1. ECE 466/658: Performance Evaluation and Simulation Introduction Instructor: Christos Panayiotou

2. Syllabus Topics  System Modeling and Modeling approaches  Discrete Event Simulation  Markov Chains  Queueing Systems  Queueing Networks  Applications Additional Information  www.eng.ucy.ac.cy/christos/courses/ECE466  www.eng.ucy.ac.cy/christos/courses/ECE658 Topics have wide applicability…  Computer systems and networks  Manufacturing systems  Transportation systems ……

3. Need for Performance Evaluation Computer system objectives  It must perform the functions that was designed for.  It must have adequate performance Should perform its tasks under most circumstances Should do them in reasonable time and cost  When typing a text file, reasonable time is a few milliseconds whereas when running complicated simulations, reasonable may be a few days… When designing a systems people usually pay a lot of attention to the functionality but not enough attention to the performance evaluation!  People address the issue of performance once the system is built when it is generally more difficult and more costly to achieve better performance.

4. Modeling and Performance Evaluation Once a system is built, we may be able to use it to measure its performance  Opportunities to redesign and reengineer the system are lost or become a lot more costly!  When the system’s performance depends on some parameters, how can we figure out the best parameter settings? Alternatively, one can build a model of the system, analyze it, and predict the performance of the actual system based on the model.  This approach is more flexible allowing for redesign and reengineering before investing in the final system.

5. Modeling Model  It is a set of equations or a piece of software (simulator) that imitates the behavior of the real system.  There may be several models that can capture the behavior of a system. Modeling is mostly an art and not an exact science.  Depending on the answers we are looking for, models can be very detailed and complex or they can be very simple.

6. Modeling Process A model predicts what the system’s output would be given an input u(t). A model is as good as its input: garbage in, garbage out! SYSTE M INPUT OUTPUT INPUT OUTPUT MODEL u(t)u(t) y=g (u)

7. Concept of State Suppose that at a time instant t 1, u(t 1 )=a and y(t 1 )=Y. Then, at time t 2, u(t 2 )=a then what is y(t 2 )=?. Example  Let x(t)=x(t-1)+u(t)  y(u(t))=u(t)+x(t)+5 The state of a system at time t 0 is the information required at t 0 such that the output y(t), for all t≥t 0, is uniquely determined from this information and from the input u(t), t≥t 0. INPUT OUTPUT MODEL u(t)u(t) y(t) =g(u(t), t)

8. State Space Modeling State equations: The set of equations required to specify the state x(t) for all t≥t 0 given x(t 0 ) and the function u(t). State Space X : The set of all possible values that the state can take. Examples:

9. Sample Path Evolution of the state over time t x(t)x(t) Continuous StateDiscrete State t x(t)x(t) x1x1 x2x2 x3x3 x4x4 x5x5 x6x6

10. Example: Warehouse System Input u1(t)u1(t) u2(t)u2(t) System Dynamics

11. Example: Warehouse Sample Path System Input System Dynamics t u1(t)u1(t) t u2(t)u2(t) t x(t)x(t)

12. System Classification t x(t)x(t) Continuous State –Continuous Time t x(t)x(t) Discrete State –Continuous Time t x(t)x(t) Continuous State –Discrete Time t x(t)x(t) Discrete State –Discrete Time

13. Deterministic and Stochastic Systems In many occasions the input functions u(t) are not known exactly but we can only characterize them through some probability distribution.  Signal noise at a mobile receiver  Arrival time of customers at a bank …… If the input function is not known exactly, then the state cannot be determined exactly, but it constitutes a random variable A system is stochastic if at least one of its output variables is a random variable. Otherwise the system is deterministic. In general, the state of a stochastic system defines a random process.

14. Closing… Depending on the type of system and/or the objectives of the analysis, one may be interested in various measures  Average number of customers in the system  Number of packets dropped in an interval [0,T].  Average delay in a system  … The most general tool for answering the above questions is computer simulation, however, simulation does not provide good understanding of the problem. There are no general analytical tools that can address problems of some complexity with adequate accuracy, however, analytical tools can be used to gain a better understanding of the nature of the problem.

15. Closing (2)… Simple vs “real” models  Simple models can be used to gain a better “understanding”  More complex models may be used to imitate real “real” scenarios Accuracy vs Complexity  When modeling a system, it is important to always have in mind what questions the specific model will help you answer. Changing the questions, may require changing the model!  Some questions may require accuracy. Does the network meet the requirement of only 0.1% packet loss?  Some questions may not require much accuracy Comparing two designs (ordinal optimization) What does measure mean?  What does it mean “packet loss probability does not exceed 0.1”?  What does it mean “packet loss probability does not exceed 10 -3 ”?  What does it mean “packet loss probability does not exceed 10 -6 ”?