This document proposes a new modeling framework for simulating industrial production processes as continuous-time stochastic processes. The framework uses a base unit model that can represent work centers, buffers, or conveying units, and manages their working speed, accumulation, throughput time, and failures/repairs. Logical signals allow units to connect and trigger events based on parameter variations. The framework provides a more accurate representation of production flows compared to traditional discrete approaches, while avoiding increased computational effort from modeling at high resolution.

1. ON THE GENERALIZATION OF CONTINUOUS-TIME
STOCHASTIC PROCESSES
SIMULATION FOR INDUSTRIAL PRODUCTION MODELING
Fabio Bursi, Andrea Ferrara, Andrea Grassi, Chiara
Ronzoni
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)

2. • The objective
• The base unit model
• The working speed and accumulation
object
• The logic control object
• The throughtput time object
• Conclusions
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
OUTLINE

3. THE OBJECTIVE
• New modeling framework for the simulation of
• Flow manufacturing processes
• Manufacturing processes characterized by a high production
rate
• Typical approaches in simulating industrial processes:
• Flow discretization
• Identification of dummy units of material
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
Escape from system
complexity and
Less accuracy
Computational effort
proportional to the
productione rate
VS

4. THE OBJECTIVE
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
• Extention of a previous paper:
“Simulating Continuous Time Production Flows In Food Industry By Means
Of Discrete Event Simulation”.
Proceedings of the International Conference on Modeling and Applied
Simulation, 2013 ISBN 978-88-97999-23-2 Affenzeller, Bruzzone, De Felice, Del Rio,
Frydman, Massei, Merkuryev, Eds.
• Modeling framework able to:
• Represent the main units of a prduction system
• Trigger events corresponding to a status change or parameters
variations
• Manage "physical signals"
• Broadcast its functions to the downstream/upstream unit

5. THE OBJECTIVE
• Logical signals
• Connect couples of units
• Do not follow the production flow
• Are triggered by parameters variations
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
W1 W2
W4W3
B1
B3
Physical flow
Logical flow

6. THE OBJECTIVE
• Logical signals
• Connect couples of unit
• Do not follow the production flow
• Are triggered by parameters variations
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
0
0.5
1
1.5
2
2.5
values
time
Parameter k
A logical signal is triggeredThreshold 1
Threshold 2

7. Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
THE BASE UNIT MODEL
• It can behave as:
• Work centers
• Buffers
• Conveying units
• It is able to manage:
• Failures and repairs
• Working speed and accumulation
• Throughput time
• It changes the behaviour simply by the setting of variables
• It has the capability to generate and receive logical signals

8. • 2 type of signals:
• Physical signal
• Logical signal
• Dedicated I/O ports for each signal type
• Matrix of dependancies manages the paths
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
THE BASE UNIT MODEL

9. Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
THE BASE UNIT MODEL
• 2 type of signals:
• Physical signal
• Logical signal
• Dedicated I/O ports for each signal type
• Matrix of dependancies manages the paths

10. WORKING SPEED AND
ACCUMULATION OBJECT
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)

11. Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
LOGIC CONTROL
OBJECT

12. Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
LOGIC CONTROL
OBJECT
• m represents the base unit from which the input logical signal has been
sent;
• method is the events flow that need to be executed when an input
logical signal is received ;
• param is the involved parameter;
• t is the threshold achieved by the sending base unit;
• w = {up,down} represents the direction with which the threshold is
reached.

13. Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)
THROUGHTPUT TIME
OBJECT
• ‘V’ is a finite-dimensional vector where all thresholds values and physical
variables of the parameters are stored.
• ‘l’ is the vector V minimum value. It represents the minimun distance in
time to the next event.

14. CONCLUSIONS
• First modeling framework that can be used in the
Continuous-Time Stochastic Processes simulations.
• It can behave as:
• Workstations
• Buffers
• Conveying units
• It can manage:
• Failures and repairs
• Working speed and accumulation
• Throughput time
• Extention of this modeling framework by the
introduction of logical signals in order to allow the
system analyst to model the control mechanism to be
deployed in the system.
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)

15. THANK YOU FOR YOUR KIND
ATTENTION
Chiara Ronzoni – chiara.ronzoni@unimore.it
Chiara Ronzoni - Spring Simulation Multiconference '14 - Tampa (FL)