-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathLOADBAL.SIF
413 lines (349 loc) · 11.9 KB
/
LOADBAL.SIF
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
***************************
* SET UP THE INITIAL DATA *
***************************
NAME LOADBAL
* Problem:
* ********
* The problem arises in the field of computer networks and parallel
* computation. It deals with the static load balancing in a tree
* computer network with two-way traffic. A set of heterogeneous host
* computers are interconnected, in which each node processes jobs (the
* jobs arriving at each node according to a time invariant Poisson process)
* locally or sends it to a remote node,. In the latter case, there is a
* communication delay of forwarding the job and getting a response back.
* The problem is then to minimize the mean response time of a job.
* The example considered here features 11 computers arranged as follows:
* 1 6 9
* \ | /
* \ | /
* 2---4---5---8---10
* / | \
* / | \
* 3 7 11
* Source:
* J. Li and H. Kameda,
* "Optimal load balancing in tree network with two-way traffic",
* Computer networks and ISDN systems, vol. 25, pp. 1335-1348, 1993.
* SIF input: Masha Sosonkina, Virginia Tech., 1995.
* classification OLR2-MN-31-31
* Parameter assignment.
IE 1 1
IE P1 3
* Problem dimentions
IE N 11
IE NLINK 20
IE NLINK-3 17
IE NLINK-4 16
IE 4C 4
IE 5C 5
IE 6C 6
IE 7C 7
IE 8C 8
* FI = SUM(arrival rate for a node)
RE FI 514.0
R CIJE
RM 0.2*FI FI 0.2
RM 0.0125*FI FI 0.0125
RM 0.05*FI FI 0.05
GROUPS
* Objective function
DO I 1 N
XN F(I)
ZN F(I) 'SCALE' 0.2*FI
ND
DO I 1 NLINK
XL CNST(I)
XN GA(I)
ZN GA(I) 'SCALE' 0.0125*FI
XN GB(I)
ZN GB(I) 'SCALE' 0.05*FI
OD I
* Constrains
DO I 1 N
XE N(I)
OD I
* Comm. constrains
VARIABLES
* XIJ --Link flow rate.
X4,1 N1 1.00 N4 -1.00
X1,4 N1 -1.00 N4 1.00
X4,2 N2 1.00 N4 -1.00
X2,4 N2 -1.00 N4 1.00
X4,3 N3 1.00 N4 -1.00
X3,4 N3 -1.00 N4 1.00
X4,5 N5 1.00 N4 -1.00
X5,4 N5 -1.00 N4 1.00
X5,6 N6 1.00 N5 -1.00
X6,5 N6 -1.00 N5 1.00
X5,7 N7 1.00 N5 -1.00
X7,5 N7 -1.00 N5 1.00
X5,8 N8 1.00 N5 -1.00
X8,5 N8 -1.00 N5 1.00
X8,9 N9 1.00 N8 -1.00
X9,8 N9 -1.00 N8 1.00
X8,10 N10 1.00 N8 -1.00
X10,8 N10 -1.00 N8 1.00
X8,11 N11 1.00 N8 -1.00
X11,8 N11 -1.00 N8 1.00
X4,1 CNST1 20.0 CNST2 80.00
X1,4 CNST1 80.00 CNST2 20.00
X4,2 CNST3 20.0 CNST4 80.00
X2,4 CNST3 80.00 CNST4 20.0
