Abstract
The cutoff phenomenon describes a case where a Markov chain converges abruptly to stationarity. For birth and death chains starting from boundary, Chen and Saloff-Coste (2015) proved that the occurrence of a total variation cutoff is equivalent to some kind of measure concentration of hitting times. This thesis considers birth and death chains starting from, in the sense of stationary distributions, near boundary and shows that this kind of measure concentration of hitting times is sufficient but not necessary for a total variation cutoff to occur.