| # MAST # Modeling and Analysis Suite for Real-Time Applications Results of Examples

This document describes the results of applying the MAST analysis tools to the examples that appear in the "examples" directory of the MAST distribution.

## Table of Contents

- Template
- Caseva_Example
- Caseva_Multi
- Caseva_Simplified
- Caseva_With_Clock
- Caseva_With_Timer
- Controller
- Controller2
- Rmt
- Linear_Transactions_Only
- P_A_Test_Linear_Transactions_Only
- Example_5_2_4_1
- Example_5_2_4_2
- Example_5_3_5_1
- Example_5_3_5_2
- Example_5_3_5_3
- Example_5_3_5_4
- Example_5_3_6_1
- Example_5_3_6_2
- Example_5_3_6_3
- Example_5_3_6_4
- Example_5_3_7_1
- Example_6_4_8_1
- Example_6_4_8_2
- Example_6_4_8_3
- Example_6_4_9_1
- Example_6_4_9_2
- Example_6_4_9_2a
- Example_6_5_10_1
- Example_6_5_10_1a
- Example_6_5_10_2
- Example_6_5_10_2a
- Example_6_5_10_3
- Example_6_6_12
- Example_6_6_13
- Example_8_3_1
- Example_9_3_4trans
- Example_Varying_Priorities
- Example_With_Offsets
- Example_With_Delays
- Jane_Liu_Section_9_5_2
- Jane_Liu_Table_9_2
- Lehoczky_Example_3
- RTSS_98
- Simple_Linear
- WPDRST-1995

## Template

This example does not represent any practical system, but just contains a template of each of the different objects defined in MAST. It is useful for copying and pasting the desired template into your system model, and then changing it to contain the appropriate values.

This example should not be used as input to the analysis tools, but it can be used as input to the "Parse" tool.

## Caseva_Example

This example represents the software design of the CASEVA robot controller built by our group. It is a linear system running on a single processor. You will see that it contains a lot of shared resources and operations, because the software architecture of the CASEVA robot was based primarily on tasks synchronizing through Ada protected objects.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1420 | 220.31
Trajectory_Planning | 13240 | 263.28
Light Manager | 13564 | 40050.0
Reporter | 137614 | 653.13
Message_Logger | n/a | >100000.0

The system slack for this example is 100.78%.

The results are the same if the default priority assignment option is set.

## Caseva_Multi

This example represents a modification to the software design of the CASEVA robot controller, to use a multiprocessor architecture. Therefore, it is a linear system running on a multi-processor.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the linear analysis tools (Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 2714 | 210.94
Trajectory_Planning | 10775 | 433.59
Light Manager | 10599 | 66071.9
Reporter | 74974 | 1261.7
Message_Logger | n/a | >100000.0

The system slack for this example is 153.91%.

The results are the same if the default priority assignment option is set.

## Caseva_Simplified

This example represents a simplification of the software design of the CASEVA robot controller, to use less protected objects and operations. Therefore, it is a linear system running on a single processor.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1420 | 220.31
Trajectory_Planning | 13240 | 263.28
Light Manager | 13564 | 40050.0
Reporter | 137614 | 653.13
Message_Logger | n/a | >100000.0

The system slack for this example is 100.78%.

The results are the same if the default priority assignment option is set.

## Caseva_With_Clock

This example represents a modification to the CASEVA example, to incorporate the overhead effects of a hypothetical OS timer of the type Alarm Clock, which produces an interrupt each time a task requests being awakened.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, for the Classic_RM, Varying_Priorities, and Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1620 | 214.84
Trajectory_Planning | 13540 | 257.03
Light Manager | 13864 | 39079.7
Reporter | 139314 | 636.72
Message_Logger | n/a | >100000.0

The system slack for this example is 98.44%.

For the Offset_Based_Unoptimized analysis tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1770 | 214.84
Trajectory_Planning | 13690 | 257.03
Light Manager | 14014 | 39079.7
Reporter | 139464 | 636.72
Message_Logger | n/a | >100000.0

The system slack for this example is 98.44%.

And for the Holistic analysis tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1820 | 214.84
Trajectory_Planning | 13740 | 257.03
Light Manager | 14064 | 39079.7
Reporter | 139514 | 636.72
Message_Logger | n/a | >100000.0

The system slack for this example is 98.44%.

