Before revision:  We also formulate the problem theoretically and propose a sufficient condition for the scale invariance. Finally , we numerically show the range of validity of the scale invariance over various characteristic times of the starvation process, revealing the number of multifork replications is crucial for the scale invariance  .
After revision:  Further , we numerically show the range of validity of the scale invariance over various characteristic times of the starvation process, revealing the number of multifork replications is crucial for the scale invariance .