The power spectrum of the energy fluctuations in the string gas above the Hagedorn energy density in the context of Brandenberger-Vafa string cosmology is derived. I argue that that the gas of closed strings cannot lead to a scale-invariant power spectrum. Only fluctuations in open strings may result in a scale-invariant spectrum. It is, however, crucial, to have a mixture of open and closed strings so that the gravitational waves are produced. The argument here is based on the statistical mechanics of string gas and random walks. At the end I will talk about the future prospects of this scenario.