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Dynamic Allocation in Honey Bee and Internet Server Colonies

Dynamic Allocation in Honey Bee and Internet Server Colonies. Sunil Nakrani, Computing Lab., University of Oxford, England, UK Craig Tovey, ISyE, Georgia Institute of Technology, Atlanta, USA. Natural Systems Research & Education.

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Dynamic Allocation in Honey Bee and Internet Server Colonies

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  1. Dynamic Allocation in Honey Bee and Internet Server Colonies Sunil Nakrani, Computing Lab., University of Oxford, England, UK Craig Tovey, ISyE, Georgia Institute of Technology, Atlanta, USA

  2. Natural Systems Research & Education • Honey bee colony foraging (Bartholdi, Seeley, Tovey & VandeVate, J. Th. Bio. 1993); food storing to cue nectar intake (Seeley & Tovey, Animal Beh. 1993) • Dominance hierarchy formation (Chase, Tovey, et al., Proc. Nat. Acad. Sci 2002, Behaviour 2003); natural selection mechanism • Biomimetic heuristic for allocating resources in a web-hosting facility (Nakrani & Tovey, Proc. MASI II, 2003) • Time lags and overdiscounting of environmental costs, hedging value of environmental investments; replacement policies under technological change (Regnier, Sharp & Tovey, IE Trans.) • Assessing systems (Tovey, Ausenda); adjusting GDP for natural systems deterioration • Sustainability intro in sophomore course (2030); topics course on root causes of env. problems and sustainability (4833); stat and design sustainability projects OR -> BIO BIO -> OR OR -> ENV

  3. Introduction • Web-Hosting Facility • Rationale • Benefits • Server Allocation Problem: allocate servers amongst web-apps to maximize revenue • Honey Bee Colony: allocate foragers amongst flower patches to maximize nectar intake

  4. Introduction • Approach: Honey Bee Heuristics-waggle dance • Map web-apps to flower patches, servers to bees • Solution Mapping: dance floor--> advert board • Algorithms and Simulation Model • Results • Conclusions, biological insight • Future work

  5. Web-Hosting Facility Internet Hosting Center Users Web-App

  6. Web-Hosting Model • Benefits: • Economy of scale: Resource sharing means increase in utilization and better availability • Web-App shielded from over-provisioning

  7. Web-Hosting Optimisation • Web-App: pay-per-use Service Level Agreement (SLA) • Hosting Center: Allocate servers among Web-Apps to “maximize” revenue (s.t. changeover downtime) • Users: Unpredictable and highly variable request pattern

  8. Web-Hosting Optimisation • Server Allocation Problem: Allocate servers among web-Apps to “maximize” revenue

  9. Server Allocation Problem • Current Techniques: Threshold and Ad-hoc Rule based, Continuous tracking of load metrics by large operations staff, Manual management • Static provisioning altered approx. once a month • Current Literature– Jayram et. al. (2001), Chase et. al. (2001) • Commercial Domain: Proprietary methods

  10. Honey Bee Colony • Approx. 20-50 thousand bees in a colony • One queen • Few drones • Rest workers

  11. Honey Bee Colony • Typically requires 60 lb of honey per year to survive • 25% of workers engaged in food collection (nectar, pollen) • Exploit food sources (flower patches) from surrounding countryside

  12. Honey Bee Colony • Flower Patches: • Availability varies daily and seasonally; • Quality depends on exploitation, flower type, micro-climate etc.. • Round trip time (nectar collection time) • Colony: Exploit flower patches efficiently to satisfy nectar requirement

  13. Forager Allocation Problem • Forager Allocation Problem: Allocate forager bees among flower patches to “Maximize” nectar intake

  14. Server Allocation Problem: Single Server Web-Apps + User Group of servers (cluster) serving users at one web-app Forager Allocation Problem: Forager Bee Flower Patches Group of foragers collecting nectar at a specific flower patch Problem Mapping

  15. Server Allocation Problem: Request service time depends on Web-App Find a user to serve Forager Allocation Problem: Travel Time depends on Flower Patch Nectar collection time at the patch Problem Mapping

  16. Server Allocation Problem: Value-Per-Request-Served Varying rates of user request arrivals and balking behaviors Forager Allocation Problem: Nectar quality (sugar content) Varying flower patch density, quality, and replenishment rate Problem Mapping

  17. Server Allocation Problem: Server Migration Time (purge current Web-App and load new Web-App) Forager Allocation Problem: Time to learn the location of the flower patch and successful discovery (Seeley, T.D.) Problem Mapping

