingscheckpointings• Deterministic checkpointing strategyDeterministic checkpointing strategy

• Random checkpointing strategyRandom checkpointing strategy

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Deterministic Checkpointing StrategyDeterministic Checkpointing Strategy

• Deterministic: Deterministic: • Take a checkpoint when receiving Take a checkpoint when receiving a a

messages, messages, aa is a constant is a constant

• The program execution is broken into The program execution is broken into intervalsintervals

• The The iithth, i=1,2,…,m-1, i=1,2,…,m-1, interval contains , interval contains aa messages and a checkpointmessages and a checkpoint

• The message number in the The message number in the mmthth interval interval is given by is given by

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Assumptions and State TransitionAssumptions and State Transition

• State 0 : normalState 0 : normal

• State 1 : handoffState 1 : handoff

• State 2 : State 2 : Composite checkpointingComposite checkpointing

• State 3 : State 3 : Composite recoveryComposite recovery

• Generally distributed Generally distributed random variablesrandom variables• CC: checkpointing time: checkpointing time• HH: handoff time: handoff time• RR: repair time: repair time• UU: rollback time: rollback time

0

1

3

2

/a

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Composite StatesComposite States

• State 2 – Composite checkpointingState 2 – Composite checkpointing• State 4 – checkpointing, State 5 – handoffState 4 – checkpointing, State 5 – handoff

6 7 8

3 7 8

2 4 5

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• State 3 – Composite recoveryState 3 – Composite recovery• State 6 – repair, State 7 – rollback, State 8 – handoffState 6 – repair, State 7 – rollback, State 8 – handoff

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Conditional Execution TimeConditional Execution Time

• The execution time for the The execution time for the iithth interval,interval, i=1,2,…,m-1 i=1,2,…,m-1

• The execution time for the The execution time for the mmthth intervalinterval

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NotationNotation

• Laplace-Stieltjes Transform of the Laplace-Stieltjes Transform of the cumulative distribution function of a cumulative distribution function of a random variable random variable ZZ

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Expected Program Execution TimeExpected Program Execution Time

• Deterministic checkpointingDeterministic checkpointing

• Without checkpointing (Without checkpointing (a >= na >= n))

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Extended Deterministic CheckpointingExtended Deterministic Checkpointing

• Given a sequence Given a sequence aa11, a, a22, …, a, …, am-1m-1, then , then

aam m = n - a= n - a1 1 - a- a22 - … - a - … - am-1m-1

• m-1m-1 checkpoints checkpoints

• Expected program execution timeExpected program execution time

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Random Checkpointing StrategyRandom Checkpointing Strategy

• Random:Random:• Take a checkpoint when receiving Take a checkpoint when receiving I I

messages, messages, II is a random variable is a random variable

• Geometric distributionGeometric distribution• P(I=i) = p(1-p)P(I=i) = p(1-p)i-1i-1, i = 1,2, i = 1,2,…,…

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State TransitionState Transition

0

1

3

2

p

/a

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Conditional Execution TimeConditional Execution Time

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Expected Program Execution TimeExpected Program Execution Time

• Random CheckpointingRandom Checkpointing

• p = 0p = 0 indicates without checkpointing indicates without checkpointing

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Without FailuresWithout Failures

• Without CheckpointingWithout Checkpointing

• Deterministic CheckpointingDeterministic Checkpointing

• Random CheckpointingRandom Checkpointing

If 1/a = p, then p(n-1) >= m-1,

which indicates that on average the random checkpointing

takes more checkpoints than the deterministic checkpointing.

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Average EffectivenessAverage Effectiveness

• Ratio between the expected execution Ratio between the expected execution time without and with failures, handoffs time without and with failures, handoffs and checkpointsand checkpoints

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Comparisons and Discussions (1)Comparisons and Discussions (1)

• Message numberMessage number

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Comparisons and Discussions (2)Comparisons and Discussions (2)

• Failure rateFailure rate

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Comparisons and Discussions (3)Comparisons and Discussions (3)

• Checkpoint creation timeCheckpoint creation time

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Comparisons and Discussions (4)Comparisons and Discussions (4)

• Optimal checkpointing frequency (aOptimal checkpointing frequency (a-1-1, p), p)

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Comparisons and Discussions (5)Comparisons and Discussions (5)

• Message arrival rate and handoff rateMessage arrival rate and handoff rate

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Expected-Reliability AnalysisExpected-Reliability Analysis

• MotivationMotivation• Previous workPrevious work

• Two-terminal reliability: the probability of Two-terminal reliability: the probability of successful communication between the source successful communication between the source node and the target nodenode and the target node

• Mobile EnvironmentsMobile Environments• Handoff causes the change of Handoff causes the change of numbernumber and and typetype

of engaged communication components of engaged communication components

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Expected-ReliabilityExpected-Reliability

