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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

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
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

introduction
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
introduction4
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
web hosting facility
Web-Hosting Facility

Internet

Hosting Center

Users

Web-App

web hosting model
Web-Hosting Model
  • Benefits:
    • Economy of scale: Resource sharing means increase in utilization and better availability
    • Web-App shielded from over-provisioning
web hosting optimisation
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
web hosting optimisation8
Web-Hosting Optimisation
  • Server Allocation Problem: Allocate servers among web-Apps to “maximize” revenue
server allocation problem
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
honey bee colony
Honey Bee Colony
  • Approx. 20-50 thousand bees in a colony
  • One queen
  • Few drones
  • Rest workers
honey bee colony11
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
honey bee colony12
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
forager allocation problem
Forager Allocation Problem
  • Forager Allocation Problem: Allocate forager bees among flower patches to “Maximize” nectar intake
problem mapping
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
problem mapping15
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
problem mapping16
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
problem mapping17
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
forager allocation mechanism
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)
forager allocation mechanism19
Forager Allocation Mechanism:
  • Feedback sets threshold for enlisting signal (Waggle Dance)
  • Profitability + signal threshold = Waggle dance duration
forager allocation mechanism20
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
f i x i return from x i bees at patch i max i f i x i s t x i 0 i x i n
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
properties of heuristic solution from bstv 93
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

solution mapping
Server Allocation

Advert

Advert Board

Advert Duration

Reading an Advert

Forager Allocation

Waggle Dance

Dance Floor

Dance Duration

Following Waggle Dance

Solution Mapping
simulation model honey bee
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

simulation model greedy
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

simulation model greedy26
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)

simulation model others
Simulation Model: Others

Web-App: A

Users: A

New Policy

Offline Omniscient

Computation

Repurpose

Migrate

Users: B

New Policy

Web-App: B

simulation model omniscient optimum
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))}

omniscient optimum computation
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

simulation model optimal static
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)

conclusions
Conclusions
  • Bee heuristic: works well, effective in highly dynamic environment
  • Competitive against standard heuristics
  • Bee heuristic: Not tuned, Common sense scaling parameters used
conclusions39
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
conclusions40
Conclusions

Patch II

Patch I

900

500

Nectar intake increases if:

899

501

future work
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
some other interesting stuff
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
some big or questions in natural systems
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