* Example 7:
echo Example 7:
* This is an example of a reliability model of a system with 
* 8 processors.
* lambda is the failure rate of each processor. Upon the 
* Ocurrence of a fault, there is a constant time tr required
* to handle (detect + isolate + reconfigure) that fault. 
* If during this time, another (near-coicident fault occurs,
* system fails. The effect of this is taken into account using
* Behavioral Decomposition and is reflected by means of imperfect
* coverage 

bind 
lambda .001
tr  .0000277777
end

* Coverage is computed as the Laplace Transform of the fault-hadling
* time evaluated at the near-coincident fault rate. For details see
* Trivedi's chapter in the book edited by Iazeolla et al,
* North-Holland, 1984.
* Since the LT of a constant time tr is e^{-s*tr}, we have the 
* coverage expressions (note when we just use the exponent ^ sign, e is
* implied as the base):
* For HARP users, we have used a FEHM here.
var c8  ^ (-7 * lambda * tr )
var c7  ^ (-6 * lambda * tr)
var c6  ^ (-5 * lambda * tr)
var c5  ^ (-4 * lambda * tr)
var c4  ^ (-3 * lambda * tr)
var c3  ^ (-2 * lambda * tr)
var c2  ^ (-1 * lambda * tr)

var fc8 1 - c8
var fc7 1 - c7
var fc6 1 - c6
var fc5 1 - c5
var fc4 1 - c4
var fc3 1 - c3
var fc2 1 - c2

var L8 8 * lambda * c8
var L7 7 * lambda * c7
var L6 6 * lambda * c6
var L5 5 * lambda * c5
var L4 4 * lambda * c4
var L3 3 * lambda * c3
var L2 2 * lambda * c2

var fL8 8 * lambda * fc8
var fL7 7 * lambda * fc7
var fL6 6 * lambda * fc6
var fL5 5 * lambda * fc5
var fL4 4 * lambda * fc4
var fL3 3 * lambda * fc3
var fL2 2 * lambda * fc2

markov  8units
8 7 L8
7 6 L7
6 5 L6
5 4 L5
4 3 L4
3 2 L3
2 1 L2
1 ex lambda
8 ncf fL8
7 ncf fL7
6 ncf fL6
5 ncf fL5
4 ncf fL4
3 ncf fL3
2 ncf fL2
end
8 1.0
end

eval(8units,ncf) 0 10 1
eval(8units,6) 0 10 1


* Example 8a:
echo Example 8a:
* Now we consider a system with 8 processors and 3 memory units.
* Fault-error-handling time is nmow assumed to be exponentially
* distributed with mean Etr; Near-coincident faults in the same 
* component type will be catastrophic.

func c(x, k) (1/Etr) / ((1/Etr) + (k-1) * x)
func L(x, k) k * x * c(x, k)
func fL(x,k) k * x * (1 - c(x, k))

markov sift
8-3 7-3 L(lambda, 8)
7-3 6-3 L(lambda, 7)
6-3 5-3 L(lambda, 6)
5-3 4-3 L(lambda, 5)
4-3 3-3 L(lambda, 4)
3-3 2-3 L(lambda, 3)
8-3 F   fL(lambda, 8) + fL(mu, 3)
7-3 F   fL(lambda, 7) + fL(mu, 3)
6-3 F   fL(lambda, 6) + fL(mu, 3)
5-3 F   fL(lambda, 5) + fL(mu, 3)
4-3 F   fL(lambda, 4) + fL(mu, 3)
3-3 F   fL(lambda, 3) + fL(mu, 3)
2-3 F   (2 * lambda)  + fL(mu, 3)
8-3 8-2 L(mu, 3)
7-3 7-2 L(mu, 3)
6-3 6-2 L(mu, 3)
5-3 5-2 L(mu, 3)
4-3 4-2 L(mu, 3)
3-3 3-2 L(mu, 3)
2-3 2-2 L(mu, 3)
8-2 7-2 L(lambda, 8)
7-2 6-2 L(lambda, 7)
6-2 5-2 L(lambda, 6)
5-2 4-2 L(lambda, 5)
4-2 3-2 L(lambda, 4)
3-2 2-2 L(lambda, 3)
8-2 F   (2 * mu) + fL(lambda, 8)
7-2 F   (2 * mu) + fL(lambda, 7)
6-2 F   (2 * mu) + fL(lambda, 6)
5-2 F   (2 * mu) + fL(lambda, 5)
4-2 F   (2 * mu) + fL(lambda, 4)
3-2 F   (2 * mu) + fL(lambda, 3)
2-2 F   (2 * mu) + (2 * lambda)
end
8-3 1.0
end

