Maximum time delay achievable on propagation through a slow-light medium

We consider the question of whether there are any fundamental limits to the maximum time delay that can be achieved for a pulse propagating through a slow-light medium. We include in our analysis what we consider to be the dominant competing effects, and we show that in principle they do not lead to a limitation on the maximum achievable time delay. From this result we conclude that, through optimization, one should be able to delay a pulse by very many pulse lengths; the ability to do so can have important implications for the use of slow-light methods for applications in photonics.