The problem is to compare four different computer systems that handle airline reservations. 2 The single measure of performance is the expected time to system failure, E [TTF]. The system works if...

The problem is to compare four different computer systems that handle airline reservations. 2 The single measure of performance is the expected time to system failure, E [TTF]. The system works if either of two computers works, and the computers are repaired one at a time when they fail. Computer failures are rare, repair times are fast, and the resulting E[TTF] is large. The four systems arise from variations in parameters affecting the time-to-failure and time-to-repair distributions as given in the following table (all rates are in failures or repairs per minute):

Suppose that the time to failure and time to repair are exponentially distributed random variables. Find the alternative with the largest E[TTF]. (Hints: First find the embedded Markov chain and determine the expected number of transitions until system failure. Then find the expected holding time between transitions. Or use the result in Exercise 11 to calculate the expected time until system failure directly.)