bind 
lambda .0001
mu .00001
Etr 1/360
end

cdf(sift,F)
eval (sift) 5 15 1


* Example 8b:
echo Example 8b:
* We introduce repair in the above example
* Compare Instantaneous unavailability with unreliability
markov siftrep readprobs
8-3 7-3 L(lambda, 8)
7-3 6-3 L(lambda, 7)
6-3 5-3 L(lambda, 6)
5-3 4-3 L(lambda, 5)
4-3 3-3 L(lambda, 4)
3-3 2-3 L(lambda, 3)
8-3 F   fL(lambda, 8) + fL(mu, 3)
7-3 F   fL(lambda, 7) + fL(mu, 3)
6-3 F   fL(lambda, 6) + fL(mu, 3)
5-3 F   fL(lambda, 5) + fL(mu, 3)
4-3 F   fL(lambda, 4) + fL(mu, 3)
3-3 F   fL(lambda, 3) + fL(mu, 3)
2-3 F   (2 * lambda)  + fL(mu, 3)
8-3 8-2 L(mu, 3)
7-3 7-2 L(mu, 3)
6-3 6-2 L(mu, 3)
5-3 5-2 L(mu, 3)
4-3 4-2 L(mu, 3)
3-3 3-2 L(mu, 3)
2-3 2-2 L(mu, 3)
8-2 7-2 L(lambda, 8)
7-2 6-2 L(lambda, 7)
6-2 5-2 L(lambda, 6)
5-2 4-2 L(lambda, 5)
4-2 3-2 L(lambda, 4)
3-2 2-2 L(lambda, 3)
8-2 F   (2 * mu) + fL(lambda, 8)

7-2 F   (2 * mu) + fL(lambda, 7)
6-2 F   (2 * mu) + fL(lambda, 6)
5-2 F   (2 * mu) + fL(lambda, 5)
4-2 F   (2 * mu) + fL(lambda, 4)
3-2 F   (2 * mu) + fL(lambda, 3)
2-2 F   (2 * mu) + (2 * lambda)
F 8-3 1.0
end
8-3 1.0
end

func unrel(t) tvalue(t;sift,F)
func unavail(t) tvalue(t;siftrep,F)

loop t,0,1000,100
     expr unrel(t), unavail(t)
end

* Compare the inst. unavail with the steady-state unavail

expr prob(siftrep,F)

loop t,0,10000,1000
     expr unrel(t), unavail(t)
end


* Example 9:
echo Example 9:
* Example of 3 memmories and two processors
* see Sahner and Trivedi, IEEE Trans on Education, Feb. 1993

bind
lambda 0.005
mu 0.005
end
markov 3p2b
32 22 3*lambda
22 12 2*lambda
12 F1 lambda
32 31 2*mu
31 F2 mu
22 21 2*mu
21 F2 mu
12 11 2*mu
11 F2 mu
31 21 3*lambda
21 11 2*lambda
11 F1 lambda
end
32 1.0
end
eval (3p2b,F1) 10.0 10.0 1.0
eval (3p2b,F2) 10.0 10.0 1.0

