ttotal

Ttotal is a notational term used in various disciplines to denote the total time required to complete a process or set of tasks. It is commonly defined as the elapsed time from the start of the first task to the completion of the last, including any necessary setup or idle periods. In deterministic, sequential settings, Ttotal equals the sum of all task durations: Ttotal = sum_{i=1}^n t_i. In parallel or partially ordered settings, Ttotal is often characterized by the makespan, the maximum completion time along any feasible schedule, and equals the length of the critical path when tasks have fixed precedence relations.

In stochastic models, the task durations t_i are treated as random variables, and Ttotal becomes a random variable whose distribution depends on the dependency structure and the distributions of the t_i. For independent, identically distributed service times, the sum follows an Erlang or Gamma distribution in continuous time, while the makespan in parallel systems is more complex.

Applications of Ttotal appear in project management, manufacturing, software engineering, and network performance analysis. It informs scheduling, capacity planning, and cost estimation, and is frequently contrasted with related measures such as makespan, turnaround time, and throughput. In practice, data on Ttotal guides decisions about task ordering, resource allocation, and parallelization to minimize total elapsed time.

See also: turnaround time, makespan, processing time, schedule optimization.