In all cases, the results are the same if the default priority assignment option is set.

## Caseva_With_Timer

This example represents a modification to the CASEVA example, to incorporate the overhead effects of a hypothetical OS timer of the "Ticker" type , which produces a periodic interrupt and introduces jitter in the wake up times.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 2520 | 196.88
Trajectory_Planning | 14940 | 235.16
Light Manager | 16649 | 35848.4
Reporter | 148584 | 584.38
Message_Logger | n/a | >100000.0

The system slack for this example is 89.84%.

The results are the same if the default priority assignment option is set.

## Controller

This example represents a system with three periodic tasks and one aperiodic task of the sporadic kind.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
Control | 46 | 39.84
Planning | 82 | 29.69
Status | 276 | 23.44
Emergency | 5.5 | 9.38

The system slack for this example is 8.59%.

The results are the same if the default priority assignment option is set.

## Controller2

This example represents a system with three periodic tasks and two aperiodic tasks of two kinds: sporadic and unbounded.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools and no priority assignment (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
Control | 66 | 6.25
lanning | 88 | 4.69
Status | 296 | 3.91
Emergency | 5 | 13.28
Communications | n/a | n/a

The system slack for this example is 0.78125%.

The priority assignment option should not be set because the soft deadline of the communications task is not taken into account by the priority assignment tools, and it would not be met.

## RMT

This example represents a simplification of the software design of the RMT robot controller built by our group. It is a linear system running on a distributed system.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, for the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1133 | 204.69
Main_Control_Loop | 34374 | 47.66
Gui | 191358 | 434.38

The system slack for this example is 37.50%.

For the Offset_Based_Unoptimized tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1133 | 161.72
Main_Control_Loop | 40563 | 26.56
Gui | 191408 | 434.38

And the system slack for this tool is 21.88%.

For the Holistic tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 1143 | -100.00
Main_Control_Loop | 69943 | -24.22
Gui | 193749 | -100.00

And the system slack for this tool is -21.09%.

If the default priority assignment option is set, the results of the example are as follows, for the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
Servo_Control | 2380 | 208.59
Main_Control_Loop | 34336 | 47.66
Gui | 191358 | 434.38

The system slack for this example is 42.19%.

## Linear_Transactions_Only

This example represents a linear system running on a distributed system. It has two processors, a network, and two transactions.

The results of the example are as follows, for the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
Trans1 | 8140 | 70.31
Trans2 | 6780 | 23.44

The system slack for this example is 17.97%.

For the Offset_Based_Unoptimized tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Trans1 | 8940 | 58.59
Trans2 | 8700 | 19.53

And the system slack for this tool is 14.84%.

For the Holistic tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Trans1 | 8940 | 42.19
Trans2 | 11790 | 13.28

And the system slack for this tool is 10.16%.

If the default priority assignment option is set, the results of the example are as follows, for the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
Trans1 | 3620 | 349.22
Trans2 | 8550 | 246.88

The system slack for this example is 163.28%.

If the default priority assignment option is set, for the Offset_Based_Unoptimized tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Trans1 | 3910 | 310.94
Trans2 | 12090 | 126.56

And the system slack for this tool is 97.66%.

If the default priority assignment option is set, for the Holistic tool the results are:

Transaction | WC Response times (ms) | Slack (%)
Trans1 | 3910 | 300.78
Trans2 | 12730 | 118.75

And the system slack for this tool is 91.41%.

## P_A_Test_Linear_Transactions_Only

This example is the same as the Linear_Transactions_Only, but without explicit priorities. Priority assignment techniques need to be used. The results obtained are much better than with the manual priority assigment made for Linear_Transactions_Only.

The results of the example are as follows, for the Offset_Based analysis tool:

Transaction | Slack (No Priority Assignment) | Slack (HOPA) | Slack (Simulated Annealing)
Trans1 | 70.21 | 349.22 | 349.22
Trans2 | 23.44 | 246.88 | 246.88
System | 17.97 | 163.28 | 163.28

Note: Results with priority assignment may differ from one execution to another due to the randomness in the algorithms.

## Example_5_1_2_2

This is the example from Section 5.1.2.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, which uses an interrupt service routine.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools and no priority assignment (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t1 | 8 | 78.91
int2 | 2 | 632.81
t2 | 303 | 443.75
t3 | 30 | 107.03
t4 | 77 | 107.81
t5 | 297 | 50.00

The system slack for this example is 17.97%.

