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Computationally efficient algorithms are developed to implement admission control and explicit routing of label switched paths (LSPs) for individually arriving quality of service (QoS) connection requests in a multiprotocol label switching (MPLS) network domain. A greedy admissions control policy, based on the snap-shot state of the network, is applied to arriving QoS connection requests, i.e., a connection request is admitted whenever there is an available path with sufficient residual capacities along its links to support the connection without re-routing existing LSPs. Although in our novel scenario best effort (BE) traffic flows follow their usual destination-based shortest path routes, in routing QoS connections, our algorithms give consideration to the resultant BE traffic delays. Excess effective bandwidth, the margin by which a QoS connection's effective bandwidth exceeds its average consumed bandwidth, is employed to support BE traffic.