Do the same as in Exercise 9.8 but now for a preemptive dynamic policy.
Show that with X1 and X2 being independent.
Show that when X1 is exponentially distributed with rate λ and X2 exponentially distributed with rate
Compute the coefficient of variation of the Erlang(k, λ) distribution (recall that the Erlang(k, λ) distribution is a convolution of k i.i.d. exponential random variables with rate λ).
Consider the following variant of the geometric distribution:
Consider the following partial ordering between randomvariables X1 and X2. The randomvariable X1 is said to be smaller than the random variable X2 in the completion rate sense if the completion rate of X1 at time t, say λ1(t), is larger than or equal to the completion rate of X2, say λ2(t), for any t. … Continue reading "Consider the following partial ordering between randomvariables X 1 and X 2 . The randomvariable X…"
Consider a permutation flow shop with m machines in series and n jobs. The processing time of job j on machine i is Xij , distributed according to F with mean 1. Show that Are there distributions for which these bounds are attained?
Consider a single machine and n jobs. The processing time of job j is
Assume X1 ≥ st X2. Show through a counterexample that Z1 = 2X1 + X2 ≥ st 2X2 + X1 = Z2. is not necessarily true.
Consider a single machine and three jobs with i.i.d. processing times with distribution F and mean 1.