CSCE 990 Real-Time Systems
Fall 2007
Steve Goddard
Homework 1, September 4
(Total of 100 points)
1. (10 points) Because sporadic jobs may have varying release times and execution times, the periodic task model may be too inaccurate and can lead to undue under utilization of the processor even when the inter-release times of jobs are bounded from below and their executions are bounded from above. As an example, suppose that we have a stream of sporadic jobs whose inter-release times are uniformly distributed from 6 to 12. Their execution times are uniformly distributed from 2 to 4. (Note: in general, we do not assume that arrival times and execution intervals are uniformly distributed. We make this assumption here to simplify the analysis.)
(a) What are the parameters of the periodic task if we were to use such a task to model the stream?
(b) Compare the utilization of the periodic task in part (a) with the average utilization of the sporadic job stream.
2. (60 points) Consider the synchronous task set shown in Table 1 (on the next page). This task set comes from an embedded signal processing application for an anti-submarine warfare (ASW) system. More specifically, the task set is a modified subset of the tasks that implement the Directed Low Frequency Analysis and Recording (DIFAR) acoustic signal processing application from the Airborne Low Frequency Sonar (ALFS) system of the U.S. NavyÕs SH-60B LAMPS MK III anti-submarine helicopter. The ALFS system processes low frequency signals received by sonobuoys in the water. Its primary function is to detect and track submarines and to calculate range and bearing estimates to each target.
The task set shown in Table 1 represents an implementation of a portion of the DIFAR application on a Mercury PowerPC 6U VME board with a 200MHz 603e processor. This portion of the DIFAR application processes five bands of Constant Resolution (CR) data from each of five sonobuoys. In this assignment, we will assume all tasks are independent.
a. (15 pts) For all 1 £ i £ 40, what is the utilization of task Ti?
b. (5 pts) What is the system utilization?
c. (5 pts) What is the Hyperperiod of the task set?
d. (5pts) What are the possible frame sizes that could be used to create a cyclic schedule for this task set?
e. (20 pts) Create a cyclic schedule for the task set (you may want to create a program to do this using the Iterative Network Flow algorithm). Hand in the scheduled created. If you wrote a program to generate the schedule, please hand it in as well. You can retrieve a text file containing the task parameters in 4-tuple form from
http://www.cse.unl.edu/~goddard/Courses/RealTimeSystems/Assignments/HW1table1.txt.
f. (5 pts) What is the frame size f of your schedule?
g. (5 pts) How many minor cycles are there in your major cycle?
Task |
Phase |
Period |
Time/Exec |
Relative |
|
Processing |
|
ID |
in
ms |
in
ms |
in
ms |
Deadline |
|
Primitive |
|
1 |
0 |
250 |
6.4545 |
250 |
|
FLW |
|
2 |
0 |
250 |
30.1303 |
250 |
|
BDFC |
|
3 |
0 |
250 |
0.3437 |
250 |
|
MASTERMCS |
|
4 |
0 |
250 |
0.1022 |
250 |
|
SLAVEMCS |
|
5 |
0 |
250 |
5.7349 |
250 |
|
DIFARDAD |
|
6 |
0 |
250 |
5.7557 |
250 |
|
DIFARDAD |
|
7 |
0 |
250 |
5.7974 |
250 |
|
DIFARDAD |
|
8 |
0 |
250 |
5.8807 |
250 |
|
DIFARDAD |
|
9 |
0 |
250 |
6.0472 |
250 |
|
DIFARDAD |
|
10 |
0 |
250 |
4.3071 |
250 |
|
DIFARDAD |
|
11 |
0 |
250 |
7.7672 |
250 |
|
DIFARDAD |
|
12 |
0 |
250 |
14.6875 |
250 |
|
DIFARDAD |
|
13 |
0 |
250 |
7.183 |
250 |
|
CRFIL |
|
14 |
0 |
250 |
7.3999 |
250 |
|
CRFIL |
|
15 |
0 |
250 |
7.8337 |
250 |
|
CRFIL |
|
16 |
0 |
250 |
8.7012 |
250 |
|
CRFIL |
|
17 |
0 |
250 |
8.7012 |
250 |
|
CRFIL |
|
18 |
0 |
250 |
8.1264 |
250 |
|
CRSPECANAL |
|
19 |
0 |
250 |
8.1264 |
250 |
|
CRSPECANAL |
|
20 |
0 |
250 |
8.4815 |
250 |
|
CRSPECANAL |
|
21 |
0 |
250 |
9.1918 |
250 |
|
CRSPECANAL |
|
22 |
0 |
250 |
9.1918 |
250 |
|
CRSPECANAL |
|
23 |
0 |
250 |
3.217 |
250 |
|
ALLBANDMERGE |
|
24 |
0 |
250 |
3.5179 |
250 |
|
SAD |
|
25 |
0 |
250 |
3.6363 |
250 |
|
GRM |
|
26 |
0 |
250 |
5.1914 |
250 |
|
BBC |
|
27 |
0 |
250 |
0.1496 |
250 |
|
GRAMMERGE |
|
28 |
0 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
29 |
0 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
30 |
0 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
31 |
0 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
32 |
0 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
33 |
0 |
2000 |
3.1913 |
2000 |
|
ALI |
|
34 |
0 |
2000 |
5.1122 |
2000 |
|
BRG |
|
35 |
0 |
2000 |
0.5047 |
2000 |
|
ALIMERGE |
|
36 |
0 |
2000 |
0.5906 |
2000 |
|
BEARMERGE |
|
37 |
0 |
6000 |
2.4799 |
6000 |
|
AUTODETECT |
|
38 |
0 |
6000 |
0.199 |
6000 |
|
BINMERGE |
|
39 |
0 |
6000 |
0.6898 |
6000 |
|
AUTODETECTMERGE |
|
40 |
0 |
6000 |
40.823 |
6000 |
|
EXTRAMERGE |
Table 1: Synchronous signal processing task set for a 200MHz 603e PowerPC.
