Cycle Time

A system performs a set of activity cycles so its performance can be measured by how long it has taken to perform an activity cycle. The unit of this measure is time-unit/activity.

Suppose that an activity consists of two events such that one begins at $t_l$ and the other ends at $t_u$ . Then the activity duration is $t_u-t_l$ . If we have activity data as a set of time pairs $A=\{(t_{li}, t_{ui})\vert t_{li}\le t_{ui}\}$ where $i$ is in some index set, $N=\{1,2, \ldots, n\}$ , then the (average) cycle time is

$$t_{cyc}(A)= \frac{\underset{i \in N}{\sum} (t_{ui}-t_{li})}{n}.$$ (5.2)

Cycle time can be interpreted in different contexts. For example, in the system which consists of a buffer and a processor as shown in Figure 4.1, the system time can be measured over the entire processing activity from arrival to departure of the BufferProcessor system. Also waiting time can be considered as the time duration for the waiting activity in Buffer, while processing time can be the time duration between arrival to and departure from Processor.

Figure 4.1: A System having a Buffer and a Processor

Example 5.2 (Cycle Time as System Time)   Assume we have the set of time pairs $A=\{(5, 17), (7, 29), (15,41), (50, 62)\}$ from arrival to departure of the BufferProcessor system in Figure 4.1. Then the system time is $t_{cyc}(A)=(12+21+26+12)/4=17.75.$ $\square$