  18. Forager Allocation Mechanism • Active foragers return to the hive with nectar and profitability rating of the visited flower patch • Interact with food-storer bees to offload nectar (waiting time provides feedback on nectar flow into the hive)

  19. Forager Allocation Mechanism: • Feedback sets threshold for enlisting signal (Waggle Dance) • Profitability + signal threshold = Waggle dance duration

  20. Forager Allocation Mechanism: • Waggle dance performed just inside the hive entrance (Dance floor) • foragers follow dance to learn flower patch location • Suboptimal allocation in static sense

  21. OPTIMUM fi0(xi) = l8 i2 A xi = 0 8 i Ï A equalize marginal return at active patches BEE HEURISTIC fi(xi)/xi = m8 i2 A xi = 0 8 i Ï A equalize average return at active patches fi(xi) ´return from xi bees at patch i Max åi fi(xi) s.t. xi¸ 0åi xi· N

  22. Properties of Heuristic Solution(from BSTV 93) Usually not optimal Factor-2 approximation even under very weak conditions Convergence proved by potential function argument Validated experimentally in a honey bee colony

  23. Server Allocation Advert Advert Board Advert Duration Reading an Advert Forager Allocation Waggle Dance Dance Floor Dance Duration Following Waggle Dance Solution Mapping

  24. Simulation Model: Honey Bee Web-App: A Post/Read Adverts Users: A Web-App ID Duration Time Advert Board Repurpose Migrate Web-App ID Duration Time Users: B Post/Read Adverts Web-App: B

  25. Simulation Model: Greedy Web-App: A Users: A New Policy Compute optimal policy for next interval based on present queue status, present allocation, and user arrival from last interval Repurpose Migrate Users: B New Policy Web-App: B

  26. Simulation Model: Greedy St = state of world at start period t (customers,servers) At = arrivals (times, types) in period t P(p, S, A) = profit using p from state S with arrivals A f(p,S,A) = next state of world using p from S with arrivals A ptG = arg maxp P(p, St, At-1) St+1 = f(ptG, St, At)

  27. Simulation Model: Others Web-App: A Users: A New Policy Offline Omniscient Computation Repurpose Migrate Users: B New Policy Web-App: B

  28. Simulation Model: Omniscient Optimum S=state, A=arrival, P( )=profit, f( )=next state A1,L, An known vn+1(Sn+1) = 0 (no salvage value) vt (St) = maxp{P(p,St,At) + vt+1(f(p,St,At))} ptOpt(St) = arg maxp {P(p,St,At) + vt+1(f(p,St,At))}

  29. Omniscient Optimum Computation • Parallel implementation runs in 24 hours • Discretized space of possible states • Inner loop function that we maximize is theoretically concave … … but not concave numerically

  30. Simulation Model: Optimal-Static S=state, A=arrival, P( )=profit, f( )=next state A1,L, An known s.t. St+1 = f(p, St, At)

  31. Test Case: Synthetic User Load

  32. Test Case: Real Internet Trace

  33. Result: Synthetic User Load

  34. Result: Internet Service Trace Load

  35. Adaptability to Synthetic Variable Load

  36. Synthetic Load: Low Variability

  37. Conclusions • Bee heuristic: works well, effective in highly dynamic environment • Competitive against standard heuristics • Bee heuristic: Not tuned, Common sense scaling parameters used

  38. Conclusions • Trade-off static optimality for responsiveness • Static optimization requires equalization of derivatives (marginal rate bee) • Bee heuristic has no marginal “bee” but, instead, has ability to migrate several “bees” at the same time and avoids problem of measuring f’ under variability

  39. Conclusions Patch II Patch I 900 500 Nectar intake increases if: 899 501

  40. Future Work • Test to see if we were lucky or robust • Scale up to more patches/web-apps • Make autonomic --more feedback loops • Power … imitate indolent bees? • Convergence rates • Compare with IBM’s online network algorithm

  41. Some other interesting stuff • Dominance hierarchies: first experimental validation of a self-organizing social structure in animals (Chase, Tovey, Martin & Manfredonia 02) • Time lags of environmental costs: mean 10 years vs. mean 5 years for other types. (Regnier & Tovey) • Opportunities for Sr. Design sustainability projects

  42. Some Big OR Questions in Natural Systems • Individual versus group selection: classic argument against latter is essentially an OR proof, but why do forests thrive? • Discounting and EPV, intergenerational equity and intraperiod utility. Relationship to future growth? Intraperiod utility and discounting is almost equivalent to linear utility, Sobel 2000

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