Many activities are comprised of temporally dependent events that must be executed in a specific chronological order. Supportive software applications must preserve these temporal dependencies. Whenever the processing of this type of an application includes transactions submitted to a database that is shared with other such applications, the transaction concurrency control mechanisms within the database must also preserve the temporal dependencies. A basis for preserving temporal dependencies is established by using (within the applications and databases) real-time timestamps to identify and order events and transactions. The use of optimistic approaches to transaction concurrency control can be undesirable in such situations, as they allow incorrect results for database read operations. Although the incorrectness is detected prior to transaction committal and the corresponding transaction(s) restarted, the impact on the application or entity that submitted the transaction can be too costly. Three transaction concurrency control algorithms are proposed in this dissertation. These algorithms are based on timestamp ordering, and are designed to preserve temporal dependencies existing among data-dependent transactions. The algorithms produce execution schedules that are equivalent to temporally ordered serial schedules, where the temporal order is established by the transactions' start times. The algorithms provide this equivalence while supporting currency to the extent out-of-order commits and reads. With respect to the stated concern with optimistic approaches, two of the proposed algorithms are risk-free and return to read operations only committed data-item values. Risk with the third algorithm is greatly reduced by its conservative bias. All three algorithms avoid deadlock while providing risk-free or reduced-risk operation. The performance of the algorithms is determined analytically and with experimentation. Experiments are performed using functional database management system models that implement the proposed algorithms and the well-known Conservative Multiversion Timestamp Ordering algorithm.