bind epsilon 0.0000000000001


bind
c3222 0.1739
s3222 0.01975
r3222 0.80625
c2212 0.1739
s2212 0.01975
r2212 0.80625
c3121 0.1739
s3121 0.01975
r3121 0.80625
c2111 0.1739
s2111 0.01975
r2111 0.80625
c3231 0.927139
s3231 0.00007672
r3231 0.072784
c2221 0.927139
s2221 0.00007672
r2221 0.072784
c1211 0.927139
s1211 0.00007672
r1211 0.072784
end
markov 3p2bwithcov
32 22 3*lambda*c3222
32 FSPF 3*lambda*s3222
32 FNCF 3*lambda*(1.0-c3222-s3222-r3222)
22 12 2*lambda*c2212
22 FSPF 2*lambda*s2212
22 FNCF 2*lambda*(1.0-c2212-s2212-r2212)
12 F1 lambda
32 31 2*mu*c3231
32 FSPF 2*mu*s3231
32 FNCF 2*mu*(1.0-c3231-s3231-r3231)
31 F2 mu
22 21 2*mu*c2221
22 FSPF 2*mu*s2221
22 FNCF 2*mu*(1.0-c2221-s2221-r2221)
21 F2 mu
12 11 2*mu*c1211
12 FSPF 2*mu*s1211
12 FNCF 2*mu*(1.0-c1211-s1211-r1211)
11 F2 mu
31 21 3*lambda*c3121
31 FSPF 3*lambda*s3121
31 FNCF 3*lambda*(1.0-c3121-s3121-r3121)
21 11 2*lambda*c2111
21 FSPF 2*lambda*s2111
21 FNCF 2*lambda*(1.0-c2111-s2111-r2111)
11 F1 lambda
end
32 1.0
end
eval (3p2bwithcov,F1) 10.0 10.0 1.0
eval (3p2bwithcov,F2) 10.0 10.0 1.0
eval (3p2bwithcov,FSPF) 10.0 10.0 1.0
eval (3p2bwithcov,FNCF) 10.0 10.0 1.0

* Example 10: Hermann de Meer's model
echo Example 10:
markov ml4
n1 d 0.01
n2 d 0.02
n3 d 0.04
n4 d 0.1
n5 d 0.2
n6 d 0.4
reward
n1 10
n2 18
n3 30
n4 40
n5 50
n6 80
d 0
end
n1 0
n2 0 
n3 0
n4 0
n5 0.0
n6 1.0
d 0
end

cdf(ml4)
eval(ml4) 0 100 10
expr exrt(100;ml4)
expr cexrt(100;ml4)


*Example 11:
echo Example 11:

bind
LAM 1.0
MU 2.0
end

markov mm1_999
01   11 LAM
11   01 MU
11   21 LAM
21   11 MU
21   31 LAM
31   21 MU
31   41 LAM
41   31 MU
41   51 LAM
51   41 MU
51   61 LAM
61   51 MU
61   71 LAM
71   61 MU
71   81 LAM
81   71 MU
81   91 LAM
91   81 MU
91   101 LAM
101   91 MU
101   111 LAM
111   101 MU
111   121 LAM
121   111 MU
121   131 LAM
131   121 MU
131   141 LAM
141   131 MU
141   151 LAM
151   141 MU
151   161 LAM
161   151 MU
161   171 LAM
171   161 MU
171   181 LAM
181   171 MU
181   191 LAM
191   181 MU
191   201 LAM
201   191 MU
201   211 LAM
211   201 MU
211   221 LAM
221   211 MU
221   231 LAM
231   221 MU
231   241 LAM
241   231 MU
241   251 LAM
251   241 MU
251   261 LAM
261   251 MU
261   271 LAM
271   261 MU
271   281 LAM
281   271 MU
281   291 LAM
291   281 MU
291   301 LAM
301   291 MU
301   311 LAM
311   301 MU
311   321 LAM
321   311 MU
