Performance evaluation Part 2 & 3 Performance evaluation http://www.emse.fr/~xie/master
• 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
•Stochastic phenomena : which is not deterministic •Stochastic: from Greek stokhastikos(conjectural), meaning results of hasard •Stochastic phenomena : which is not deterministic
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!
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
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
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.
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
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
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
Assumptions We restrict ourselves to discrete event processes. Two types of processes will be considered: Discrete time stochastic process {Xn}nIN Example: inventory level at the beginning of each day. Continuous time stochastic process {Xt}t > 0 Example: number of customers in a queue.