A the firms current capital event list t e t e the

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a = the firm’s current capital. Event List: t E t E = the time at which the next events occurs. Output variable I [ ] = otherwise 0, 0,1 t throughou e nonnegativ is capital s firm' the if 1, I Initialize Set t = 0, a = a 0 , n = n 0 . Generate X and initialize t E = X. Update Step Case 2: t E > T: Set I = 1 and end ren. Case 2: t E T:
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Reset: a = a + nc(t E –t) Reset: t = t E . Generate J: J = 1: reset n = n + 1. J = 2: reset n = n - 1. J = 3: Generate Y. If Y > a, set I = 0 and end this run; otherwise reset a = a –Y. Generate X: reset t E = t + X. 7. A system needs n working machines to be operational. To guard against machine breakdown, additional machines are kept available as spares. Whenever a machine breaks down it is immediately replaced by a spare and is itself sent to the repair facility, which consists of a single repair person who repair failed machines one at a time. Once a failed machine has been repaired it becomes available as a spare to be used when the need arises. All repair times are independent random variables having the common distribution function G. Each time a machine is put into use the amount of time it functions before breaking down is a random variable, independent of the past, having distribution function f. The system is said to “Crash” when a machine fails and no spares are available. Define variables and events to analyze this system and write a model in simulating to estimate the time at which the system crashes. (20 marks) solution (A Repair Problem) Time variables t System State Variables r i 1 = the number of machine that are down at time t. Event List: t 1 t 2 t 3 …… t n , t* t 1, t 2 , t 3 ,…t n = time (in order) at which the n machines presently in use will fail. t* = time at which the machines presently in repair will become operational. Initialize Set t = r = 0, t* = . Generate X 1 ,……,X n , independent random variables each having distribution F. order these values and let t i be the i th smallest one, i = 1,..,n. Set Event List: t 1 ,…, t n , t*. Case 2: t 1 < t* Reset: t = t 1 . Reset: r = r + 1. If r = s + 1, stop this run and collect the data T = t. If r < s + 1, generate random variable X having distribution F. Order the value t 2 , t 3, t n , t + X and let t i be the i th smallest one, i = 1,..,n. If r = 1, generate random variable Y having distribution G and reset t* = t = Y. Case 2: t* t 1 Reset: t = t*. Reset: r = r - 1. If r > 0, generate random variable Y having distribution G and reset t* = t = Y. If r < s + 1, generate random variable X having distribution F. Order the value t 2 , t 3,, t n , t + X and let t i be the i th smallest one, i = 1,..,n. If r = 0, set t* = .
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8. Draw a flow diagram for simulating the Repair model. (10-marks) Simulating the repair model 9. The quantity X = which is the arithmetic average of the n data values, is c called Initialize t = r-0, t = Generate Xi,….., Xn ,f Ti= i th smallest of X1,….,Xn Evenlist t1,….,tn,t Reset t=t*, r=r-1 If r=0, set t*= If r>0, generate Y~G and Reset t*= t+Y t,r Event List t1,….., tn , t* Reset t-t1 End run Collect data T=t Generate X ~ f Reorder t2,…,tn and call reordering t1,…,tn Gnerate Y ~ G t* = t+Y r = r+1 r = r+1 If t* t If t1<t* Is r=s?
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