Is OBS Void Filling Necessary

1
Is OBS Void Filling Necessary?

• Lachlan Andrew
• with Stephen Hanly, Jolyon White and Hai Vu

2
Outline

• Review of Optical Burst Switching
• Causes of Voids
• Offset times
• QoS separation
• Long Offsets are Unnecessary
• Most voids are short
• Filling short voids gains little

3
Review of OBS

• Bufferless
• WDM
• Wavelength conversion needed for tolerable
  utilisation
• Far future technology
• Hundreds of wavelengths
• Header sent in advance to allow setup
• Offset of header reduces along a path

4
Causes of voids
New arrival
Now
Offset
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Causes of Voids -- QoS

• Longer offsets give higher priority
• First header wins
• Less blocking

6
Causes of Voids -- QoS

• Longer offsets give higher priority
• First header wins
• Less blocking
• Very long offsets proposed
• Many times mean burst length
• Void filling
• schedule new bursts into voids

7
Long offsets not necessary

• WDM systems will have many wavelengths
• Law of large numbers
• Assume arrival rate ? wavelengths
• Small offsets ? big difference in blocking
• Show this in two scenarios
• Little high priority traffic, Exponential burst
  lengths
• Bounds for the general case

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1 -- very little high-priority traffic

• Low priority all full at time t
• High priority all still full at time t?
• Assume memoryless burst durations

t?
t
k
Low offset
High offset
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1 -- very little high-priority traffic

• Remaining times are independent
• belong to independent bursts, independent of the
  past
• Let h Pr(burst still going at t? going at
  t)
• P(block, hi) / P(block, lo) hk

t?
t
h
k
Low offset
High offset
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2 -- general case

• High priority bursts may also be blocked by other
  high priority bursts
• Can bound ratio Pr(hi)/Pr(lo)
• Similar to Dolzer et al. (2001)
• Pr(hi) lt Erlang (hi p lo)
• p Pr (burst length gt ?)

hi
hi
k
t
t?
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2 -- general case

• High priority bursts may also be blocked by other
  high priority bursts
• Can bound ratio Pr(hi)/Pr(lo)
• Similar to Dolzer et al. (2001)
• Pr(hi) lt Erlang (hi p lo)
• p Pr (burst length gt ?). Ignores blocking
• Pr(lo) gt Erlang (hi lo)
• Priority cant help low priority bursts
• Bound very loose for small offsets

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Results 1 -- 3 high-priority traffic

• 77 load
• 3 high priority
• 20 wavelengths
• exponential burst lengths

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Results 2 -- 10 high-priority traffic

• 77 load
• 3 high priority
• 20 wavelengths
• exponential burst lengths

14
Large offsets not necessary

• Voids caused by offset times
• Void can be no longer than maximum offset
• With many wavelengths, large offsets not needed
  for priority
• Burst segmentation a better form of priority
  anyway
• Still some offset needed for routing
• Much shorter than a burst

15
Most voids are short

• Voids cannot be longer than offsets
• Can be much shorter
• Use wavelength which becomes free just before
  burst arrives
• Intuitively, more wavelengths ? less gap

k
High offset
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Most voids are short
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Most voids are short
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Voids are M/M/1 busy periods

• Void times can be bounded by the busy period of
  an M/M/1 queue
• Does not require exponential burst lengths
• With probability ?1, voids length is O(1/k)
• Void bounded by ?
• Average void length tends to zero
• Complicated first-principles proof
• Thin events from Poisson processes to get
  independence
• Simpler proof possible?

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Burst segmentation analogy

• Burst segmentation If all wavelengths busy,
  overwrite the burst with least remaining

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Burst segmentation analogy

• Burst segmentation If all wavelengths busy,
  overwrite the burst with least remaining
• Overlap between bursts becomes small
• Rosberg, Vu, Zukerman (2003)
• Analysed in terms of M/G/k/k and M/G/? queues
• Void corresponds to burst overlap
• Not sure if the analogy can simplify our proof
• M/M/1 analogy may give distribution of overlap ?
  priority

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Filling short voids gains little

• Each void is O(1/k)
• Arrival rate O(k)
• O(1) total void time
• Many small voids are hard to fill
• Total void actually filled is O(1/k)
• With exponentially distributed burst lengths and
  reasonable approximations
• Fractional capacity increase is O(1/k2)

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Some voids are long

• M/M/1 Busy periods have thick tails
• Some voids will be long
• Void filling can record only long voids
• Most gain with least pain
• Even if void filling is used, analysis of systems
  without void filling may be useful.

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Conclusion

• OBS does not need long offsets
• Mean void times are small
• Most voids cannot be filled
• Void filling is unnecessary

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Conclusion

• Yes, I know that OBS itself is unnecessary