If we set the priority asisgnment option to default, the results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t1 | 8 | 161.72
int2 | 2 | 1200
t2 | 83 | 417.97
t3 | 30 | 204.69
t4 | 77 | 285.94
t5 | 404 | 200

The system slack for this example is 42.97%.

## Example_5_2_4_1

This is the example from Section 5.2.4.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which the calculation of blocking times is the goal.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%) | Blocking Time
t1 | 2 | 66.41 | 0
t2 | 53 | 10.16 | 18
t3 | 73 | 19.53 | 18
t4 | 182 | 14.06 | 16
t5 | 251 | 46.88 | 16
t6 | 300 | 25.00 | 0

The system slack for this example is 3.13%.

The results are the same if the default priority assignment option is set.

## Example_5_2_4_2

This is the example from Section 5.2.4.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which the calculation of blocking times is the goal.

The analysis tools should be executed with the "Calculate Ceilings" option set. The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%) | Blocking Time
t1 | 2 | 66.41 | 0
t2 | 69 | 10.16 | 34
t3 | 91 | 19.53 | 34
t4 | 182 | 14.06 | 16
t5 | 251 | 46.88 | 16
t6 | 300 | 25.00 | 0

The system slack for this example is 3.13%.

The results are the same if the default priority assignment option is set.

## Example_5_3_5_1

This is the example from Section 5.3.5.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there are two sporadic tasks that are handled through interrupt service routines.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_i1 | 32 | -100.00
t_a2 | 146 | -100.00
t_i3 | 32 | -96.88
t_a4 | 39 | -100.00

The system slack for this example is -84.38%.

The results are the same if the default priority assignment option is set.

## Example_5_3_5_2

This is the example from Section 5.3.5.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there are two sporadic tasks that are each handled through a short interrupt service routine, followed by an application task.

The results of the example are as follows, with the Offset_Based analysis tools:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 2.5 | 25.00
t_2 | 146 | 10.16
t_3 | 46 | 13.28
t_4 | 9.5 | 7.03

The system slack for this example is 3.91%.

If we use the Offset_Based_Unoptimized analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 3 | 25.00
t_2 | 146 | 8.59
t_3 | 46.5 | 10.94
t_4 | 9.5 | 7.03

And the system slack for this tool is 3.13%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 3.5 | 25.00
t_2 | 146 | 8.59
t_3 | 47 | 10.94
t_4 | 9.5 | 7.03

And the system slack for this tool is 3.13%.

In all cases, the results are the same if the default priority assignment option is set.

## Example_5_3_5_3

This is the example from Section 5.3.5.3 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there are two sporadic tasks that are each handled through polling servers.

The results of the example are as follows, with any of the analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 5 | -100.00
t_2 | 231.1 | -15.63
t_3 | 127.5 | -19.53
t_4 | 9.9 | -23.44

The system slack for this example is -6.25%. The results are different than in the Real-Time Analysis Handbook because MAST uses a more precise technique to model the polling tasks.

The results are the same if the default priority assignment option is set.

## Example_5_3_5_4

This is the example from Section 5.3.5.4 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there are two sporadic tasks that are each handled through sporadic servers.

The results of the example are as follows, with the Holistic, Offset_Based, or Offset_Based_Unoptimized analysis tools.

Transaction | WC Response times (ms) | Slack (%)
t_1 | 3.5 | 0.00
t_2 | 146 | 10.16
t_3 | 47 | 0.00
t_4 | 9.5 | 7.03

The system slack for this example is 0.00%, because the capacity of the sporadic servers is just equal to the maximum load.

The results are the same if the default priority assignment option is set.

## Example_5_3_6_1

This is the example from Section 5.3.6.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there is one bursty task that is handled through an interrupt service routine.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 35 | -100.00
t_2 | 25 | -40.63
t_3 | 290 | -100.0

The system slack for this example is -28.91%.

The results are the same if the default priority assignment option is set.

## Example_5_3_6_2

This is the example from Section 5.3.6.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there in which there is one bursty task that is handled through a short interrupt service routine, that triggers an application task.

