la-ur-03-8665 approved for public release; distribution is unlimited title: sequential dynamical...
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LA-UR-03-8665Approved for public release; distribution is unlimited
Title: Sequential Dynamical Systems, Socio-Technical Simulations and Interaction Based Computing
Author: Madhav M. Marathe
Submitted to: IMA, Minneapolis, MN
Los Alamos National Laboratory
Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the University of California for the U.S. Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory request that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher’s right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.
Form 836(8/00)
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Sequential Dynamical Systems, Socio-Sequential Dynamical Systems, Socio-Technical Simulations and Interaction Technical Simulations and Interaction
Based ComputingBased Computing
Madhav V. MaratheBasic and Applied Simulation Science (CCS-5)
Los Alamos National [email protected]
Joint work with: H.B. Hunt III, S.S. Ravi, D.J. Rosenkrantz and R.E. Stearns (SUNY-Albany)
and group members in CCS-5
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Urban Infrastructure Suite: Interdependent Infrastructure Simulations
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Sequential Dynamical Systems (SDS)
nor3(x1,x2,x3) = (x1 x2 x3),
–Local functions (e.g. Boolean): correspond to agent or entity decision rules.
–Dependency graph: represents inter-agent communication capabilities.
–Partial orders (permutation): capture the update order of agent updates
GraphGraph
Phase space Phase space withwith
Л= Л= (1,2,3,4)(1,2,3,4)
Phase space withPhase space with
Л= (1,3,2,4)Л= (1,3,2,4)
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Why Computational SDS (cSDS)
• Motivation:
– Size: 107 travelers, 109 nodes, 109 transceivers & 1012pkts/hr
• Efficiently scalable on HPC. Usual agent based concepts do not
scale
– Composed of smaller heterogeneous, inter-operable simulations
– Need to formalize simulation methods (esp. ST simulations)
• cSDS: Enabling Idea-- local functions can be viewed procedurally
– Computational cost and semantics of implementing simulations
– A formal framework for design, analysis and specifications of socio-
technical simulations
– A bridge between a mathematical theory of simulation and HPC algorithm design and implementation
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Examples: CA Based Simulation of Roadway Traffic
7.5 meter 1 lane cellularautomaton grid cells
intersection with multipleturn buffers (not internallydivided into grid cells)
single-cell vehicle
multiple-cell vehicle
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ResultsComputational Complexity and
Tractability
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Modeling & Computational Power of SDS
• Simple SDS are Universal Computing devices
– SDS as formal systems encompass such models as Hopfield networks, cellular automata, communicating finite state machines, etc
– capable of simulating Turing machines for all “natural” complexity classes
• Are simulations optional : NO ( often no shorter computation possible)
• Simple interactions with simple local functions are intractable (Global algorithms are intractable: e.g. Reachability)
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Example: REACHABILITY Problem (RP)
• REACHABILITY Problem : Starting from a configuration P can SDS S reach
a configuration T in less than r steps ?
• Dichotomy based on local functionsDichotomy based on local functions
– RP for SDS is PSPACE-hard when
• all nodes have identical symmetric Boolean function
• A fixed permutation is used to update the local states
• graph is constant degree & bandwidth bounded (fixed radius size)
– RPT for SDSs is in P when each local function is
• Boolean Symmetric and Monotone (threshold):
• individual nodes need no have same local function.
• Ordering need not be strict so far as it is fair
• Interaction graph can be arbitrary
– Corollary:Transient lengths < O(# of edges), no limit cycles > 1 threshold
SDS
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Basic Technique: Local Simulations
SS
SS11
Local Transformation of the interaction Local Transformation of the interaction graphgraph
•Structure Preserving Local Transformations
• Very Efficient and Distributed
•Phase Space of S is embedded in the phase space of S1
c & F (c): configurations of Sc & F (c): configurations of S
c’ & F(c’): configurations of Sc’ & F(c’): configurations of S11
Each node replaced by a Each node replaced by a constant # of nodesconstant # of nodes
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Local Inter-simulations: SDS Compliers
SynchronousSynchronous
Finite arityFinite arity
Simple pathSimple path
SynchronousSynchronous
Boolean SymmetricBoolean Symmetric
Bandwidth boundedBandwidth bounded
SequentialSequential
Boolean SymmetricBoolean Symmetric
Bandwidth boundedBandwidth bounded
SequentialSequential
Boolean SymmetricBoolean Symmetric
Identical functionsIdentical functions
Bounded degreeBounded degree
Bandwidth boundedBandwidth bounded
DeterministicDeterministic
Space BoundedSpace Bounded
LBALBA
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Results
Parametric Local Algorithms
Example: Local Provable Algorithm for
Contention Resolution at MAC layer
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Distance-2 Interference in 802.11
• Two way transmission needed in 802.11
• s to t transmission received at x y cannot transmit
• w to a transmission received at t w cannot transmit
• No transmission on edges within distance-2 of (s,t) in interference graph
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Network Capacity: Distance-2 Matching
Transceivers on a plane with identical power levels: capacity of this network is 2
Red edges are not within distance 2. Similarly nodes a and f are not within distance 2.
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Network Capacity and MAC layer scheduling
• Efficient provable methods for computing the instantaneous media-
access layer capacity of ad-hoc networks
– Concentration results for computing capacity in Erdos Renyi
random graphs and geometric random graphs.