321   331 LAM
331   321 MU
331   341 LAM
341   331 MU
341   351 LAM
351   341 MU
351   361 LAM
361   351 MU
361   371 LAM
371   361 MU
371   381 LAM
381   371 MU
381   391 LAM
391   381 MU
391   401 LAM
401   391 MU
401   411 LAM
411   401 MU
411   421 LAM
421   411 MU
421   431 LAM
431   421 MU
431   441 LAM
441   431 MU
441   451 LAM
451   441 MU
451   461 LAM
461   451 MU
461   471 LAM
471   461 MU
471   481 LAM
481   471 MU
481   491 LAM
491   481 MU
491   501 LAM
501   491 MU
501   511 LAM
511   501 MU
511   521 LAM
521   511 MU
521   531 LAM
531   521 MU
531   541 LAM
541   531 MU
541   551 LAM
551   541 MU
551   561 LAM
561   551 MU
561   571 LAM
571   561 MU
571   581 LAM
581   571 MU
581   591 LAM
591   581 MU
591   601 LAM
601   591 MU
601   611 LAM
611   601 MU
611   621 LAM
621   611 MU
621   631 LAM
631   621 MU
631   641 LAM
641   631 MU
641   651 LAM
651   641 MU
651   661 LAM
661   651 MU
661   671 LAM
671   661 MU
671   681 LAM
681   671 MU
681   691 LAM
691   681 MU
691   701 LAM
701   691 MU
701   711 LAM
711   701 MU
711   721 LAM
721   711 MU
721   731 LAM
731   721 MU
731   741 LAM
741   731 MU
741   751 LAM
751   741 MU
751   761 LAM
761   751 MU
761   771 LAM
771   761 MU
771   781 LAM
781   771 MU
781   791 LAM
791   781 MU
791   801 LAM
801   791 MU
801   811 LAM
811   801 MU
811   821 LAM
821   811 MU
821   831 LAM
831   821 MU
831   841 LAM
841   831 MU
841   851 LAM
851   841 MU
851   861 LAM
861   851 MU
861   871 LAM
871   861 MU
871   881 LAM
881   871 MU
881   891 LAM
891   881 MU
891   901 LAM
901   891 MU
901   911 LAM
911   901 MU
911   921 LAM
921   911 MU
921   931 LAM
931   921 MU
931   941 LAM
941   931 MU
941   951 LAM
951   941 MU
951   961 LAM
961   951 MU
961   971 LAM
971   961 MU
971   981 LAM
981   971 MU
981   991 LAM
991   981 MU
991   1001 LAM
1001   991 MU
1001   1011 LAM
1011   1001 MU
1011   1021 LAM
1021   1011 MU
1021   1031 LAM
1031   1021 MU
1031   1041 LAM
1041   1031 MU
1041   1051 LAM
1051   1041 MU
1051   1061 LAM
1061   1051 MU
1061   1071 LAM
1071   1061 MU
1071   1081 LAM
1081   1071 MU
1081   1091 LAM
1091   1081 MU
1091   1101 LAM
1101   1091 MU
1101   1111 LAM
1111   1101 MU
1111   1121 LAM
1121   1111 MU
1121   1131 LAM
1131   1121 MU
1131   1141 LAM
1141   1131 MU
1141   1151 LAM
1151   1141 MU
1151   1161 LAM

