Question

The exponential average formula used to predict the length of the next CPU burst is given by the recursion equation: tau_n + 1 = alpha tau_n + (1 - alpha)t_n. Where t denotes the nth CPU bust time, and 0 lessthanorequalto alpha lessthanorequalto 1. Explain the roll of alpha in the equation. suppose the first five actual CPU bursts of a process in milliseconds are: t_0 = 6, t_1 = 4, t_2 = 6, t_3 = 8, t_4 = 6. And suppose the initial predicted time is tau_0 = 7. Compute the next predicted time tau_5. What are the implications of assigning the following values to the parameters used by the algorithm? alpha = 0 and tau_0 = 100milliseconds alpha = 1and tau = 10milliseconds i

Answer 1

a) In this formula tn is most recent information. Tn stores past history.The parameter α controles the relative weights of recent and past history in out prediction.

b) let α=0.5 T1 = T0 * α + ( 1 - α ) * t0 T1 = (0.5 x 7) + ( (1 - 0.5) x 6 )      = 3.5 +3.0    = 6.5 T1 = T1 * α + ( 1 - α ) * t1 T2 = (0.5 x 6.5) + ( (1 - 0.5) x 4 )      = 3.25 +2.0    = 5.25 T3 = T2 * α + ( 1 - α ) * t2 T3 = (0.5 x 5.25) + ( (1 - 0.5) x 6 )     = 2.625 +3.0     = 5.625 T4 = T3 * α + ( 1 - α ) * t3 T4 = (0.5 x 5.625) + ( (1 - 0.5) x 8 )     = 2.8125 +4.0     = 6.8125 T5 = T4* α + ( 1 - α ) * t4 T5 = (0.5 x 6.8125) + ( (1 - 0.5) x 6 )     = 3.40625 +3.0     = 6.40625

c) 1) if α=0 Tn+1 = α tn + (α-1) Tn          =0*tn + (0-1)Tn         = 0 - Tn        = - Tn (Time always is in postive) so     = Tn Tn+1 = Tn = so T0 = T1 = T2 = T3 = T4...............=Tn = 100 milliseconds

2) if α=1 Tn+1 = α tn + (α-1) Tn          =1 *tn + (1 -1)Tn         = tn - 0 * Tn        = tn     Tn+1 = tn so T0 = T1 = T2 = T3 = T4...............=Tn = tn = 10 milli seconds