3 Manipulating the E[Lq] Equation An interesting problem is deconstructing the familiar M/M/1 diagram to solve for unknown parameters. Given all of the statistical manipulation has been done to get steady-state solutions, moving things around is now in the realm of algebra, and familiar to most of you. At this point, all we've done is basic addition, subtraction, multiplication, and division, without all the need for more complex operators. One simple piece we have not covered so far is that, given E[Lq], we could solve for the input parameter, , via the quadratic equation: =2E[Lq](E[Lq]+4)E[Lq] I know some of you may be looking at the minus sign "_" in the numerator and thinking it should be replaced with the " you learned in high school. Unfortunately, this would give us a crazy answer (namely, a bigger than one). Think about the quadratic equation in the following questions. 11. Given =10 per hour and E[Lq]=0.9 people, what is the distribution of the interarrival time, A ? (Hint: make sure to first derive the input parameter .)