• Two-terminal expected-reliability at time Two-terminal expected-reliability at time tt

• QQss(t)(t)• the probability of the system in state the probability of the system in state ss at time at time tt

• RRss(t)(t)• the reliability of the system in state the reliability of the system in state ss at time at time tt

• Mean Time to FailureMean Time to Failure

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Four Communication SchemesFour Communication Schemes

• Static Host to Static Host (SS)Static Host to Static Host (SS)• Traditional communication schemeTraditional communication scheme

• Mobile Host to Static Host (MS)Mobile Host to Static Host (MS)• 2 system states2 system states

• Static Host to Mobile Host (SM)Static Host to Mobile Host (SM)• 4 system states4 system states

• Mobile Host to Mobile Host (MM)Mobile Host to Mobile Host (MM)• 8 system states8 system states

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MS SchemeMS Scheme

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SM SchemeSM Scheme

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MM SchemeMM Scheme

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MM Scheme (Cont’d)MM Scheme (Cont’d)

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MM Scheme (Cont’d)MM Scheme (Cont’d)

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Message Sojourn Time in Access BridgeMessage Sojourn Time in Access Bridge

• MotivationMotivation• Previous workPrevious work

• Task sojourn time in the presence of server Task sojourn time in the presence of server breakdownsbreakdowns

• Mobile EnvironmentsMobile Environments• Due to failures and handoffs of Mobile Hosts, Due to failures and handoffs of Mobile Hosts,

the messages in Access Bridge cannot be the messages in Access Bridge cannot be dispatcheddispatched

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ObjectiveObjective

• To derive the expected message To derive the expected message sojourn time in an Access Bridge with sojourn time in an Access Bridge with different dispatch strategies in the different dispatch strategies in the presence of failures and handoffs of presence of failures and handoffs of Mobile HostsMobile Hosts

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Differences between previous work and Differences between previous work and our workour work

Previous workPrevious work Our workOur workThe task response timeThe task response time The message sojourn timeThe message sojourn time

The server is failure-proneThe server is failure-prone The Access Bridge is The Access Bridge is failure-freefailure-free

In the presence of server In the presence of server breakdowns, the task breakdowns, the task cannot progresscannot progress

In the presence of Mobile In the presence of Mobile Host breakdown and Host breakdown and handoff, other message handoff, other message may be still be dispatchedmay be still be dispatched

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Message Dispatch Model (1)Message Dispatch Model (1)

• Basic dispatch modelBasic dispatch model

n

q0

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Message Dispatch Model (2)Message Dispatch Model (2)

• Static processor-sharing dispatch modelStatic processor-sharing dispatch model

/n

q1

/n

q2

/n

qn

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Message Dispatch Model (3)Message Dispatch Model (3)

• Dynamic processor-sharing dispatch modelDynamic processor-sharing dispatch model

q1 q2 qn

/K /K /K K

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Message Dispatch Model (4)Message Dispatch Model (4)

• Round-robin dispatch modelRound-robin dispatch model

q1 q2 qn

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Message Dispatch Model (5)Message Dispatch Model (5)

• Feedback dispatch modelFeedback dispatch model

n

q0

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Analytical Results and Comparisons (1)Analytical Results and Comparisons (1)

• Number of mobile hostsNumber of mobile hosts

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Analytical Results and Comparisons (2)Analytical Results and Comparisons (2)

• Failure rateFailure rate

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Analytical Results and Comparisons (3)Analytical Results and Comparisons (3)

• Message arrival rateMessage arrival rate

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Analytical Results and Comparisons (4)Analytical Results and Comparisons (4)

• Expected message dispatch requirementExpected message dispatch requirement

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ConclusionsConclusions

• Derive the cumulative distribution function of Derive the cumulative distribution function of the program execution time with various the program execution time with various checkpointing strategies and its expectationcheckpointing strategies and its expectation• Observe that random checkpointing is more stable Observe that random checkpointing is more stable

against the variation of parameters than against the variation of parameters than deterministic checkpointingdeterministic checkpointing

• Define expected-reliability to embody the Define expected-reliability to embody the mobility characteristic introduced by handoffmobility characteristic introduced by handoff

• Analyze the message sojourn time in Access Analyze the message sojourn time in Access Bridge with fives dispatch models Bridge with fives dispatch models

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Future WorkFuture Work

• Relax some assumptions to derive more Relax some assumptions to derive more general program execution timegeneral program execution time• Failures may not be detected instantlyFailures may not be detected instantly

• Further the expected-reliability analysis to Further the expected-reliability analysis to include links failures. The reliability with include links failures. The reliability with multiple terminals will be consideredmultiple terminals will be considered

• Provide fault tolerance mechanism for other Provide fault tolerance mechanism for other mobile environments, such as ad-hoc mobile mobile environments, such as ad-hoc mobile networks and sensor networksnetworks and sensor networks