1161   1151 MU
1161   1171 LAM
1171   1161 MU
1171   1181 LAM
1181   1171 MU
1181   1191 LAM
1191   1181 MU
1191   1201 LAM
1201   1191 MU
1201   1211 LAM
1211   1201 MU
1211   1221 LAM
1221   1211 MU
1221   1231 LAM
1231   1221 MU
1231   1241 LAM
1241   1231 MU
1241   1251 LAM
1251   1241 MU
1251   1261 LAM
1261   1251 MU
1261   1271 LAM
1271   1261 MU
1271   1281 LAM
1281   1271 MU
1281   1291 LAM
1291   1281 MU
1291   1301 LAM
1301   1291 MU
1301   1311 LAM
1311   1301 MU
1311   1321 LAM
1321   1311 MU
1321   1331 LAM
1331   1321 MU
1331   1341 LAM
1341   1331 MU
1341   1351 LAM
1351   1341 MU
1351   1361 LAM
1361   1351 MU
1361   1371 LAM
1371   1361 MU
1371   1381 LAM
1381   1371 MU
1381   1391 LAM
1391   1381 MU
1391   1401 LAM
1401   1391 MU
1401   1411 LAM
1411   1401 MU
1411   1421 LAM
1421   1411 MU
1421   1431 LAM
1431   1421 MU
1431   1441 LAM
1441   1431 MU
1441   1451 LAM
1451   1441 MU
1451   1461 LAM
1461   1451 MU
1461   1471 LAM
1471   1461 MU
1471   1481 LAM
1481   1471 MU
1481   1491 LAM
1491   1481 MU
1491   1501 LAM
1501   1491 MU
1501   1511 LAM
1511   1501 MU
1511   1521 LAM
1521   1511 MU
1521   1531 LAM
1531   1521 MU
1531   1541 LAM
1541   1531 MU
1541   1551 LAM
1551   1541 MU
1551   1561 LAM
1561   1551 MU
1561   1571 LAM
1571   1561 MU
1571   1581 LAM
1581   1571 MU
1581   1591 LAM
1591   1581 MU
1591   1601 LAM
1601   1591 MU
1601   1611 LAM
1611   1601 MU
1611   1621 LAM
1621   1611 MU
1621   1631 LAM
1631   1621 MU
1631   1641 LAM
1641   1631 MU
1641   1651 LAM
1651   1641 MU
1651   1661 LAM
1661   1651 MU
1661   1671 LAM
1671   1661 MU
1671   1681 LAM
1681   1671 MU
1681   1691 LAM
1691   1681 MU
1691   1701 LAM
1701   1691 MU
1701   1711 LAM
1711   1701 MU
1711   1721 LAM
1721   1711 MU
1721   1731 LAM
1731   1721 MU
1731   1741 LAM
1741   1731 MU
1741   1751 LAM
1751   1741 MU
1751   1761 LAM
1761   1751 MU
1761   1771 LAM
1771   1761 MU
1771   1781 LAM
1781   1771 MU
1781   1791 LAM
1791   1781 MU
1791   1801 LAM
1801   1791 MU
1801   1811 LAM
1811   1801 MU
1811   1821 LAM
1821   1811 MU
1821   1831 LAM
1831   1821 MU
1831   1841 LAM
1841   1831 MU
1841   1851 LAM
1851   1841 MU
1851   1861 LAM
1861   1851 MU
1861   1871 LAM
1871   1861 MU
1871   1881 LAM
1881   1871 MU
1881   1891 LAM
1891   1881 MU
1891   1901 LAM
1901   1891 MU
1901   1911 LAM
1911   1901 MU
1911   1921 LAM
1921   1911 MU
1921   1931 LAM
1931   1921 MU
1931   1941 LAM
1941   1931 MU
1941   1951 LAM
1951   1941 MU
1951   1961 LAM
1961   1951 MU
1961   1971 LAM
1971   1961 MU
1971   1981 LAM
1981   1971 MU
1981   1991 LAM
1991   1981 MU
1991   2001 LAM
2001   1991 MU
2001   2011 LAM
2011   2001 MU
2011   2021 LAM
2021   2011 MU
2021   2031 LAM
2031   2021 MU
2031   2041 LAM
2041   2031 MU
2041   2051 LAM
2051   2041 MU
2051   2061 LAM
2061   2051 MU
2061   2071 LAM
2071   2061 MU
2071   2081 LAM
2081   2071 MU
2081   2091 LAM
2091   2081 MU
2091   2101 LAM
2101   2091 MU
2101   2111 LAM
2111   2101 MU
2111   2121 LAM
2121   2111 MU
2121   2131 LAM
2131   2121 MU
2131   2141 LAM
2141   2131 MU
2141   2151 LAM
2151   2141 MU
2151   2161 LAM
2161   2151 MU
2161   2171 LAM
2171   2161 MU
2171   2181 LAM
2181   2171 MU
2181   2191 LAM
2191   2181 MU
