In today's distributed computing systems, a large amount files contain huge data need to be transferred to their
destination as soon as possible or else the quality of these systems will be seriously affected, and these transfer requests
arrived dynamically. We propose some effective heuristic algorithm to this problem with the purposes of minimizing the
maximal file transmitting time, and we can get some primal results from the algorithm. However, as we known, the
problem of routing and scheduling for the dynamic arriving files in the optical network has a large number of constrains
and the exact solution is computationally expensive, so it is hard to get the optimal result about this problem and we can
not know whether the heuristic results is good or how closed it closed to its optimal result. In order to get some more
detail results, we apply the approach called Lagrangian relaxation combined with subgradient-based method and utility
the heuristic result to compute the lower bound of the optimal solution, and we consider the optimal target of minimizing
the maximal file transmitting complete time for it's an important aspect with the file transmitting problem.
We mainly use Lagrangian relaxation (LR) to research the dynamical lager file transmitting problem. Firstly, in order to
apply the LR method we formulation our dynamic file routing scheduling and distributing problem in WDM optical
network into mathematic model with some corresponding constraints. Secondly, change the formulation with some
added variables to let it more suitable for LR and then introduce the Lagrangian multipliers into the model to obtain the
Lagrangian function. With this function we can divided it into some small independent problems that could let it be
solved more easily and at last we utilize the result received from the heuristic algorithm to solve the Lagrangian
multiplier problem with subgradient-based method in order to getting the sharpest possible lower bound.
With the comparison of our simulation results, we can prove that the Subgradient algorithm based on LR can get better
results of the file transmitting time than the heuristic algorithm, and with the theorem of Lagrangian Bounding Principle
we can know that value of LR method is a lower bound on the optimal value.