X4,3 CNST5 20.0 CNST6 80.00
X3,4 CNST5 80.00 CNST6 20.00
X5,6 CNST7 20.0 CNST8 80.00
X6,5 CNST7 80.00 CNST8 20.0
X5,7 CNST9 20.0 CNST10 80.00
X7,5 CNST9 80.00 CNST10 20.0
X8,9 CNST11 20.0 CNST12 80.00
X9,8 CNST11 80.00 CNST12 20.0
X8,10 CNST13 20.0 CNST14 80.00
X10,8 CNST13 80.00 CNST14 20.0
X8,11 CNST15 20.0 CNST16 80.00
X11,8 CNST15 80.0 CNST16 20.00
X4,5 CNST17 20.00 CNST18 80.0
X5,4 CNST17 80.0 CNST18 20.00
X5,8 CNST19 20.00 CNST20 80.0
X8,5 CNST19 80.0 CNST20 20.00
* BI is a mean processing time of node i. (beta(i) in the paper)
DO I 1 N
X B(I) N(I) -1.0
OD I
CONSTANTS
LOADBAL N1 -95.0
LOADBAL N2 -95.0
LOADBAL N3 -19.0
LOADBAL N4 -70.0
LOADBAL N5 -70.0
LOADBAL N6 -19.0
LOADBAL N7 -19.0
LOADBAL N8 -70.0
LOADBAL N9 -19.0
LOADBAL N10 -19.0
LOADBAL N11 -19.0
RE CIJE 999.99
DO I 1 NLINK-4
Z LOADBAL CNST(I) CIJE
OD I
RE CIJE 9999.99
DO I NLINK-3 NLINK
Z LOADBAL CNST(I) CIJE
OD I
BOUNDS
XU LOADBAL B1 99.99
XU LOADBAL B2 99.99
XU LOADBAL B4 99.99
XU LOADBAL B5 99.99
XU LOADBAL B8 99.99
XU LOADBAL B3 19.99
XU LOADBAL B6 19.99
XU LOADBAL B7 19.99
XU LOADBAL B9 19.99
XU LOADBAL B10 19.99
XU LOADBAL B11 19.99
START POINT
LOADBAL X1,4 00.0
LOADBAL X4,1 0.0
LOADBAL B1 95.0
LOADBAL X2,4 0.00
LOADBAL X4,2 0.00
LOADBAL B2 95.0
LOADBAL X3,4 0.00
LOADBAL X4,3 0.0
LOADBAL B3 19.0
LOADBAL B4 70.0
LOADBAL X5,4 0.0
LOADBAL X4,5 00.0
LOADBAL X6,5 0.0
LOADBAL X5,6 0.0
LOADBAL X7,5 0.0
LOADBAL X5,7 0.0
LOADBAL B5 70.0
LOADBAL B6 19.0
LOADBAL B7 19.0
LOADBAL X8,5 0.0
LOADBAL X5,8 0.0
LOADBAL X9,8 0.0
LOADBAL X8,9 0.0
LOADBAL X10,8 0.0
LOADBAL X8,10 0.0
LOADBAL X11,8 0.0
LOADBAL X8,11 0.0
LOADBAL B8 70.0
LOADBAL B9 19.0
LOADBAL B10 19.0
LOADBAL B11 19.0
ELEMENT TYPE
EV BETA1 V
EV BETA2 V
EV COMA1 V W
EV COMA2 V W
EV COMB1 V W
EV COMB2 V W
ELEMENT USES
T EB1 BETA1
V EB1 V B1
T EB2 BETA1
V EB2 V B2
T EB3 BETA2
V EB3 V B3
T EB4 BETA1
V EB4 V B4
T EB5 BETA1
V EB5 V B5
T EB6 BETA2
V EB6 V B6
T EB7 BETA2
V EB7 V B7
T EB8 BETA1
V EB8 V B8
T EB9 BETA2
V EB9 V B9
T EB10 BETA2
V EB10 V B10
T EB11 BETA2
V EB11 V B11
DO I 1 P1
XT EGA(I) COMA1
ZV EGA(I) V X(4C,I)
ZV EGA(I) W X(I,4C)
XT EGB(I) COMB1
ZV EGB(I) V X(4C,I)
ZV EGB(I) W X(I,4C)
IA I+3 I 3
XT EGA(I+3) COMA1
ZV EGA(I+3) V X(I,4C)
ZV EGA(I+3) W X(4C,I)
XT EGB(I+3) COMB1
ZV EGB(I+3) V X(I,4C)
ZV EGB(I+3) W X(4C,I)
IA I+6 I 6
IA I+8 I 8
XT EGA(I+6) COMA1
ZV EGA(I+6) V X(8C,I+8)