2191   2201 LAM
2201   2191 MU
2201   2211 LAM
2211   2201 MU
2211   2221 LAM
2221   2211 MU
2221   2231 LAM
2231   2221 MU
2231   2241 LAM
2241   2231 MU
2241   2251 LAM
2251   2241 MU
2251   2261 LAM
2261   2251 MU
2261   2271 LAM
2271   2261 MU
2271   2281 LAM
2281   2271 MU
2281   2291 LAM
2291   2281 MU
2291   2301 LAM
2301   2291 MU
2301   2311 LAM
2311   2301 MU
2311   2321 LAM
2321   2311 MU
2321   2331 LAM
2331   2321 MU
2331   2341 LAM
2341   2331 MU
2341   2351 LAM
2351   2341 MU
2351   2361 LAM
2361   2351 MU
2361   2371 LAM
2371   2361 MU
2371   2381 LAM
2381   2371 MU
2381   2391 LAM
2391   2381 MU
2391   2401 LAM
2401   2391 MU
2401   2411 LAM
2411   2401 MU
2411   2421 LAM
2421   2411 MU
2421   2431 LAM
2431   2421 MU
2431   2441 LAM
2441   2431 MU
2441   2451 LAM
2451   2441 MU
2451   2461 LAM
2461   2451 MU
2461   2471 LAM
2471   2461 MU
2471   2481 LAM
2481   2471 MU
2481   2491 LAM
2491   2481 MU
2491   2501 LAM
2501   2491 MU
2501   2511 LAM
2511   2501 MU
2511   2521 LAM
2521   2511 MU
2521   2531 LAM
2531   2521 MU
2531   2541 LAM
2541   2531 MU
2541   2551 LAM
2551   2541 MU
2551   2561 LAM
2561   2551 MU
2561   2571 LAM
2571   2561 MU
2571   2581 LAM
2581   2571 MU
2581   2591 LAM
2591   2581 MU
2591   2601 LAM
2601   2591 MU
2601   2611 LAM
2611   2601 MU
2611   2621 LAM
2621   2611 MU
2621   2631 LAM
2631   2621 MU
2631   2641 LAM
2641   2631 MU
2641   2651 LAM
2651   2641 MU
2651   2661 LAM
2661   2651 MU
2661   2671 LAM
2671   2661 MU
2671   2681 LAM
2681   2671 MU
2681   2691 LAM
2691   2681 MU
2691   2701 LAM
2701   2691 MU
2701   2711 LAM
2711   2701 MU
2711   2721 LAM
2721   2711 MU
2721   2731 LAM
2731   2721 MU
2731   2741 LAM
2741   2731 MU
2741   2751 LAM
2751   2741 MU
2751   2761 LAM
2761   2751 MU
2761   2771 LAM
2771   2761 MU
2771   2781 LAM
2781   2771 MU
2781   2791 LAM
2791   2781 MU
2791   2801 LAM
2801   2791 MU
2801   2811 LAM
2811   2801 MU
2811   2821 LAM
2821   2811 MU
2821   2831 LAM
2831   2821 MU
2831   2841 LAM
2841   2831 MU
2841   2851 LAM
2851   2841 MU
2851   2861 LAM
2861   2851 MU
2861   2871 LAM
2871   2861 MU
2871   2881 LAM
2881   2871 MU
2881   2891 LAM
2891   2881 MU
2891   2901 LAM
2901   2891 MU
2901   2911 LAM
2911   2901 MU
2911   2921 LAM
2921   2911 MU
2921   2931 LAM
2931   2921 MU
2931   2941 LAM
2941   2931 MU
2941   2951 LAM
2951   2941 MU
2951   2961 LAM
2961   2951 MU
2961   2971 LAM
2971   2961 MU
2971   2981 LAM
2981   2971 MU
2981   2991 LAM
2991   2981 MU
2991   3001 LAM
3001   2991 MU
3001   3011 LAM
3011   3001 MU
3011   3021 LAM
3021   3011 MU
3021   3031 LAM
3031   3021 MU
3031   3041 LAM
3041   3031 MU
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7821   7831 LAM
7831   7821 MU
7831   7841 LAM
7841   7831 MU
7841   7851 LAM
7851   7841 MU
7851   7861 LAM
7861   7851 MU
7861   7871 LAM
7871   7861 MU
7871   7881 LAM
7881   7871 MU
7881   7891 LAM
7891   7881 MU
7891   7901 LAM
7901   7891 MU
7901   7911 LAM
7911   7901 MU
7911   7921 LAM
7921   7911 MU
7921   7931 LAM
7931   7921 MU
7931   7941 LAM
7941   7931 MU
7941   7951 LAM
7951   7941 MU
7951   7961 LAM
7961   7951 MU
7961   7971 LAM
7971   7961 MU
7971   7981 LAM
7981   7971 MU
7981   7991 LAM