The results of the example are as follows, with with the Offset_Based or the Offset_Based_Unoptimized analysis tools:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 12.5 | 25.00
t_2 | 47.5 | 63.28
t_3 | 295 | 28.91

The system slack for this example is 10.94%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 12.5 | 25.00
t_2 | 50 | 63.28
t_3 | 295 | 28.91

The system slack for this tool is 10.94%.

In all cases, the results are the same if the default priority assignment option is set.

## Example_5_3_6_3

This is the example from Section 5.3.6.3 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there in which there is one bursty task that is handled through a short interrupt service routine, that triggers an application task running under a polling server.

The results of the example are as follows, with with any of the monoprocessor or linear analysis tools (classic_RM, Varying_Priorities, Holistic, Offset_Based, or the Offset_Based_Unoptimized):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 13 | 29.69
t_2 | 191 | 90.63
t_3 | 266 | 35.16

The system slack for this example is 13.28%.

In all cases, the results are the same if the default priority assignment option is set.

The results are different than in the Real-Time Analysis Handbook, because MAST uses a more precise technique to model polling server tasks.

## Example_5_3_6_4

This is the example from Section 5.3.6.4 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there is one bursty task that is handled through a sporadic server.

The results of the example are as follows, with any of the linear analysis tools (Holistic, Offset_Based_Unoptimized, or Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 12.5 | -100.00
t_2 | 270 | -20.31
t_3 | 271 | -100.0

The system slack for this example is -20.31%.

With the default priority assignment option set, the system slack obtained is the same, although the response times are different because some priorities are exchanged.

## Example_5_3_7_1

This is the example from Section 5.3.7.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). It is a linear system running on a single processor, in which there is one unbounded task that is handled through a sporadic server.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | >>1E100 | >100000
t_2 | 42 | 134.38
t_3 | 146 | 115.63

The system slack for this example is 59.38%.

The results of the example are as follows if the default priority assignment option is set, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | >>1E100 | >100000
t_2 | 40 | 150
t_3 | 140 | 129.69

The system slack for this example is 66.41%.

## Example_6_4_8_1

This is the example from Section 6.4.8.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 106.8 | -17.19
t_2 | 67.6 | -10.16
t_3 | 283.2 | -100

The system slack for this example is -6.25%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 173.4 | -100
t_2 | 133 | -96.09
t_3 | 496.6 | -100

The system slack for this example is -96.09%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 173.6 | -100
t_2 | 134.4 | -96.88
t_3 | 496.8 | -100

The system slack for this tool is -96.09%.

If the default priority assignment option is used, the results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 41.6 | 2.34
t_2 | 147.8 | 3.13
t_3 | 283.2 | 51.56

The system slack for this example is 0.78125%.

## Example_6_4_8_2

This is the example from Section 6.4.8.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 41.6 | 2.34
t_2 | 147.8 | 3.13
t_3 | 283.2 | 51.56

The system slack for this example is 0.78125%.

The results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 42.0 | 1.56
t_2 | 148.2 | 2.34
t_3 | 283.6 | 46.88

The system slack for this example is 0.78125%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 42.2 | 0
t_2 | 149.6 | 0
t_3 | 283.8 | 46.09

The system slack for this tool is 0%.

In all cases, the results are the same if we set the priority assignment option.

## Example_6_4_8_3

This is the example from Section 6.4.8.3 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 41.6 | 0
t_2 | 169 | 0
t_3 | 298.2 | 14.84

The system slack for this example is 0%.

The results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 42 | -0.78125
t_2 | 169.4 | -0.78125
t_3 | 591.8 | -11.72

The system slack for this example is -0.78125%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 42.2 | -0.78125
t_2 | 170.8 | -0.78125
t_3 | 592 | -14.84

The system slack for this tool is -0.78125%.

The results are the same if the default priority assignment option is set.

## Example_6_4_9_1

This is the example from Section 6.4.9.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 102 | -100
t_2a | 62.8 | -100
t_2b | 62.8 | -100
t_3 | 273.6 | -100

The system slack for this example is -99.22%.

The results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 102.6 | -100
t_2a | 63 | -100
t_2b | 63 | -100
t_3 | 274.2 | -100

The system slack for this example is -99.22%.

If the default priority assignment option is set, the tool does not find a better solution.

## Example_6_4_9_2

This is the example from Section 6.4.9.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 102 | -4.69
t_2 | 62.8 | -3.13
t_3 | 2.8 | -100
t_4 | 273.6 | -100

The system slack for this example is -2.34%.