ZV EGA(I+6) W X(I+8,8C)
XT EGB(I+6) COMB1
ZV EGB(I+6) V X(8C,I+8)
ZV EGB(I+6) W X(I+8,8C)
IA I+9 I 9
XT EGA(I+9) COMA1
ZV EGA(I+9) V X(I+8,8C)
ZV EGA(I+9) W X(8C,I+8)
XT EGB(I+9) COMB1
ZV EGB(I+9) V X(I+8,8C)
ZV EGB(I+9) W X(8C,I+8)
OD I
DO I 6C 7C
IM I2 I 2
IA I2+1 I2 1
XT EGA(I2+1) COMA1
ZV EGA(I2+1) V X(5C,I)
ZV EGA(I2+1) W X(I,5C)
XT EGB(I2+1) COMB1
ZV EGB(I2+1) V X(5C,I)
ZV EGB(I2+1) W X(I,5C)
IA I2+2 I2 2
XT EGA(I2+2) COMA1
ZV EGA(I2+2) V X(I,5C)
ZV EGA(I2+2) W X(5C,I)
XT EGB(I2+2) COMB1
ZV EGB(I2+2) V X(I,5C)
ZV EGB(I2+2) W X(5C,I)
OD I
XT EGA17 COMA2
ZV EGA17 V X5,4
ZV EGA17 W X4,5
XT EGB17 COMB2
ZV EGB17 V X5,4
ZV EGB17 W X4,5
XT EGA18 COMA2
ZV EGA18 V X4,5
ZV EGA18 W X5,4
XT EGB18 COMB2
ZV EGB18 V X4,5
ZV EGB18 W X5,4
XT EGA19 COMA2
ZV EGA19 V X5,8
ZV EGA19 W X8,5
XT EGB19 COMB2
ZV EGB19 V X5,8
ZV EGB19 W X8,5
XT EGA20 COMA2
ZV EGA20 V X8,5
ZV EGA20 W X5,8
XT EGB20 COMB2
ZV EGB20 V X8,5
ZV EGB20 W X5,8
GROUP USES
DO I 1 N
XE F(I) EB(I)
OD I
DO I 1 NLINK
XE GB(I) EGB(I)
XE GA(I) EGA(I)
OD I
OBJECT BOUND
LO LOADBAL 0.0
ENDATA
***********************
* SET UP THE ELEMENTS *
* ROUTINE *
***********************
ELEMENTS LOADBAL
TEMPORARIES
R CB
R CIJ
R A
R B
GLOBALS
A A 80.0
A B 20.0
INDIVIDUALS
** Beta types.
* nodes 3,6,7,9,10,11
T BETA2
A CB 20.0
F V/(CB-V)
G V CB/((CB-V)**2)
H V V 2*CB/((CB-V)**3)
* nodes 1,2,4,5,8
T BETA1
A CB 100.0
F V/(CB-V)
G V CB/((CB-V)**2)
H V V 2*CB/((CB-V)**3)
** Com types.
* nodes .not. 4<->5<->8
T COMA1
A CIJ 1000.0
F V/(CIJ-(A*V+B*W))
G V (CIJ-B*W)/(CIJ-(A*V+B*W))**2
G W V*B/(CIJ-(A*V+B*W))**2
H V V 2*A*(CIJ-B*W)/(CIJ-(A*V+B*W))**3
H V W B*(CIJ+A*V-B*W)/(CIJ-(A*V+B*W))**3
H W W 2*B*B*V/(CIJ-(A*V+B*W))**3
T COMB1
A CIJ 1000.0
F V/(CIJ-(B*V+A*W))
G V (CIJ-A*W)/(CIJ-(B*V+A*W))**2
G W V*A/(CIJ-(B*V+A*W))**2
H V V 2*B*(CIJ-A*W)/(CIJ-(B*V+A*W))**3
H V W A*(CIJ+B*V-A*W)/(CIJ-(B*V+A*W))**3
H W W 2*A*A*V/(CIJ-(B*V+A*W))**3
T COMA2
A CIJ 10000.0
F V/(CIJ-(A*V+B*W))
G V (CIJ-B*W)/(CIJ-(A*V+B*W))**2
G W V*B/(CIJ-(A*V+B*W))**2
H V V 2*A*(CIJ-B*W)/(CIJ-(A*V+B*W))**3
H V W B*(CIJ+A*V-B*W)/(CIJ-(A*V+B*W))**3
H W W 2*B*B*V/(CIJ-(A*V+B*W))**3
T COMB2
A CIJ 10000.0
F V/(CIJ-(B*V+A*W))
G V (CIJ-A*W)/(CIJ-(B*V+A*W))**2
G W V*A/(CIJ-(B*V+A*W))**2
H V V 2*B*(CIJ-A*W)/(CIJ-(B*V+A*W))**3
H V W A*(CIJ+B*V-A*W)/(CIJ-(B*V+A*W))**3
H W W 2*A*A*V/(CIJ-(B*V+A*W))**3
ENDATA