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Dynamic Hot-Potato Routing Algorithm for Fully Utilizing Network Links

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This paper presents a novel dynamic routing algorithm that operates without flow control, ensuring all free links in a network are utilized effectively. By adopting hot-potato routing principles, packets are injected continuously and forwarded immediately, optimizing delivery times. The algorithm guarantees injection time while allowing for rapid conflict resolution among packets through states such as running, excited, and sleeping. Our analysis covers time efficiency, stability, and future enhancements needed for arbitrary network topologies devoid of randomization.

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Dynamic Hot-Potato Routing Algorithm for Fully Utilizing Network Links

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  1. Routing without Flow ControlCostas BuschRensselaer Polytechnic InstituteMaurice HerlihyBrown UniversityRoger WattenhoferMicrosoft Research

  2. The network: mesh • Discrete time • Bi-directional links • At most one packet per link direction

  3. Dynamic Routing: Packets are injected continuously destination

  4. A new packet can be injected when there is a free link: A link direction is empty

  5. Most dynamic routing algorithms use flow control: Don’t utilize all the free links Disadvantage: Network is under-utilized

  6. Our Routing Algorithm: • No flow control • Utilizes all the free links Advantage: Network is fully-utilized

  7. Features of our algorithm: • Dynamic • Hot potato • Optimal delivery time: • Injection time guaranty:

  8. Talk Outline • The Algorithm • Time Analysis • Stability • Future Work

  9. Hot-Potato Routing: • Nodes are buffer-less • Packets are immediately forwarded

  10. Conflicts

  11. Conflicts Conflict

  12. Conflicts Deflected

  13. Priorities: high low Packet states: Running Excited Active Sleeping

  14. Sleeping packet destination Random destination

  15. Sleeping packet destination Follows a path to destination

  16. Sleeping packet becomes Active with probability

  17. Active packet Follows a greedy path

  18. Active packet Follows a greedy path

  19. Active packet A conflict situation

  20. Active packet Conflict A conflict situation

  21. Active packet Deflected A conflict situation

  22. Active packet becomes Excited with probability Deflected A conflict situation

  23. Excited packet Follows a one-bend path

  24. Excited packet becomes Running Follows a one-bend path

  25. Running packet Follows a one-bend path

  26. Talk Outline • The Algorithm • Time Analysis • Stability • Future Work

  27. Good condition for a column: at most non-sleeping packets with destination in the column

  28. Expected delivery time for one packet: (when the destination column is in good condition)

  29. In expected time steps becomes active We will show: An active packet is delivered in expected time steps Initially a packet is sleeping

  30. Interrupting a one-bend path Excited Time 1

  31. Interrupting a one-bend path Running Time 2

  32. Interrupting a one-bend path Excited Running Time 2

  33. Interrupting a one-bend path Running Running Time 3

  34. Interrupting a one-bend path Running conflict Running Time 4

  35. Interrupting a one-bend path deflected Active Running Time 5

  36. No interruption probability: Excitement probability Number of non-sleeping packets with destinations in same column

  37. No interruption probability: constant (when the destination column is in good condition)

  38. Expected number of deflections until success: Expected delivery time for an active packet: Probability of success after a deflection:

  39. Talk Outline • The Algorithm • Time Analysis • Stability • Future Work

  40. Divide time in time periods: Examine the condition of a column

  41. 1 time period Good condition Bad condition

  42. 1 time period Good condition Bad condition 4n time periods

  43. 1 time period Good condition Bad condition

  44. Proof Outline In a time period: • At most new non-sleeping • packets are generated with • destinations in the column • At least non-sleeping packets • are delivered (if )

  45. Good condition Bad condition 4n time periods

  46. Proof Outline In a time period: • At most new non-sleeping • packets are generated with • destinations in the column • At least non-sleeping packets • are delivered

  47. Consequences: • Most of the time, the columns • are in good condition • Each packet is delivered in • expected time

  48. Talk Outline • The Algorithm • Time Analysis • Stability • Future Work

  49. Arbitrary network topologies • De-randomization: • Determistic destinations • No randomized algorithm • Small number of packets

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