The results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 102.6 | -6.25
t_2 | 63 | -4.69
t_3 | 3 | -100
t_4 | 274.2 | -100

The system slack for this example is -3.13%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 102.8 | -100
t_2 | 63.2 | -100
t_3 | 3.2 | -100
t_4 | 274.4 | -100

The system slack for this tool is -14.84%.

If the default priority assignment option is set, the tool does not find a better solution.

## Example_6_4_9_2a

This is the example from Section 6.4.9.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993). modified to use permanent overridden priorities to represent the changes of priorities in the same trasnaction. Notice that the behavior is different under this new model, because a job of a transaction cannot start executing until the previous job had finished.

The results of the example are as follows, with the Varying_Priorities analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 101.8 | -4.69
t_2 | 62.8 | -3.13
t_3 | 2.8 | -100
t_4 | 273.6 | -100

The system slack for this example is -2.34%.

In this case, because the system is not schedulable, the priority assignment techniques do not find a solution.

## Example_6_5_10_1

This is the example from Section 6.5.10.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 121 | -42.97
t_2 | 113 | -29.69
t_3 | 98 | -100
t_4 | 197 | -17.97
t_5 | 354 | -100
t_6 | 372 | -17.97

The system slack for this example is -17.97%.

The results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -89.06
t_3 | >> | -100
t_4 | >> | -69.53
t_5 | >> | -100
t_6 | >> | -82.03

The system slack for this example is -51.56%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -100
t_3 | >> | -100
t_4 | >> | -77.34
t_5 | >> | -100
t_6 | >> | -96.09

The system slack for this tool is -58.59%.

If the default priority assignment option is set, the results of the example with the Offset_Based analysis tool are not improved, because the system remains unschedulable.

If the default priority assignment option is set, the results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -100
t_3 | >> | -100
t_4 | >> | -66.41
t_5 | >> | -100
t_6 | >> | -100

The system slack for this example is -38.28%.

If the default priority assignment option is set, and if we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -100
t_3 | >> | -100
t_4 | >> | -82.72
t_5 | >> | -100
t_6 | >> | -100

The system slack for this tool is -50%.

## Example_6_5_10_1a

This is the example from Section 6.5.10.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993), modified to use permanent overridden priorities to represent the changes of priorities in the same trasnaction. Notice that the behavior is different under this new model, because a job of a transaction cannot start executing until the previous job had finished.

The results of the example are as follows, with the Varying_Priorities analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 55 | -5.47
t_2 | 89 | -3.91
t_3 | 98 | -17.19
t_4 | 187 | -3.13
t_5 | 338 | -10.94
t_6 | 372 | -3.91

The system slack for this example is -1.56%.

The priority assignment tools do not find a better solution in this case because they do not take into account the permanent overridden priorities used in this model.

## Example_6_5_10_2

This is the example from Section 6.5.10.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 49 | 9.38
t_2 | 108 | 5.47
t_3 | 80 | 28.91
t_4 | 178 | 3.91
t_5 | 219 | 14.06
t_6 | 372 | 5.47

The system slack for this example is 1.56%.

The results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -100
t_3 | >> | -100
t_4 | >> | -71.88
t_5 | >> | -100
t_6 | >> | -99.22

The system slack for this example is -48.44%.

If we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -100
t_3 | >> | -100
t_4 | >> | -73.44
t_5 | >> | -100
t_6 | >> | -99.22

The system slack for this tool is -55.47%.

If the default priority assignment option is set with the Offset_Based analysis tool, no results better than the original are obtained.

If the default priority assignment option is set, the results of the example are as follows, with with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -92.19
t_3 | >> | -100
t_4 | >> | -66.41
t_5 | >> | -100
t_6 | >> | -100

The system slack for this example is -36.06%.

If the default priority assignment option is set, and if we use the Holistic analysis tool, we get:

Transaction | WC Response times (ms) | Slack (%)
t_1 | >> | -100
t_2 | >> | -100
t_3 | >> | -100
t_4 | >> | -78.91
t_5 | >> | -100
t_6 | >> | -100

The system slack for this tool is -50.78%.

## Example_6_5_10_2a

This is the example from Section 6.5.10.2 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993), modified to use permanent overridden priorities to represent the changes of priorities in the same trasnaction. Notice that the behavior is different under this new model, because a job of a transaction cannot start executing until the previous job had finished.

