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tAllocation tMargin
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Event 2
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Task A Time Allocation Maximum Budgeted Performance
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Queue Time Transport Time
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tMin. tMean tBudget -3s +3s tMargin
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Figure 49.7 Task Timeline Elements
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49.6 Applying Statistics to Multi-Task System Performance
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bution, we also expect the task to be completed no sooner than the -3s point the early nish point. If we translate this analysis into the Requirements Domain Solution, we generate a requirements statement that captures the capability and its associated performance allocation. Let s suppose that Capability B requires that Capability A complete processing and transmit data within 250 milliseconds AFTER Event 1 occurs. Consider the following example of a speci cation requirement statement.
EXAMPLE 49.2
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When event 1 occurs, (Capability A) shall process the incoming data and transmit the results to (Capability B) within 250 milliseconds.
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Now let s suppose that Capability B requires receipt of the data within a window of time between 240 milliseconds and 260 milliseconds. The requirement might read as follows:
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EXAMPLE 49.3
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When event 1 occurs, (Capability A) shall process the incoming data and transmit the results to (Capability B) within 250 10 milliseconds.
Guidepost 49.2 Our discussion emphasizes how overall system task performance can vary. To understand how this variation occurs, let s take it one step further and discuss it relative to the key task phases.
49.6 APPLYING STATISTICS TO MULTI-TASK SYSTEM PERFORMANCE
Our previous discussion focused on the performance of a single capability. If the statistical variations for a single capability are aggregated for a multi-level system, we can easily see how this impacts overall system performance. We can illustrate this by the example shown in Figure 49.8. Let s assume we have an overall task called Perform Task A. The purpose of Task A is to perform a computation using variable inputs, I1 and I2, and produce a computed value as an output. The key point of our discussion here is to illustrate time-based statistical variances to complete processing.
EXAMPLE 49.4
Let s assume that Task A consists of two subtasks, Subtask A1 and Subtask A2. Subtask A1 enters inputs I1 and I2. Each input, I1 and I2, has values that vary about a mean.
When Subtask A1 is initiated, it produces a response within tA1Mean that varies from tA1Min to tA1Max. The output of Subtask A1 serves as an input to Subtask A2. Subtask A2 produces a response within tA2Mean that may occur as early as tA2Min or as late as tA2Max. If we investigate the overall performance of Task A, we nd that Task A is computed within tCompute as indicated by the central mean. The overall Task A performance is determined by the statistical variance of the summation of Subtask A1 and Subtask A2 processing times.
49
System Performance Analysis, Budgets, and Safety Margins
Perform Task A
-3s +3s -3s +3s
Value tCompute
Time
Variable Input I1 Perform Perform SubTask A1 SubTask A1 Task A1 Cycle Time Mean (mA1)
-3s +3s
Perform Perform SubTask A2 SubTask A2 Task A2 Cycle Time Mean (mA2)
Value tA1Min. tA1Mean tA1Max. tA1Transport
-3s +3s
Variable Input I2
tA2Min.
Time
tA2Mean tA2Max. tA2Transport
Figure 49.8 Task Timeline (MET) Statistical Analysis
Guidepost 49.3 We have seen how statistical variations in inputs and processing affect system performance from a timing perspective. Similar methods are applied to the statistical variations of inputs 1 and 2 as independent variables over a range of values. The point of our discussion is to heighten your awareness of these variances. THINK about and CONSIDER statistical variability when allocating performance budgets and margins as well as analyzing data produced by the system to determine compliance with requirements. Referral For more information about statistical variability, refer to 48 on Statistical In uences on System Design Practices. Given this understanding, let s return to a previous discussion about applying statistical variations to phases of a task.
49.7 APPLYING STATISTICAL VARIATIONS TO INTRA-TASK PHASES
In our earlier discussion of task phases consisting of queue time, capability performance time, and transport time we identi ed the various time segments within each phase. Let s examine how statistical in uences affect those phases. Figure 49.9 serves as the focal point for our discussion. The central part of the gure represents an overall task and its respective queue time, processing time, and transport time phases. Below each phase is a statistical representation of the execution time. The top portion of the chart illustrates the aggregate performance of the overall task execution.