In this paper, we study a two-stage tandem queueing network with MAP inputs and buffer sharing. The two stages share the same buffer. By using Markov process, we give an exact analysis of the queueing network. Since the customer arrival is not a Poisson process, the PASTA (Poisson Arrivals See Time Averages) property does not hold. A matrix filtration technique is proposed to derive the probability distribution of queue length at arrivals. Our objective is to investigate how the buffer sharing policy is mitigate the tradeoff between the probability that an arriving customer is lost and the probability that the first-stage server is blocked. The numerical results show that buffer sharing policy is more flexible, especially when the inputs have large variant and are correlated.