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Summary MS2
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This is the summary of Modelling and simulation 2. The SIMIO part is a little bit described but not enough for the exam.
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Lecture 1A Simulation is the limitation of the operation of a real-world process or system over time.
most widely used tool for decision making. Can be used as Analysis Tool for predicating the
effect of changes or as Design Tool to predict the performance of new system. It is better to
do simulation before implementation
A System is defined as ‘a set of interrelated (verbonden) component working together
toward some common objective (gemeenschappelijk doel)’.
A Model is a simplified representation (vereenvoudigde weergave) of the system of which
we are interested in study, modify it, predict its behavior or performance control it.
Discrete-Event System (DES)
Deterministic/Stochastic Some state variables are random
If the simulation model has no probabilistic component, is called deterministic
Otherwise it is called stochastic
Static/Dynamic Time evolution is important
Continuous/Discrete System state changes when an event occur
(voorkomen)
Components of a system
Entity Iets dat bestaat (Machines in factory, Customers in a bank, PAX)
1 iets wat door het systeem heengaat.
Attribute Property (eigendom) of an entity (Speed, Capacity, Number of BAX)
Activity Time period of specified length (Travelling, Transmitting, Checking-in)
Event Iets wat onmiddelijk de toestand van het system veranderd (Arrival or
Departure of an aircraft, breakdown)
State Collection of variables that describe the system in any time (status of
a machine (busy, inactief, down), number of customers waiting)
Steps in Simulation of DES
1. Initial phase
Problem formulation, setting objectives and overall project plan
2. Model building & Data collection
Model conceptualization, data collection, model translation, verification,
validation
3. Run the model
Experimental design, production runs and analysis, more runs?
4. Implementation
Documentation and reporting, implementation
Verification Validation
- Building the model correctly - Building the correct model
- Model has the right input and - Accurate representation of the real
structure system
- Performed during building the - Performed after finishing the model
model
, Lecture 2
Queueing Systems
1. Calling Population
The population of potential customers. For example, all PAX departing at a certain day.
2. System capacity
Maximum number of customers that can be accommodated on the queue. If the system is
full no new customers are accepted.
3. Arrival Process
Interarrival times of successive customers.
‘Random Arrivals’ Most cases used, often Poisson distribution
‘Scheduled Arrivals’ Example of airplane
Denoted with λ Arrival Rate is hoeveel mensen er per minuut komen. 1 customer per 5
1
minuten λ=
5
4. Queue Behavior and Queue Discipline
Balking (leave when queue is too long), reneging (leave when line is moving to slow),
jockeying (move from one line to another when more parallel queues)
LIFO Last In First Out De lift
FIFO First In First Out Check-in
SPT Shortest Processing Time First Fabriek
SIRO Service In Random Order Vragenstel rondje
PR Service according to Priority Business VS Economy
5. Service Time and Service Mechanisms
The time taking by a server to server, often exponential distribution.
1
Mean Service Time Mean Service Rate (of one server) μ (Poisson)
μ
Service Rate = how many PAX can I help per minute
Service Time = how many time will it take to service my people
Kendall’s Notation
Notation for Queues: A/B/c/N/K/Q
A Interarrival-Time Distribution (λ = Arrival Rate)
B Service-Time Distribution (μ = Servicerate)
c Number of parallel servers
N System Capacity (often ∞)
K calling population (often ∞)
M Markov, Exponential, Poisson
D Constant, Deterministic
EK Erlang Distribution of order k
G General, Arbitary (can be anything)
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