This work discusses the interest of protocol network technologies, to deal with big data and voluminous informations,witch are heavy in front off the physical implementation and programmation actually given, such as IP (Internet protocol) and MPLS (Multiprotocol Label Switching), the interactions between them and their mode of cohabitation, afterwards we will approach the problem of mono path of LSPs based on a bandwidth approach in the form of a nonlinear program of probabilistic decision variables.Finally a stochastic mathematical model in the form of a Markov decision process with hidden information and memory that results in the density of a subgraph representing the correct routing path from end to end, respecting the probability of having such a routing strategy.The work related to this problem was designed based on a purely deterministic model to take into consideration some finesse of the studied system we tried to modelize in stochastic model and besides the results are very encouraging.