The results of the example are as follows, with the Varying_Priorities analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 22 | -16.41
t_2 | 87 | -10.16
t_3 | 96 | -50
t_4 | 150 | -7.81
t_5 | 344 | -32.81
t_6 | 234 | -9.38

The system slack for this example is -3.91%.

In this case, because the system is not schedulable, the priority assignment techniques do not find a solution.

## Example_6_5_10_3

This is the example from Section 6.5.10.3 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 13 | 9.38
t_2 | 47 | 5.47
t_3 | 56 | 28.91
t_4 | 123 | 3.91
t_5 | 194 | 14.06
t_6 | 372 | 5.47

The system slack for this example is 1.56%.

The results are the same if the default priority assignment option is set.

## Example_6_6_12

This is the example from Section 6.6.12 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with any of the linear analysis tools (Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 40 | -100
t_2 | 220 | -25
t_3 | 30 | -33.59
t_4 | 380 | -30.47
t_5 | 90 | -100

The system slack for this example is -10.16%.

The results are the same if the default priority assignment option is set.

## Example_6_6_13

This is the example from Section 6.6.13 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 30 | -22.66
t_2 | 170 | -18.75
t_3 | 300 | -100
t_4 | 40 | -100

The system slack for this example is -7.03%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 30 | -67.19
t_2 | 220 | -44.53
t_3 | 370 | -100
t_4 | 40 | -100

The system slack for this example is -21.09%.

The results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 30 | -83.59
t_2 | 230 | -50
t_3 | 370 | -100
t_4 | 40 | -100

The system slack for this example is -25%.

The priority asisgnment option does not find a schedulable solution for the Holistic or Offset_Based_Unoptimized analysis tools. However, with the Offset_Based tool it does find a solution:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 70 | 0
t_2 | 60 | 0
t_3 | 270 | 0
t_4 | 60 | 50

The system slack for this example is 0.00%.

## Example_8_3_1

This is the example from Section 8.3.1 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993).

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
alpha1 | 109 | -100
alpha1_1 | 1146 | -100
alpha2 | 3838 | -100
alpha2_1 | 3519 | -100
alpha3 | 27 | -100
alpha3_1 | 7374 | -100
alpha3_2 | 199 | -100
alpha3_3 | 317 | -100
charlie | 115 | -100
charlie_1 | 107 | -100
charlie_2 | 1146 | -100
charlie_3 | 4150 | -100
charlie_4 | 4891 | -100
charlie_5 | 11857 | -100
echo_1 | 1041 | -100
echo_2 | 1194 | -100
fox_1 | 324 | -100
for_1_1 | 4866 | -100
fox_2 | 2060 | -100
gamma | 912 | -100
hector | 1012 | -100
monkey | 4555 | -100

The system slack for this example is -68.75%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
alpha1 | 215 | -100
alpha1_1 | 2717 | -100
alpha2 | 8527 | -100
alpha2_1 | 7854 | -100
alpha3 | 27 | -100
alpha3_1 | 12457 | -100
alpha3_2 | 199 | -100
alpha3_3 | 656 | -100
charlie | 205 | -100
charlie_1 | 193 | -100
charlie_2 | 2717 | -100
charlie_3 | 9162 | -100
charlie_4 | 10007 | -100
charlie_5 | 22464 | -100
echo_1 | 2451 | -100
echo_2 | 2784 | -100
fox_1 | 696 | -100
for_1_1 | 9571 | -100
fox_2 | 4402 | -100
gamma | 2053 | -100
hector | 2301 | -100
monkey | 8921 | -100

The system slack for this example is -76.56%.

The results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
alpha1 | 236 | -100
alpha1_1 | 2947 | -100
alpha2 | 8866 | -100
alpha2_1 | 8512 | -100
alpha3 | 27 | -100
alpha3_1 | 12789 | -100
alpha3_2 | 209 | -100
alpha3_3 | 704 | -100
charlie | 217 | -100
charlie_1 | 205 | -100
charlie_2 | 2947 | -100
charlie_3 | 9538 | -100
charlie_4 | 10573 | -100
charlie_5 | 23362 | -100
echo_1 | 2651 | -100
echo_2 | 2971 | -100
fox_1 | 775 | -100
for_1_1 | 10231 | -100
fox_2 | 4837 | -100
gamma | 2241 | -100
hector | 2451 | -100
monkey | 9546 | -100

The system slack for this example is -77.34%.

