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Synchronous Digital Hierarchy (SDH) and Synchronous Optical Network (SONET) are time-division multiplexing technologies widely used in transport networks to provide bandwidth services. Dynamic service provisioning requires the use of online algorithms that automatically compute the path to be taken to satisfy the given service request. SDH/SONET multiplexing structure imposes restrictions on the allocation of bandwidth. Bandwidth services mostly require protection so that they are resilient to failures in the network. Two types of protection techniques-namely, dedicated protection and shared protection-are commonly used to protect bandwidth. Also, SDH/SONET provides standard protection mechanisms like linear MSP/APS, MS-SPRing/BLSR and SNCP/UPSR. In shared protection, complete path information for all the existing connections has to be maintained to maximize sharing for future service requests. This information will be typically very large. To overcome this problem, a minimum information scenario is proposed as a tradeoff between maintaining less information and maximizing sharing. In this work, heuristic algorithms are proposed for dedicated and shared protection that take into account the above-mentioned factors. These algorithms use the path computation algorithms for SDH networks proposed in a previous work of the authors, which compute paths for service requests without considering protection. The performance is evaluated for different values for the relative weight of sharing for the complete and minimum information scenarios. An extension to these algorithms for satisfying bandwidth requests that use various inverse multiplexing techniques is also proposed.