Managing the bandwidth allocated to a Label Switched Path in MPLS networks plays a major role for provisioning of Quality of Service and efficient use of resources. In doing so, two main contrasting factors have to be considered: not only the bandwidth should be adapted to the traffic profile but also the effort for bandwidth renegotiation associated with a variation of the allocated bandwidth should be kept at low levels. In this context, we formulate a problem of optimal LSP bandwidth reservation as the one of minimizing a convex combination of the difference between the assigned bandwidth and the estimated future traffic, and of a measure of the frequency of bandwidth variations. The contribution of this paper is to propose a new method to reserve optimally the bandwidth of an LSP, avoiding an excess of bandwidth renegotiations on the basis of prediction of future traffic, assuming a simple birth-and-death model to describe the traffic dynamics. Whenever the prediction is inaccurat...