In these cases, because the system is not schedulable, the priority assignment techniques do not find a solution.

## Example_9_3_4trans

This is the example from Section 9.3.4 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993), but transformed to achieve a utilization under 100% that allows the analysis.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
tc1 | 121 | 508.59
tc2 | 60.2 | 799.22
tt1 | 3.2 | 14789.8
tt2 | 1.2 | 73950
om | 23.2 | 2053.9
s1 | 0.8 | 12878.1
s2 | 0.4 | 12878.1

The system slack for this example is 248.44%.

If the default priority assignment option is set, the results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
tc1 | 98.6 | 508.59
tc2 | 37.8 | 825.78
tt1 | 101 | 15280.5
tt2 | 99 | 76404.7
om | 121 | 3352.3
s1 | 0.4 | 13576.6
s2 | 0.8 | 13576.6

The system slack for this example is 267.19%.

## Example_Varying_Priorities

This is the example from Section 9.3.4 of "A Practitioner's Handbook for Real-Time Analysis" (K. Klein et al, Kluwer Academic Pub., 1993), but transofmed to achieve a utilization under 100% that allows the analysis.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
t_1 | 28 | 9.38
t_2 | 98 | 7.03
t_3 | 47 | 3.13
t_4 | 195 | 8.59
t_5 | 223 | 19.53

The system slack for this example is 0.78125%.

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based) and the default priority option set:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 31 | 13.28
t_2 | 90 | 9.38
t_3 | 25 | 4.69
t_4 | 195 | 11.72
t_5 | 223 | 32.81

The system slack for this example is 1.56%.

## Example_With_Offsets

This is an example using offsets.

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 60 | 75
t_2 | 85 | 42.19
t_3 | 215 | 50

The system slack for this example is 17.19%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool

Transaction | WC Response times (ms) | Slack (%)
t_1 | 60 | 50
t_2 | 85 | 25
t_3 | 215 | 32.81

The system slack for this example is 10.94%.

The results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 140 | -100
t_2 | 85 | -67.19
t_3 | 420 | -100

The system slack for this example is 10.94%.

The results of the example are as follows, with the Offset_Based analysis tool and the default priority assignment option set:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 90 | 75
t_2 | 75 | 32.81
t_3 | 215 | 50

The system slack for this example is 17.19%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool and the default priority assignment option set:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 90 | 75
t_2 | 75 | 25
t_3 | 215 | 50

The system slack for this example is 17.19%.

If the default priority assignment option is set with the Holistic analysis tool, no better solution is found.

## Example_With_Delays

This is an example using delays.

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 70 | -100
t_2 | 145 | -67.19
t_3 | 425 | -100

The system slack for this example is -28.91%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool

Transaction | WC Response times (ms) | Slack (%)
t_1 | 70 | -100
t_2 | 155 | -71.88
t_3 | 570 | -100

The system slack for this example is -33.59%.

The results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 90 | -100
t_2 | 235 | -100
t_3 | 675 | -100

The system slack for this example is -70.31%.

If the default priority assignment option is set, the tool does not find a better solution.

## Jane_Liu_Section_9_5_2

This is the example from Section 9.5.2 of "Real-Time Systems" (Jane Liu, Prentice Hall, 2000).

The results of the example are as follows, with any of the linear analysis tools (Holitic, Ofsfet_Based_Unoptimized, or Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
trans_1 | >> | -83.59
trans_2 | >> | -83.59

The system slack for this example is -42.97%.

In all the cases, the results of the example are as follows, with the default priority assignment option set:

Transaction | WC Response times (ms) | Slack (%)
trans_1 | 10 | 16.41
trans_2 | 10 | 16.41

The system slack for this example is 8.59%.

## Jane_Liu_Table_9_2

This is the example from Table 9.2 of "Real-Time Systems" (Jane Liu, Prentice Hall, 2000).

The results of the example are as follows, with either the Offset_Based_Unoptimized, or the Offset_Based alanysis tools:

Transaction | WC Response times (ms) | Slack (%)
task_1 | 10 | 25
task_2 | 7 | 166.41
task_3 | 1 | 9.38
task_4 | 14 | 19.53

The system slack for this example is 4.69%.

