This paper presents an exact analysis of a general asymmetric polling system which has a finite-capacity buffer and exhaustive service discipline at each station. To analyze the system we consider a model system in which each station is assumed to have a temporary virtual buffer with infinite capacity attached to the real buffer, while the server is unavailable. It is introduced to store all the messages which are to be lost due to the limitation of the real buffer capacity during the vacation period. At the instant when the server visits a station, using the marginal queue length distribution of the station including the virtual buffer, the intervisit time distribution of the station is derived. The system behavior using the relationship between performance measures and the intervisit time distribution is then investigated.