In this paper we propose a concurrent admission control scheme for the QoS sensitivity traffic in core-stateless networks. In this scheme, the ingress router of core-stateless network domain is capable of performing admissibility test in concurrent for requests by per-assigning core-link resource to each edge routers. Then, we introduce a novel two phase token passing mechanism to adaptively optimize the proportion of bandwidth dividing among contending edge routers according to the dynamic of their traffic. In addition, we adopt a measurement based admission decisionmaking criterion to gain the benefit of high utilization of statistical multiplexing. Our simulation results are very promising indicating that even under very high request load it is possible to perform admission control and resource allocation in concurrent without suffering in terms of response time, packet loss rate, or utilization.