Why not experiment with the system itself? Ways to study a system System. Application areas. Different kinds of systems

Transcription

1 Simulaion Wha is simulaion? Simple synonym: imiaion We are ineresed in sudying a Insead of experimening wih he iself we experimen wih a model of he Experimen wih he Acual Ways o sudy a Sysem Experimen wih a Physical model Experimen wih a model of he Analyical soluion A concepual model Simulaion Why no experimen wih he iself? I migh be dangerous (conrol in a nuclear power plan) The does no exis ye I is expensive o experimen wih he I is impossible o experimen wih a Differen kinds of s Coninuous s Examples: emperaure in an engine, air pressure around an aeroplane ec Are usually modelled by differenial equaions Discree s Examples: s described by queues Hybrid s Applicaion areas Communicaion s Compuer s performance Transporaion Manufacuring and maerial handling Healh s Public services Miliary s 1

2 Advanages of simulaion Disadvanages of simulaion Makes i possible o predic impac of changes Makes i possible o look a deailed behaviour Can give a good undersanding of a Can visualize a Find bolenecks in a Gives a possibiliy o rain a eam Model building requires special raining Time consuming and expensive Limiaions of accuracy (rare evens) Modelling conceps A model is an absrac represenaion of a A discree model has Sae variables Evens ha change he sae Rules ha describes wha shall happen a an even Two approaches o simulaion Even-scheduling mehod Process-ineracion mehod Even-scheduling mehod The following is needed: A descripion of he sae The evens ha can occur Rules describing wha will happen if an even occurs The even lis Keeps rack of when evens shall happen T1 E1 A1 T2 E2 A2 T3 E3 A3 Ti = ime when even Ei will ake place Ai = aribues o even I The lis is sored: T1 < T2 < T3 < T4 e T4 E4 A4 2

3 How a simulaion run is done 1. Exrac he firs elemen in he even lis 2. Se Time = he ime of he exraced even 3. Updae he sae of he and inser new evens if needed 4. If no finished, Go o 1 Arrivals An example: a queuing Rejeced Waiing line Server Deparures I migh be of ineres o find Probabiliy of rejecion Mean of ime spen in The mean number of cusomers in he sy The sae descripion Assume ha we wan o find he mean number of cusomers in he queue. N = number of cusomers in he Evens ha may ake place Arrival Deparure (when service is ready) Measuremen (does no change he sae) The appropriae sae descripion depends on he resuls we desire Wha we also need o know Assume he following: The service ime is always 2 The mean ime beween arrivals is random beween 2 and 4 The number of places in he waiing line is infinie Rule a arrival N := N + 1; If N=1 hen add deparure o even lis; Add a new arrival o even lis; When we add arrival even we have o draw a random number (exponenially disribued) 3

4 Rule a deparure Rule a N := N - 1; If N>0 hen add deparure o even lis ; Wrie(N); Add a new o even lis; When he simulaion s Sep 1 Time = 0 N = 0 3 Arrival Time = 3 N = 1 4 Arrival 9 Deparure Sep 2 Sep 3 Time = 4 N = 2 9 Deparure Time = N = 2 9 Deparure 14 Measuremen 4

5 Time = 9 N = 1 Sep 4 12 Deparure 14 Measuremen simulaionlengh := 1000; No_in_queue := 0; ime := 0; inser_even(,random(2,4)); inser_even(arrival, Exp(a)); while ime < simulaionlengh do dummy := FirsInQueue(evenlis); ime := dummy.evenime; case dummy.evenkind of arrival: arrive; deparure: depar; : measure; end. Dea är pseudokod procedure arrive; if No_in_queue = 0 hen inser_even(deparure,exp(s)); No_in_queue := No_in_queue + 1; inser_even(arrival, Exp(a)); procedure depar; No_in_queue := No_in_queue - 1; if No_in_queue > 0 hen inser_even(deparure, Exp(s)); procedure measure; wrie(ufil, No_in_queue); inser_even(, Exp(m));