TBSAMlink, a variant of TBSAM, is an access methods for processing aggregate queries in a multi-user environment. Designs are made of deadlock-free operations which search and/or update a single data node or a range of data nodes. The correctness of these concurrent operations and the deadlock-free property are proved. When the techniques of right-link[14], lock-coupling[13], and the proposed rechecking are used to update the value in a single data node, at most two nodes are required to be locked. For updating a range of r (r>1) data nodes, at most r+1 nodes (r data nodes and one non-leaf node) should be locked. To evaluate the efficiency of these concurrent operations, mathematical formulas for the number of nodes to be accessed and/or locked are derived.