Generalized Perturbation andSimulation
Generalized Perturbation and Simulation
Ideas of Generalized PAGenerate one set of common randomvariables for sample paths with different 'sTiming and State transition are independentmechanismsIn Markov casestandard clock cut-&-paste of trajectory segmentsReal time applications
Ideas of Generalized PA Generate one set of common random variables for sample paths with different q’s Timing and State transition are independent mechanisms In Markov case − standard clock − cut-&-paste of trajectory segments Real time applications
Review of the Clock MechanismIntroduction ofTIME"for quantitative performance analysispurposesClock Mechanism (a two dimensional array of numbers)Cn(α) = the nth lifetime of the event αte(n) = the time of the nth occurrence of the event αcn(α)Eventtype αtimet(1)ta(n-1)T(2)Te(n)
Review of the Clock Mechanism Introduction of “TIME” for quantitative performance analysis purposes Clock Mechanism (a two dimensional array of numbers) cn (a) = the nth lifetime of the event a ta (n) = the time of the nth occurrence of the event a cn (a) ta (1) ta (2) ta (n-1) ta (n) Event type a time
Time Evolution of a DEDSOneEventαMin. OfStateLife timeenablingeventlifetimestransitiongenerationI(x)delayXCn(α)Simulation of a DEDSSearchGeneratePlace inNewTransitionlife time offor nextfuturestateto nextnew eventevent toevent liststateoccur
Time Evolution of a DEDS Event enabling G(x) One event delay Life time generation Min. Of lifetimes State transition x a a* cn (a) Simulation of a DEDS Search for next event to occur New state Generate life time of new event Place in future event list Transition to next state
Standard Clock MechanismUnder Markov Assumption further simplification is possible!(exponentiallydistributedinter-arrivaltimeswithrates=sumofalleventrates)Canbethinnedintocomponentexponentialeventstreamsoflesserrate=>theClockMechanismDetermining event type and timing separately for eacheventonthemaster stream
Standard Clock Mechanism Under Markov Assumption further simplification is possible! t (exponentially distributed inter-arrival times with rates = sum of all event rates) t t t Can be thinned into component exponential event streams of lesser rate =>the Clock Mechanism Determining event type and timing separately for each event on the master stream