– Alternative proof of network capacity
• Distributed provable protocols for MAC layer scheduling
– Extension to MAC-aware routing protocols (designing unified
protocols for routing and scheduling)
Theorem: A local algorithm running in O(log n) rounds can compute a
constant factor approximation for the disance-2 matching in a unit
disk graph
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Distributed vs Sequential Algorithm: Performance Comparison
• Large fraction of edges selected in the first few roundsLarge fraction of edges selected in the first few rounds
• Size of matching is within 4 times the optimalSize of matching is within 4 times the optimal
• Number of rounds required is quite smallNumber of rounds required is quite small
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Network Capacity and Topology
• MAC layer capacity critically depends on topology
• Protocols need to be optimized for specific topologies
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ILLUSTRATIONAdHopNet: Simulation Based
Analytical Tool for 3G+ Telecommunication Networks
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Urban Infrastructure Suite: Interdependent Infrastructure Simulations
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Schematic of a Hybrid Communication Network
System MobilityUPMoST Technology
Radio Packet Network:SORSRER
Wireline/BasestationNetwork
Satellite Network
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Functional Design of AdHopNet
Device Generator
Session Generator
PacketSimulator
TopologicalGraph Module
UPMoST Module
UPMoST Entities
Filter
UPMoSTData File
Survey Data
DeviceMobility
Device Data
Device Data
PolygonDefinitionsOptional
Device Status
Session File
Graph File
Packet Stream
Packet Data
ANALYSIS
Survey Data
Topography Data
Occlusion Data
Graph Data
Packet Twist
PacketDuplication
NetworkDynamics QoS
RESTORED
NetworkAnalysis
DynamicsAnalysis
Vulnerability Analysis
Packet Stream
Packet Data
Graph Data
LARGE-SCALE ANALYSIS AND MEASUREMENTS
AdHopNet
UPMoST
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Module 1: Device Assignment
Cell phone/PDA
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Activity variation in time
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Mobile Entities Colored by Age
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Module 2: Session Generation
John DoeJohn Doe
•In carIn car
•Age = 34Age = 34
•Income > $26kIncome > $26k
Jane SmithJane Smith
•At WorkAt Work
•Age = 57Age = 57
•Income > $100kIncome > $100k
Video stream, 14.5 kbps, 3.48 minutes
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Cell Assignment
Coverage region
Base Station
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Locations at which devices begin active sessions
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Connections between devices
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Active connections in each cell (BTS load)
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Handoffs per second per cell
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Module 3: Dynamic Construction of (interaction) Network
Timestep: 200
Transceiver connectivity at an instant in time after executing MAC layer protocol.
radio range
radioOcclusionNo No connection
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Enlarged view of the focused area
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Simulated Cars using TRANSIMS
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Dynamic Ad-hoc Network of Transceivers on Cars
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Ad-hoc Network as broadcast radius increases
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Variation in Clustering Coefficient (CC) with Node degree in TRANSIMS and Random Way Point Generated Networks
Mobility Models Matters for Ad-hoc NetworksMobility Models Matters for Ad-hoc Networks
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Mobility Models Matter: Degree Distributions
SD: Structured DistributionSD: Structured Distribution
RD: Random DistributionRD: Random Distribution
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Mobility Affects Protocol Performance: Packet Delivery Success Rate
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Module 4: Packet Simulator
• Connecting in and out-channels in a network of three transceivers. Left: Network
- Middle: Channel connections.
• Internal functions f1, f2 and f3.
• Each function is a composition of functions representing the MAC layer, the
routing layer and the transport layer.
• Resulting function: f3 o f2 o f1
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Parametric Routing and Scheduling in AdHopNETF
lood
ing
Des
tinat
ionA
ttra
ctor
Dire
cted
Tra
nsm
issi
on
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RESTORED: Receiver Oriented Stochastic Re-generation of Data
Module 5: RESTORED: Constructing Smaller Monte-Carlo Simulations
kk
kkk
kkk
tj
iij
arctan
1
0
1
(index distortion)
(time and index distortion)
(phase angle)
Packets sent at rate 1/0, ik is index of kth packet arriving at destination
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Unified view of Computing and Simulations
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A Unified view of Computing and ST systems: Interaction based Representation
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Natural Questions with this perspective
• Algorithmic Semantics: What are we computing ? Traditional View: How to
compute
– What does a market Compute ?
– What are the semantics of TCP ?
• Computational Complexity: How hard is it to compute/design global system
properties
– Who will be sick after 5 days of an epidemic
– How can we design local functions so that a given algorithmic semantic
is implemented
• HPC Implementation: How can we implement our abstraction efficiently
(distributed algorithms)
– Paralel (parametric, approximate, local, efficient) Algorithms
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A Unified theory of Computing and Simulations ?
• Unified approach for the entire spectrum of computing
– Nanoscale computing to Grid Computing
– Next generation computing systems are formally speaking simulations
• Unified approach for specifying and analyzing large scale socio-technical
simulations
• (Prof. Abramsky):There is a unified science of information embracing both
``artificial'' and ``natural'' computation
Modified Thesis: There is a unified science of computing and simulations
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Summary
• First Steps in a Computational theory of SDS (and Simulations)
– Computational Complexity
– Designing Efficient HPC capable local algorithms
– Algorthmic Semantics & Formal Specifications of Simulations
• SDS and their generalizations can be used to design, specify and
analyze the socio-technical simulations that such as AdHopNET
• Open Questions:
– Complexity of REACHABILITY problem for NOR SDS
• Is NOR Universal local function ? Conjecture: PSPACE-hard.
– Complete Characterization of complexity of Predecessor
existence Dichotomy result
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Interdependent Infrastructure and Social Systems: Interdependent Infrastructure and Social Systems:
Transport NetworkTransport Network
Wireless Ad-hoc Network
Social Contact Network
Portland Power Grid