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Program Execution Time, Reliability, and Queueing Analysis in Mobile Environments

Program Execution Time, Reliability, and Queueing Analysis in Mobile Environments. Chen Xinyu 2003-12-08 Term Presentation. Handoff: a mechanism for a Mobile Host to seamlessly change a connection from one Access Bridge to another. Access Bridge. Mobile Host. Static Host. Wired Link.

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Program Execution Time, Reliability, and Queueing Analysis in Mobile Environments

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  1. Program Execution Time, Reliability, and Queueing Analysis in Mobile Environments Chen Xinyu 2003-12-08 Term Presentation

  2. Handoff: a mechanism for a Mobile Host to seamlessly change a connection from one Access Bridge to another Access Bridge Mobile Host Static Host Wired Link Radio Link Cell Home Location Agent Wireless CORBA Architecture Wired Network

  3. Outline • Analysis of Program Execution Time Based on Various Checkpointing Strategies • Expected-Reliability Analysis • Analysis of Message Sojourn Time in Access Bridge • Conclusions and Future Work

  4. Program Execution Time • Motivation • Previous work • program execution time with and without checkpointing in the presence of failures on Static Hosts with given time requirement without failures • Mobile Environments • Underlying message-passing mechanism • Interactions with other hosts • Network communications • Discrete message exchange • Handoff

  5. The Program’s Termination Condition • A program on a Mobile Host is successfully terminated if it continuously receives ncomputational messages

  6. Objective • To derive the cumulative distribution function of the program execution time on a Mobile Host and its expectation with message number n in the advent of failures, handoffs, and checkpointings • Deterministic checkpointing strategy • Random checkpointing strategy

  7. Deterministic Checkpointing Strategy • Deterministic: • Take a checkpoint when receiving a messages, a is a constant • The program execution is broken into intervals • The ith, i=1,2,…,m-1, interval contains a messages and a checkpoint • The message number in the mth interval is given by

  8. /a      Assumptions and State Transition • State 0 : normal • State 1 : handoff • State 2 : Composite checkpointing • State 3 : Composite recovery • Generally distributed random variables • C: checkpointing time • H: handoff time • R: repair time • U: rollback time 2 0 1 3

  9. Composite States • State 2 – Composite checkpointing • State 4 – checkpointing, State 5 – handoff 2 4 5 5    • State 3 – Composite recovery • State 6 – repair, State 7 – rollback, State 8 – handoff   3 7 7 6 6 8 8  

  10. Conditional Execution Time • The execution time for the ithinterval, i=1,2,…,m-1 • The execution time for the mthinterval

  11. Notation • Laplace-Stieltjes Transform of the cumulative distribution function of a random variable Z

  12. Expected Program Execution Time • Deterministic checkpointing • Without checkpointing (a >= n)

  13. Extended Deterministic Checkpointing • Given a sequence a1, a2, …, am-1, then am = n - a1 - a2 - … - am-1 • m-1 checkpoints • Expected program execution time

  14. Random Checkpointing Strategy • Random: • Take a checkpoint when receiving I messages, I is a random variable • Geometric distribution • P(I=i) = p(1-p)i-1, i = 1,2,…

  15. /a p      State Transition 2 0 1 3

  16. Conditional Execution Time

  17. Expected Program Execution Time • Random Checkpointing • p = 0 indicates without checkpointing

  18. Without Failures • Without 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. • Deterministic Checkpointing • Random Checkpointing

  19. Average Effectiveness • Ratio between the expected execution time without and with failures, handoffs and checkpoints

  20. Comparisons and Discussions (1) • Message number

  21. Comparisons and Discussions (2) • Failure rate

  22. Comparisons and Discussions (3) • Checkpoint creation time

  23. Comparisons and Discussions (4) • Optimal checkpointing frequency (a-1, p)

  24. Comparisons and Discussions (5) • Message arrival rate and handoff rate

  25. Expected-Reliability Analysis • Motivation • Previous work • Two-terminal reliability: the probability of successful communication between the source node and the target node • Mobile Environments • Handoff causes the change of number and type of engaged communication components

  26. Expected-Reliability • Two-terminal expected-reliability at time t • Qs(t) • the probability of the system in state s at time t • Rs(t) • the reliability of the system in state s at time t • Mean Time to Failure

  27. Four Communication Schemes • Static Host to Static Host (SS) • Traditional communication scheme • Mobile Host to Static Host (MS) • 2 system states • Static Host to Mobile Host (SM) • 4 system states • Mobile Host to Mobile Host (MM) • 8 system states

  28. MS Scheme

  29. SM Scheme

  30. MM Scheme

  31. MM Scheme (Cont’d)

  32. MM Scheme (Cont’d)

  33. Message Sojourn Time in Access Bridge • Motivation • Previous work • Task sojourn time in the presence of server breakdowns • Mobile Environments • Due to failures and handoffs of Mobile Hosts, the messages in Access Bridge cannot be dispatched

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

  35. Differences between previous work and our work

  36. n  q0 Message Dispatch Model (1) • Basic dispatch model

  37.   q1 q2 qn /n /n /n Message Dispatch Model (2) • Static processor-sharing dispatch model

  38.   q1 q2 qn /K /K /K K Message Dispatch Model (3) • Dynamic processor-sharing dispatch model

  39.   q1 q2 qn    Message Dispatch Model (4) • Round-robin dispatch model

  40. n  q0 Message Dispatch Model (5) • Feedback dispatch model

  41. Analytical Results and Comparisons (1) • Number of mobile hosts

  42. Analytical Results and Comparisons (2) • Failure rate

  43. Analytical Results and Comparisons (3) • Message arrival rate

  44. Analytical Results and Comparisons (4) • Expected message dispatch requirement

  45. Conclusions • Derive the cumulative distribution function of the program execution time with various checkpointing strategies and its expectation • Observe that random checkpointing is more stable against the variation of parameters than deterministic checkpointing • Define expected-reliability to embody the mobility characteristic introduced by handoff • Analyze the message sojourn time in Access Bridge with fives dispatch models

  46. Future Work • Relax some assumptions to derive more general program execution time • Failures may not be detected instantly • Further the expected-reliability analysis to include links failures. The reliability with multiple terminals will be considered • Provide fault tolerance mechanism for other mobile environments, such as ad-hoc mobile networks and sensor networks

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