A quasi-birth-death(QBD) process is a two-dimensional continuous-time Markov chain in which its transition matrix has a block-tridiagonal structure. The first component of the QBD process is called the phase, the second component is called the level. If the number of phases in each level is finite, various properties on QBD processes are known. For example the level process of a positive-recurrent QBD process with a finite phase space possesses a stationary distribution which decays geometrically as the level is increased. The decay parameter is equal to the spectral radius of Neuts`s R-matrix, which is strictly less than 1. For QBD processes with an infinite phase space the situation becomes more complicated. The purpose of thesis is to study of the behavior of infinite-phase QBD processes by considering a special case. This special case is two-node Jackson network, in which the number of customers in the first queue gives the phase variable and the number of customers in the second queue gives the level variable. In general, the decay rates are hard to compute for stationary distribution of multi-dimensional Markov processes unless they have product-form stationary distribution and are more easily computed for one dimensional Markov process. So, it is natural to approximate the decay rates of the origin chain, for queueing networks by truncating the buffers of all queue except for the ones in which we are interested. This referred to as a finite truncation. We expects that such a truncation approximates the original decay rates well as the truncation becomes large. In general, the purpose of this thesis is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer which is not necessarily equal to the decay rate of the origin chain.