Simulation+DYNAMICS__Lectures++-+F2010+handouts.+pdf

# Simulation+DYNAMICS__Lectures++-+F2010+handouts.+pdf -...

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1 Building Discrete Event Simulation Models E10 9/19/2010 AB t (i) Whenever event A occurs, if condition (i) is true, then event B will be scheduled to occur after a delay of t. Event Relationship Graph Single Resource Model •V a r i a b l e s R = Number of Resources R = 0: Resource is busy R > 0: Resource is idle Q = Number of jobs waiting in line (initially = 6 ) •T im i n g D a t a t a = interarrivals t s = service times • Events – Jobs ENTER the system every t a time units –STARTse rv ic ing the job tak t s time units – Jobs LEAVE the system Single Resource Model RU N (Q) START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s

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2 Minimalist Approach Discrete Event Simulations model both the passage of Time and Uncertainty. ...SIGMA has two basic variables. •C LK C u r r e n t s im u l a t e d c l o c k t e . For modeling dynamics. •RND R a n d om l y c h o s e n n um b e r , greater than 0 and less than 1. For modeling randomness. EVENT OCCURANCES Advance TIME - Graph Edges Change the STATE - Vertices Tied together into a Model by the Event Graph Verbal Event Graph of a Single Server Queue Initialize the RUN Customer ENTER System Customer LEAVEs System Customer STARTs Service (Are Customers Waiting?) (Is Server Idle?) ~ t a t s t a t s = Time Between Customer Arrivals (Possibly Random) = Time to Service a Single Customer (Possibly Random) What are the necessary state variables? AB t (i) Whenever event A occurs, if condition (i) is true, then event B will be scheduled to occur after a delay of t. Reading an Event Graph Simply read the edges in the graph. ..
3 Single Resource Model RUN (Q) START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s Single Resource Model RUN START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s A simulation run is started by having the first job enter the system. Single Resource Model RUN START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s New jobs enter the system at random intervals. Single Resource Model RUN START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s When a job enters, if the resource is available the job can start service.

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4 Single Resource Model RUN START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s Once a job starts, it will leave after a service time delay. Single Resource Model RUN START LEAVE {R=1} {Q=Q+1} {R=R-1, Q=Q-1} {R=R+1} (R>0) (Q>0) ENTER t a t s Whenever a job leaves, if there is more work waiting, then service can start on the next job. Putting the “edge” sentences together. .. A simulation run is started by having the first job enter the system. New jobs enter the system at random intervals. When a job enters, if the resource is available the job can start service. Once a job starts, it will leave after a service time delay. Whenever a job leaves, if there is more work waiting, then service can start on the next job.
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## This note was uploaded on 01/26/2011 for the course E 10 taught by Professor Righter during the Spring '08 term at University of California, Berkeley.

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Simulation+DYNAMICS__Lectures++-+F2010+handouts.+pdf -...

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