系统仿真 System Simulation

1. 系统仿真System Simulation 2008

2. What’s simulation • Asimulation is • The imitation of the operation of a real-world process or system over time. • A technique, whereby a model of a system, is run in compressed time, to perform experimentation for analyzing system performance. • Whether done by hand or on a computer, simulation involves the generation of an artificial history of a system, and the observation of that artificial history to draw inferences concerning the operating characteristics of the real system.

3. Discrete system simulation

4. Simulation Category • General-purpose programming languages • FORTRAN, C, C++ “build your own, use someone else’s“ • Simulation programming languages • ns-2, QualNet/GloMoSim, Opnet, RTSS • GPSS/H, SIMAN V • Simulation technology • Time-driven simulation • They work on a strictly unit-time basis • automatically scanning thousands of fixed time units to discover the next significant change • Event-driven simulation • automatically skip to the next known event • saving execute-time

5. Customers Server Queue Queuing System Model Queuing System • Use Queuing models to • Describe the behavior of queuing systems • Evaluate system performance

6. Customer n Arrival event Begin service End service Delay Activity Time Interarrival Arrival event Begin service End service Delay Activity Time Customer n+1

7. example • Single-server queue simulation • Mean Interarrival time 4.5 • Mean Service Time 3.2 • Standard Deviation of Service Times 0.6 • Number of Customers served 1000 • Server Utilization 0.68362 • Maximum Line Length 9 • Average Response Time 6.739 • Proportion who Spend Four Minutes or More in System 0.663 • Simulation RunLength 4677.74 • Number of Departures 1000

8. RTSS Simulator -- A model contains two parts • First, a set of processors • The simulation software stores the processor parameters, such as service rate etc., in a set of arrays – “the processor table”. • Each processor has his own queue to store waiting jobs. • Second, the characterization of the workload (i.e. jobs) • The job parameters, such as job arriving time, job length of a job etc., are stored in a set of arrays - ”the job table”. • The job parameters can be either deterministic or probabilistic.

9. RTSS Simulator

10. events • All events can be divided into three types • Type 1 marks the arrival of a job in the system • Type 2 corresponds to a job’s entering a server • Type 3 corresponds to a job’s exiting from a server • The event service routines are the arrival routine, the incoming routine and the outgoing routine • There is an event list to drive the simulation process • Each event has 3 elements in the event list • One element is an event identifier which is used for identifying the event type. • The second element is the event time • The third element is a pointer to the job table

11. control routine • The control routine is the heart of the simulator, its loop is executed once for each event handled • At the start of each loop, the control routine • selects the earliest event in the event list • calls the corresponding event service routine • advances the simulation clock to the event time, removes the event from the event list • The event service routine • performs the required processing for the job • determines its next event, calculates the event time and inserts the next event in the event list • returns control to the control routine

12. arrival routine • the arrival routine corresponds to event type 1, and does the following things: • 1. The next event (type 2) for the arriving job is inserted in the event list. • 2. If the arriving job belongs to a job sequence and it is not the last job of the sequence, a new job of the sequence is generated and inserted in the job table. • 3. The event (type 1) for the new job is inserted in the event list. • Random-variant generators • Routines to generate samples from desired probability distributions

13. incoming routine • The incoming routine corresponds to event type 2, and simulates a job entering a processor; it does the following things: • 1. If the processor is busy, the input job enters a processor queue. • 2. If the processor is not busy, it serves the input job. The next event (type 3) to occur for the input job is inserted in the event list. • 3. The states of the job and processor are updated • Random-variant generators • Routines to generate samples from desired probability distributions

14. outgoing routine • The outgoing routine corresponds to event type 3, and simulates a job exiting from a processor; it does the following things: • 1. The processor is released by the output job, • 2. Then, the queue of the released processor is examined; if there are jobs waiting, the one which has the highest priority is selected from the queue and scheduled to be served

15. report routine • A group of variables describes the simulator state when the simulation clock is advanced by the occurrence of a series of events. • The report routine records these variables, so that analysis and statistic programs give the final simulation result.

