There are two priority control mechanisms in priority control as a ATM traffic control: one is a loss priority control which assigns the high priority to the traffic which is sensitive to the loss and the other is a time priority control which assigns the high priority to the traffic which is sensitive to the delay. The partial buffer sharing mechanism with two thresholds which deals with two priority sources is well-known as the loss priority control. In this thesis, we analyze the partial buffer sharing mechanism with multiple thresholds which deals with multiple priority sources. We take a M/G/1/K queueing model with multiple priority classes in order to analyze this mechanism. We obtain the system size distribution at the arbitrary time, the loss probability of each priority source and the numerical results for the three thresholds mechanism. It is confirmed that the loss probability decreases as the threshold size increases and increases as the input rate increases.