http://www.cse.unl.edu/~goddard/Courses/RealTimeSystems/Assignments/HW1table2.txt.
Task |
Phase |
Period |
Time/Exec |
Relative |
|
Processing |
|
ID |
in
ms |
in
ms |
in
ms |
Deadline |
|
Primitive |
|
1 |
0 |
250 |
6.4545 |
250 |
|
FLW |
|
2 |
0.001 |
250 |
30.1303 |
250 |
|
BDFC |
|
3 |
0.002 |
250 |
0.3437 |
250 |
|
MASTERMCS |
|
4 |
0.003 |
250 |
0.1022 |
250 |
|
SLAVEMCS |
|
5 |
0.004 |
250 |
5.7349 |
250 |
|
DIFARDAD |
|
6 |
0.004 |
250 |
5.7557 |
250 |
|
DIFARDAD |
|
7 |
0.004 |
250 |
5.7974 |
250 |
|
DIFARDAD |
|
8 |
0.004 |
250 |
5.8807 |
250 |
|
DIFARDAD |
|
9 |
0.004 |
250 |
6.0472 |
250 |
|
DIFARDAD |
|
10 |
0.004 |
250 |
4.3071 |
250 |
|
DIFARDAD |
|
11 |
0.004 |
250 |
7.7672 |
250 |
|
DIFARDAD |
|
12 |
0.004 |
250 |
14.6875 |
250 |
|
DIFARDAD |
|
13 |
0.005 |
250 |
7.183 |
250 |
|
CRFIL |
|
14 |
0.005 |
250 |
7.3999 |
250 |
|
CRFIL |
|
15 |
0.005 |
250 |
7.8337 |
250 |
|
CRFIL |
|
16 |
0.005 |
250 |
8.7012 |
250 |
|
CRFIL |
|
17 |
0.005 |
250 |
8.7012 |
250 |
|
CRFIL |
|
18 |
0.006 |
250 |
8.1264 |
250 |
|
CRSPECANAL |
|
19 |
0.006 |
250 |
8.1264 |
250 |
|
CRSPECANAL |
|
20 |
0.006 |
250 |
8.4815 |
250 |
|
CRSPECANAL |
|
21 |
0.006 |
250 |
9.1918 |
250 |
|
CRSPECANAL |
|
22 |
0.006 |
250 |
9.1918 |
250 |
|
CRSPECANAL |
|
23 |
250.007 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
24 |
250.007 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
25 |
250.007 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
26 |
250.007 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
27 |
250.007 |
500 |
3.3671 |
500 |
|
CRDETECT |
|
28 |
250.008 |
250 |
3.217 |
250 |
|
ALLBANDMERGE |
|
29 |
250.009 |
250 |
3.5179 |
250 |
|
SAD |
|
30 |
250.010 |
250 |
3.6363 |
250 |
|
GRM |
|
31 |
250.010 |
250 |
5.1914 |
250 |
|
BBC |
|
32 |
250.011 |
250 |
0.1496 |
250 |
|
GRAMMERGE |
|
33 |
1750.011 |
2000 |
3.1913 |
2000 |
|
ALI |
|
34 |
1750.011 |
2000 |
5.1122 |
2000 |
|
BRG |
|
35 |
1750.012 |
2000 |
0.5047 |
2000 |
|
ALIMERGE |
|
36 |
1750.012 |
2000 |
0.5906 |
2000 |
|
BEARMERGE |
|
37 |
5750.012 |
6000 |
2.4799 |
6000 |
|
AUTODETECT |
|
38 |
5750.013 |
6000 |
0.199 |
6000 |
|
BINMERGE |
|
39 |
5750.013 |
6000 |
0.6898 |
6000 |
|
AUTODETECTMERGE |
|
40 |
0 |
6000 |
40.823 |
6000 |
|
EXTRAMERGE |
Table 2: Asynchronous signal processing task set for a 200MHz 603e PowerPC.