16. Simulation in C++ • Main program • Provides overall control of the event-scheduling algorithm • Clock • A variable defining simulated time • Initialization subroutine • A routine to define the system state at time 0 • Min-time event subroutine • A routine that identifies the imminent event, FEL

17. Simulation in C++ • Event subroutines • For each event type, a subroutine to update system state (and cumulative statistics) when that event occurs • Random-variant generators • Routines to generate samples from desired probability distributions • Report generator • A routine that computers summary statistics from cumulative statistics and prints a report at the end of the simulation

24. example • Single-server queue simulation

27. Definitions tab. 4.6, p. 108 • Variables • System state • QueueLength • NumberInService • Entity attributes and sets • Customers

28. Variables(cont’d) • Future event list • FutureEventList • Activity duration • Service time

29. Variables(cont’d) • Input Parameters • MeanInterarrivalTime • MeanServiceTime • SIGMA, Standard deviation of service time • TotalCustomers, stopping criteria

30. Variables(cont’d) • Simulation variables • Clock • Statistical Accumulators • LastEventTime • TotalBusy • MaxQueueLength

31. Statistical Accumulators • SumResponseTime • NumberOfDepartures • LongService, Number of customers who spend 4 or more minutes

32. Variables(cont’d) • Summary statistics • RHO = BusyTime/Clock • AVGR : average response time • PC4 : Proportion of customers who spend 4 or more minutes at the checkout counter

33. Functions • exponential ( mu ) • normal ( xmu, SIGMA )

34. Subroutines • Initialization • ProcessArrival • ProcessDeparture • ReportGeneration

35. Class Event{ Friend bool operator < (const Event& e1, const Event& e2); Friend bool operator == (const Event& e1, const Event& e2); public: Event(){}; enum EvtType { arrival, departure };

36. Event ( EvtType type, double etime) : _type(type), _etime(etime){}; EvtType get_type() { return _type;} double get_time() { return _etime;} protected: EvtType _type; double _etime; };

37. …… priority_queue<Event> FutureEventList Queue<Event> Customers

38. Main( int argc, char* argv[ ] ){ MeanInterArrivalTime = 4.5 …… Long seed = atoi ( argv[1] ); SetSeed(seed); Initialization();

39. While ( NumberOfDeparture < TotalCustomers ){ Event evt = FutureEventList.top(); FutureEventList.pop(); Clock = evt.get_time(); If ( evt.get_type() == Event::arrival ) ProcessArrival ( evt ); Else ProcessDeparture ( evt ); } ReportGeneration();}

40. Void Initialization (){ Clock = 0; QueueLength = 0; …… Event evt( Event::arrival, exponential ( MeanInterArrivalTime ) ); FutureEventList.push ( evt ); }

41. Void ProcessArrival( Event evt ){ Customer.push ( evt ); QueueLength ++; If ( NumberInService == 0 ) ScheduleDeparture (); Else TotalBusy += ( Clock – LastEventTime ); If ( MaxQueueLength < QueueLength ) MaxQueueLength = QueueLength;

42. Event next_arrival ( Event::arrival, Clock + exponential ( MeanInterArrivalTime ) ); FutureEventList.push ( next_arrival ); LastEventTime = Clock; }

43. Void scheduleDeparture () { double ServiceTime; while( ( ServiceTime = normal ( MeanServiceTime, SIGMA )) < 0 ); Event depart ( Event::departure, Clock + ServiceTime ); FutureEventList.push ( depart ); NumberInservice = 1; QueueLength --; }

44. Void ProcessDeparture ( Evevt evt) { Event finished = Customers.front (); Customers.pop (); if ( QueueLength ) ScheduleDeparture (); else NumberInService = 0;

45. double response = Clock – finished.get_time (); SumResponseTime + = response; …… NumberOfDepartures ++; LastEventTime = Clock; }

46. Void ReportGeneration (){ double RHO = TotalBusy/Clock; double AVGR = SumResponseTime/ TotalCustomers; double PC4 = ((double)LongService)/ TotalCustomers; …… }

47. Mean Interarrival time 4.5 Mean Service Time 3.2 Standard Deviation of Service Times 0.6 Number of Customers served 1000 Server Utilization 0.68362 Maximum Line Length 9 Average Response Time 6.739

48. Proportion who Spend Four Minutes or More in System 0.663 Simulation RunLength 4677.74 Number of Departures 1000