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The current Internet has a single class of service, i.e., best-effort service, whereas multimedia information is actually transmitted there. Recently, many researchers have focused on a mechanism to provide some quality of service (QoS) required for applications such as delay-sensitive ones. With such a mechanism, a real-time communication request is sent to a server, such as a policy server, that will try to find a path that meets the request's QoS requirement. If several available paths meet the requirement, the connection will be established on one of them. Otherwise, the request will be rejected. In all likelihood, though, delaying the path reservation to some extent if no available path meets the requirement, rather than immediately rejecting a request, will improve the blocking probability. We assume here that the communication can tolerate some initial setup delay, which we refer to as acceptable delay. Our major objective is to clarify whether or not the delay schemes are effective in improving the blocking probability. Therefore, we examine two schemes for managing buffered requests and two different network topologies, i.e., Mesh and ISP. Through an extensive simulation, we have found that the blocking probability can be improved even when a small acceptable delay and a small buffer size are assumed. In particular, we found that the scheme works well in actual network topologies such as an ISP model.