Real time traffic in Virtual Private Network (VPN) connections can tolerate minor violations to their end to end delay bounds. This allowed Service Providers (SP) to increase the number of admitted requests by taking advantage of the statistical multiplexing behavior of such traffic. Usually, each VPN connection has different QoS requirements such as delay and violation probability bounds. Also, each set of requirements are to be fulfilled in isolation, independently from requirements of other connections. Several Measurement Based Admission Control (MBAC) algorithms were designed to meet the soft real time services quality of service (QoS) requirements. However, intensive studies of the existing MBAC algorithms revealed that almost none of these algorithms can meet the distinct violation probability requirements of the connections. This motivated designing a novel algorithm that is capable of reserving resources to distinctly satisfy the desired violation probability and delay bounds of a connection's QoS requirements. The proposed algorithm is an online distributed algorithm. It is based on measuring the delay of the link traffic. The empirical histogram of the measured delay is fitted to a gamma distribution, which is used to calculate the required bandwidth to be reserved in order to meet the connections' QoS requirements. The simulation results for evaluating the algorithm performance show that the algorithm is capable of meeting the distinct QoS requirements of the connections while admitting two to three times the number of connections a deterministic admission control algorithm can admit.