HW6_sol - IEOR 4404 Simulation Assignment 6 Solution Jing...

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IEOR 4404 Simulation Assignment 6 Solution Jing Dong 1. λ ( t ) = 4 + 3 t for 0 t < 5 and λ ( t ) = 34 - 3 t for 5 t < 10 λ ( t ) = λ ( t - 10) for t 10 λ ( t ) 19 for all t 0 Using the third method outlined in the lecture notes for simulating nonhomegeneous Pois- son process, we have: %Simulate the next arrival of the nonhomogeneous Poisson process %t is the current time function T=ATime(t) lambda=19; I=0; while (I==0) T0=-log(rand)/lambda; t=t+T0; %lambda(t+10)=lambda(t) t0=t-floor(t/10)*10; if t0 < 5 lambda_t=4+3*t0; else lambda_t=34-3*t0; end C=lambda_t/lambda; U=rand; if U<=C I=1; T=t; end end We then simulate the expected amount of time that the server is on break: %Qn1 mu=25; n=500; Id=zeros(1,n); for i=1:n t=0; SS=0; V=0.3*rand; Id(i)=V; tD=V; tA=ATime(t); t=min([tA,tD]); while t <= 100 1
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if t==tA SS=SS+1; tA=ATime(t); else if SS==0 V=0.3*rand; tD=t+V; if tD <= 100 Id(i)=I(i)+V; else Id(i)=I(i)+100-t; end else SS=SS-1; tD=t-log(rand)/mu; end end t=min([tA,tD]); end end B=mean(Id) B = 54.1716 2. t : time variable N A : the number of arrivals N : the number of lost W t : waiting time of a new arrival. It is the time it takes to serve all the customers before the arriving customer.
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This note was uploaded on 01/16/2012 for the course IEOR 4404 taught by Professor Joseblanchet during the Spring '11 term at Columbia College.

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HW6_sol - IEOR 4404 Simulation Assignment 6 Solution Jing...

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