Discrete Event System Modeling and Simulation in Metropolis

1
Discrete Event System Modeling and Simulation in
Metropolis

• Guang Yang
• 12/10/2004

2
Outline

• Separation of Capability and Cost
• Quantity Manager and Quantity Annotation
• Discrete Event Systems in Metropolis
• Discrete Event Systems Simulation
• Challenges
• Conclusion and Future Work

3
Capability v.s. Cost

• One of the pairs of concerns whose
  orthogonalization increases model reusability
• Capability a sequence of events
• Cost captured by various quantities

Instruction Set
4
Capability v.s. Cost in TSM

• Capability
• Cost

(v1, ?) (v2, ?) (vn, ?)
m-event tag ?
(v1, 0) (v2, ?) (vn, 10)
costs correspond to tags
5
Quantity Annotation Quantity Manager

• Quantity Annotation

(v1, ?)
(v1, 0)

• Quantity Manager
• Data type
• Functions
• Axioms

6
Discrete Event Systems in Metropolis

• Tag is the key

Process 1 (v11, 0) (v12, ?) (v1n, 10)
Process 2 (v21, ?) (v22, 4) (v2n, 8)
Process 3 (v31, 2) (v32, 5) (v3n, ?)
7
Discrete Event Systems Simulation

• Formally,
• N processes p1, p2, , pN
• N m-event sequences me1, me2, , meN
• Annotated tag for the ith m-event in mej
  , Tmej(i)
• The most recent but prior to the ith annotated
  m-event in mej
• The next annotated m-event in mej after the ith
  m-event

8
DES Simulation (cont)

• is the segment of
  m-events that could be interleaved with other
  m-events from other processes
• In order for and
  
• to be arbitrarily
  interleaved, the following condition must be
  satisfied
• The end point e.g. can join
  the interleaving if it falls into the other
  segment

9
DES Simulation (cont)

• Simulation proceeds round by round.
• At each round, each process issues one m-event or
  event.
• Based on time tags information and other
  constraints (e.g. mutual exclusion,
  simultaneity), disable some of (m-)events and let
  the rest run.

10
DES Simulation (cont)

• An example

Process 1 (v11, 0) (v12, ?) (v1n, 10)
Process 2 (v21, ?) (v22, 4) (v2n, 8)
Process 3 (v31, 2) (v32, 5) (v3n, ?)
11
Challenges

• No history information
• ? No rollback
• No future information
• ? Cannot avoid rollback if do blind interleaving

12
Solution

• Postpone interleaving until there is enough
  information
• Whenever there is a m-event, let it run.
• Resolve time quantity only if all processes come
  to events or m-events get stuck

13
Example
Process 1 (v11, 0) (v12, ?) (v1n, 10)
Process 2 (v21, ?) (v22, 4) (v2n, 8)
Process 3 (v31, 2) (v32, 5) (v3n, ?)
14
Solution

• Postpone interleaving until there is enough
  information
• Whenever there is a m-event, let it run.
• Resolve time quantity only if all processes come
  to events or events get stuck
• Works but not so efficient
• Waste on constraint resolution
• Increase the number of simulation rounds

15
Get hints from designers

• Identify regularities in the tags
• Periodical tasks
• Tasks with latency/rate constraints
• Introduce built-in logic of constraints (LOC)
• to be able to predict future
• period(event, p)
• maxrate/minrate(event1, event2, r)
• maxlatency/minlatency(event1, event2, r)

16
Quantity Annotation Quantity Manager

• Quantity Annotation

(v1, ?)
(v1, 0)

• Quantity Manager
• Data type
• Functions
• Axioms

Built-in LOC
17
Experiments
P0 write(w) (10)
C read() (15)
M
P1 write(w) (10)
18
Simulation Statistics

• Postpone interleaving
• Number of Scheduling Rounds Done by Simulation
  Manager 2120
• Average Number of RUN Processes Scheduled per
  Scheduling Round 1.25283
• Total Simulation Time 280000 us
• Built-in loc
• Number of Scheduling Rounds Done by Simulation
  Manager 1168
• Average Number of RUN Processes Scheduled per
  Scheduling Round 1.49914
• Total Simulation Time 190000 us

19
Conclusion and Future Work

• Formally analyze the simulation strategy
• Identify problems in terms of simulation
  efficiency
• Discuss the possible solutions
• Future work
• Are there better solutions to the efficiency
  problem?
• How to co-simulate Metropolis DES with external
  CT/Hybrid system simulators?

20
Thank you!!! Questions?