Transforming DEVS to NonModular Form For Faster Cellular Space Simulation

1
Transforming DEVS to Non-Modular Form For Faster
Cellular Space Simulation
Fahad A. Shiginah, Bernard P. Zeigler
shiginah, zeigler_at_ece.arizona.edu

• Arizona Center for Integrative Modeling and
  Simulation
• Electrical and Computer Engineering Department
• University of Arizona

2
Content

• Introduction
• Cellular Space Modeling
• Cellular Models in DEVS
• The New Approach for Message Reduction
• Transforming to Non-Modular DEVS
• Experimental Results
• Conclusions

3
Introduction

• DEVS has been attracting researchers as a basis
  of Cellular modeling in complex physical systems.
  
• Parallel DEVS made it possible to implement
  cellular models in DEVS.
• DEVS models are modular units that can access
  the states of other models through message
  passing.
• Representing cellular spaces in modular DEVS
  resulted in having cells communicating with each
  other to know neighboring states.
• In large scale cellular space, huge number of
  inter-cell messages will be employed which result
  in performance reduction.
• To overcome this problem, the non-modular form of
  DEVS should be consider as an alternative for
  faster large cellular space simulations.

4
Cellular Space Modeling

• 2-D Physical space is discretized spatially in
  x-y axis
• Depending on the resolution required, it will be
  divided into N N cells.
• Each cell covers a small space in which it carry
  out computations to find its next states based on
  its current state as well as neighbors states.

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Cellular Models in DEVS
N

• A cell is implemented as DEVS atomic model.
• The whole cellular space will be a
  coupled/hierarchical model containing all cells
  (atomic models).
• Modularity in DEVS allow cell to communicate
  through ports only.
• Each cell calculates its next state based on its
  current state and external inputs from neighbors
  (if exists at ports).
• All cells run in parallel (Parallel DEVS)
• Simulation continues until all cells are in
  passive mode or reaches a predefined stopping
  point.

N
6
Encapsulation Scheme

• Our goal is to reduce number of inter-cell
  communication.
• The new encapsulation will divide the cellular
  space into smaller subspace.
• Each subspace will encapsulate a group of cells.
• In each subspace, cells will be arranged in
  arrays to preserve their states and variables
  where they can access their neighbors states
  directly.
• This eliminates the ports and messages between
  all cells in one subspace where ports will be
  needed at the boundaries of the subspace only.
• Now, subspace is implemented as DEVS atomic model
  having ports to carry out the communication
  between cells at the boundaries.

N
N
7
Messages in conventional Approach
Figure 3. Message Reduction Approach. A cellular
space of N
In a cellular space of N N dimension, each
cell can send messages to its 4 neighboring cells
(Neumann neighbors). Assuming that in a single
iteration a cell will send V messages in each of
the 4 directions as the worst case scenario. The
conventional approach will result in 4VN2-4VN
messages per iteration given that the cells at
the boundaries will not send to at least one of
its neighbors.
N dimension can be divided into S
S subspaces. Each subspace will have (N/S)
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Message Reduction in Our Approach
That cellular space of N N dimension can be
divided into S S subspaces (Atomic DEVS) with
N2/S2 internal cells each. A subspace will just
send VN/S in each direction and the total number
of messages per iteration will be 4VNS-4VN given
that the subspaces at the boundaries will not
send to at least one of its neighbors. The
percentage reduction of messages will be
(N-S)/(N-1) which will result in 100 reduction
if S1 or 0 if SN.
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Review Parallel DEVS 1
M lt X,Y,S, dint, dext, dcon, ?, tagt X is a
set of input values. S is a set of states. Y is
a set of output values. dint S ? S is the
internal transition function. dext Q Xb ? S
is the external transition function, where Q
(s,e) s ? S, 0 e ta(s) is the total
state set e is the time elapsed since last
transition Xb denotes the collection of bags
over X dcon Q Xb ? S is the confluent
transition function, ? S ? Yb is the output
function ta S ? R 0 ? 8 is the time advance
function.
Atomic DEVS Model (M)
CMltX,Y,D,Mi,Ii,Zi,jgt X is the set of
input values. Y is the set of output values. D
is the set of components. for each i in D Mi is
a component which is an atomic model Mi lt Xi,
Yi ,Si , dint i , dext i , dcon i , ?i, taigt for
each i in D ? self Ii is the influencees of i,
i is not in Ii. self is the coupled model itself
CM which allow external inputs and outputs. for
each j in Ii Zi,j is the i to j output
translation function (coupling). Zself,j Xself
? Xj Zi,self Yi ? Yself Zi,j Xi ? Yj
Coupled DEVS Model (CM)
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Review Parallel DEVS (cont)
Closure Under Coupling
Every coupled DEVS model has a DEVS atomic
equivalent.
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Transforming to Non-Modular Form

• The encapsulation technique will require to
  convert a subspace (coupled model has group of
  cells) into its equivalent atomic model.
• This is the inverse process of transforming DEVS
  into modular form illustrated in 2.
• Cell ports are removed and all state variables
  arranged in arrays.
• Events handler will now take care of all
  activities inside these arrays.
• Activity scanner is employed so that active cells
  are scanned only.
• Equivalence to the original model insured.

12
Experimental Results

• A slope criticality landslide model (32 32) was
  implemented using our approach and run over
  DEVSJAVA Simulator (DJSim).
• Different runs were made to compare performance
  with variable size (S) of encapsulation.
• The runs were then repeated using new
  Activity-based DEVSJAVA Simulator (ADJSim),
  presented in 3, aiming to compare our modeling
  enhancement versus simulator enhancement.
• Results shows that in addition to the messages
  reduction, we saved a significant number of
  simulator iterations (at S1, 121569 it. saved).
• In addition, a speed up of around 50 was achieved
  when using our approach alone (DJSim at S1 )
  where using simulator enhancement alone (ADJSim
  at N32) gives 4 speedups compared to the
  conventional implementation (DJSim at N32).

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CONCLUSION

• The new approach significantly enhances the
  performance of cellular space simulation in DEVS
  because of the following
• Reducing inter-cell communications
• Reducing number of simulator iterations that
  deals with messages only.
• Efficiently scan active cells in the system only.
• Simulation restructuring does not deal with
  inter-cell messaging overhead. Therefore, both
  model and simulator enhancements must by employed
  together to simulate large scale cellular
  modeling environments.
• Best performance was achieved when all cells are
  in one atomic model. This may give a great
  enhancement in distributed cellular simulation by
  transforming the sub-cellular space in a single
  machine entirely into non-modular form.
• Further investigation is required to test our
  approach on large distributed cellular space
  simulation to justify this claim.
• The new approach can be applied to any other
  non-hierarchal cellular model. However, applying
  it manually is complex and error prone.
• An automated way of conversion needs to be
  implemented for fast, accurate conversion process.

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REFERENCES

• Chow, A.C., and Zeigler, B. P. 1994. Parallel
  DEVS a parallel, hierarchical, modular modeling
  formalism and its distributed simulator. In
  Winter Simulation Conference Proceedings,
  Orlando, FL.
• Zeigler, B. P., Kim T., and Praehofer, H. 2000.
  Theory of Modeling and Simulation Integrating
  Discrete Event and Continuous Complex Dynamic
  Systems. Academic Press.
• Hu, X., and Zeigler, B.P. 2004. A High
  Performance Simulation Engine for Large-Scale
  Cellular DEVS Models. High Performance Computing
  Symposium (HPC'04), Advanced Simulation
  Technologies Conference.