1. Performance evaluation
Part 2 & 3
Performance evaluation

2. • Learn performance evalation methods and tools
Goals
• Understand the complex behavior of systems subject to "random phenomena"
• Develop intuitive understanding of the behaviors of stochastic systems
• Learn performance evalation methods and tools
• Able to model real-life systems for analysis of both qualitative behaviors and quantitative performances

3. •Stochastic phenomena : which is not deterministic
•Stochastic: from Greek stokhastikos(conjectural), meaning results of hasard
•Stochastic phenomena : which is not deterministic

4. Performance evaluation
System
Modeling
Models
Analysis of the results
Performance evaluation
Performances
! Attention: the results are performances of the model and not those of the system!

5. A possible model Queue Server Customer arrival
N(t) : nb of customers in the queue
Ta : time between two consecutive arrivals
ga: probability density of Ta
Ts : Service time
gs: probability density of Ts

6. Performance measures
•4 important performance indicators of queueing systems
–Throughput rate X (or TH)
–Number of customers Q
–Resource utilisation ratio U
–Response time R

7. Performance evaluation methods
•Discrete event simulation
–A very general approach
–Long computation time
–Difficulty of results analysis
•Analytical methods
–Limited to simple models under restrictions
–Quick computation time
–Allow better understanding of the system
•The two approaches are complementary in practice.

8. Another example : a production line
Machine M1 M2 M3 M4
Raw material
Finished Good Inventory
buffer
•Examples of state variables :
–Nb of parts in intermediate buffers (0, 1, 2,…, capacity of the buffer)
–State of the machine (UP or DOWN)
•Examples of events :
–Completion of a part on a machine
–Failure of a machine

9. Performance indicators
Mean buffer level
Production rate of M3
Machine M1 M2 M3 M4
Raw material
Utilization ratio of machine M3
Finished Good Inventory
buffer
Mean response time

10. Stochastic processes
A stochastic process {Xt, t  T} is a sequence of random variables defined on the same state space E.
It describes the evolution of a random variable over time.
The state space and time can be either discrete or continuous.
E continuous and T discrete
E and T discrete
E discrete and T continuous
E and T continuous

11. Assumptions We restrict ourselves to discrete event processes.
Two types of processes will be considered:
Discrete time stochastic process {Xn}nIN
Example: inventory level at the beginning of each day.
Continuous time stochastic process {Xt}t > 0
Example: number of customers in a queue.