In this paper, we introduce a probabilistic lower bound for the amount of work arrived for a multifractal process. The obtained bound is accurate and tight. In the optical burst switching context, using the developed lower bound we obtained an analytical expression for the minimum burst length generated by a timer-based burst assembly algorithm, the maximum delay imposed by a burstlength-based burst assembly algorithm and project constraints of a mixed timer/burstlength-based burst assembly algorithm when the incoming traffic is multifractal. Our results are very useful when designing optical burst switching networks and analyzing the performance of burst assembly algorithms at the presence of multifractality.