The results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
task_1 | 11 | 25
task_2 | 7 | 166.41
task_3 | 1 | 9.38
task_4 | 14 | 19.53

The system slack for this example is 4.69%.

In all the cases, the results of the example are the same when the default priority assignment option is set.

## Lehoczky_Example_3

The results of the example are as follows, with any of the monoprocessor or linear analysis tools (Classic_RM, Varying_Priorities, Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
c1 | 52 | -2.34
c2 | 156 | -3.91

The system slack for this example is -1.56%.

In all cases, if the default priority assignment option is set the results obtained are:

Transaction | WC Response times (ms) | Slack (%)
c1 | 108 | 1.56
c2 | 52 | 1.56

The system slack for this example is 0.78125%.

## RTSS_98

The results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 4 | 235.94
t_2 | 145 | 70.31
t_3 | 5 | 142.19
t_4 | 140 | 50

The system slack for this example is 32.81%.

The results of the example are as follows, with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 4 | 210
t_2 | 145 | 70.31
t_3 | 5 | 142.19
t_4 | 140 | 50

The system slack for this example is 32.81%.

The results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 4 | -50
t_2 | 270 | -5.47
t_3 | 5 | -100
t_4 | 140 | -100

The system slack for this example is -4.69%.

If the default priority assignment option is set, the results of the example are as follows, with the Offset_Based analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 4 | 235.94
t_2 | 145 | 70.31
t_3 | 5 | 142.19
t_4 | 140 | 50

The system slack for this example is 32.81%.

If the default priority assignment option is set, the results of the example are as follows, with the Offset_Based_Unoptimized analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 4 | 235.94
t_2 | 145 | 70.31
t_3 | 5 | 142.19
t_4 | 140 | 50

The system slack for this example is 32.81%.

If the default priority assignment option is set, the results of the example are as follows, with the Holistic analysis tool:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 4 | 150
t_2 | 198 | 28.13
t_3 | 5 | 142.19
t_4 | 140 | 50

The system slack for this example is 23.44%.

## Simple_Linear

The results of the example are as follows, with any of the linear analysis tools (Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
trans_1 | 27.4 | -7.03
trans_2 | 73 | -12.5

The system slack for this example is -4.69%.

If the default priority assignment option is set, the results of the example are as follows, with any of the linear analysis tools (Holistic, Offset_Based_Unoptimized, and Offset_Based):

Transaction | WC Response times (ms) | Slack (%)
trans_1 | 42.8 | 28.13
trans_2 | 27.4 | 21.88

The system slack for this example is 15.63%.

## WPDRTS_1995

The results of this example with the Offset_Based and the Offset_Based_Unoptimized analysis tools are:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 620 | -100
t_2 | 3220 | -100
t_3 | 7835 | -100
t_4 | 1160 | -100
t_5 | 5095 | -100
t_6 | 205 | -100
t_7 | 1265 | -100

The system slack for this example is -25%.

The results of this example with the Holistic analysis tool are:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 760 | -100
t_2 | 3730 | -100
t_3 | 9360 | -100
t_4 | 1380 | -100
t_5 | 6005 | -100
t_6 | 265 | -100
t_7 | 1410 | -100

The system slack for this example is -28.13%.

The results of this example with the Offset_Based analysis tool are:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 1265 | 2.34
t_2 | 2445 | 4.69
t_3 | 2870 | 10.94
t_4 | 990 | 2.34
t_5 | 2050 | 7.81
t_6 | 1165 | 16.41
t_7 | 2130 | 75

The system slack for this example is 0.78125%.

The results of this example with the Offset_Based_Unoptimized analysis tool are:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 1345 | 1.56
t_2 | 2465 | 3.13
t_3 | 2870 | 10.94
t_4 | 990 | 0.78125
t_5 | 2055 | 6.25
t_6 | 1165 | 12.5
t_7 | 2150 | 27.34

The system slack for this example is 0%.

The results of this example with the Holistic analysis tool are:

Transaction | WC Response times (ms) | Slack (%)
t_1 | 1485 | 3.13
t_2 | 2360 | 7.03
t_3 | 2995 | 16.41
t_4 | 1120 | 9.38
t_5 | 2255 | 16.41
t_6 | 1225 | 16.41
t_7 | 2255 | 50

The system slack for this example is 0.78125%.