7991   7981 MU
7991   8001 LAM
8001   7991 MU
8001   8011 LAM
8011   8001 MU
8011   8021 LAM
8021   8011 MU
8021   8031 LAM
8031   8021 MU
8031   8041 LAM
8041   8031 MU
8041   8051 LAM
8051   8041 MU
8051   8061 LAM
8061   8051 MU
8061   8071 LAM
8071   8061 MU
8071   8081 LAM
8081   8071 MU
8081   8091 LAM
8091   8081 MU
8091   8101 LAM
8101   8091 MU
8101   8111 LAM
8111   8101 MU
8111   8121 LAM
8121   8111 MU
8121   8131 LAM
8131   8121 MU
8131   8141 LAM
8141   8131 MU
8141   8151 LAM
8151   8141 MU
8151   8161 LAM
8161   8151 MU
8161   8171 LAM
8171   8161 MU
8171   8181 LAM
8181   8171 MU
8181   8191 LAM
8191   8181 MU
8191   8201 LAM
8201   8191 MU
8201   8211 LAM
8211   8201 MU
8211   8221 LAM
8221   8211 MU
8221   8231 LAM
8231   8221 MU
8231   8241 LAM
8241   8231 MU
8241   8251 LAM
8251   8241 MU
8251   8261 LAM
8261   8251 MU
8261   8271 LAM
8271   8261 MU
8271   8281 LAM
8281   8271 MU
8281   8291 LAM
8291   8281 MU
8291   8301 LAM
8301   8291 MU
8301   8311 LAM
8311   8301 MU
8311   8321 LAM
8321   8311 MU
8321   8331 LAM
8331   8321 MU
8331   8341 LAM
8341   8331 MU
8341   8351 LAM
8351   8341 MU
8351   8361 LAM
8361   8351 MU
8361   8371 LAM
8371   8361 MU
8371   8381 LAM
8381   8371 MU
8381   8391 LAM
8391   8381 MU
8391   8401 LAM
8401   8391 MU
8401   8411 LAM
8411   8401 MU
8411   8421 LAM
8421   8411 MU
8421   8431 LAM
8431   8421 MU
8431   8441 LAM
8441   8431 MU
8441   8451 LAM
8451   8441 MU
8451   8461 LAM
8461   8451 MU
8461   8471 LAM
8471   8461 MU
8471   8481 LAM
8481   8471 MU
8481   8491 LAM
8491   8481 MU
8491   8501 LAM
8501   8491 MU
8501   8511 LAM
8511   8501 MU
8511   8521 LAM
8521   8511 MU
8521   8531 LAM
8531   8521 MU
8531   8541 LAM
8541   8531 MU
8541   8551 LAM
8551   8541 MU
8551   8561 LAM
8561   8551 MU
8561   8571 LAM
8571   8561 MU
8571   8581 LAM
8581   8571 MU
8581   8591 LAM
8591   8581 MU
8591   8601 LAM
8601   8591 MU
8601   8611 LAM
8611   8601 MU
8611   8621 LAM
8621   8611 MU
8621   8631 LAM
8631   8621 MU
8631   8641 LAM
8641   8631 MU
8641   8651 LAM
8651   8641 MU
8651   8661 LAM
8661   8651 MU
8661   8671 LAM
8671   8661 MU
8671   8681 LAM
8681   8671 MU
8681   8691 LAM
8691   8681 MU
8691   8701 LAM
8701   8691 MU
8701   8711 LAM
8711   8701 MU
8711   8721 LAM
8721   8711 MU
8721   8731 LAM
8731   8721 MU
8731   8741 LAM
8741   8731 MU
8741   8751 LAM
8751   8741 MU
8751   8761 LAM
8761   8751 MU
8761   8771 LAM
8771   8761 MU
8771   8781 LAM
8781   8771 MU
8781   8791 LAM
8791   8781 MU
8791   8801 LAM
8801   8791 MU
8801   8811 LAM
8811   8801 MU
8811   8821 LAM
8821   8811 MU
8821   8831 LAM
8831   8821 MU
8831   8841 LAM
8841   8831 MU
8841   8851 LAM
8851   8841 MU
8851   8861 LAM
8861   8851 MU
8861   8871 LAM
8871   8861 MU
8871   8881 LAM
8881   8871 MU
8881   8891 LAM
8891   8881 MU
8891   8901 LAM
8901   8891 MU
8901   8911 LAM
8911   8901 MU
8911   8921 LAM
8921   8911 MU
8921   8931 LAM
8931   8921 MU
8931   8941 LAM
8941   8931 MU
8941   8951 LAM
8951   8941 MU
8951   8961 LAM
8961   8951 MU
8961   8971 LAM
8971   8961 MU
8971   8981 LAM
8981   8971 MU
8981   8991 LAM
8991   8981 MU
8991   9001 LAM
9001   8991 MU
9001   9011 LAM
9011   9001 MU
9011   9021 LAM
9021   9011 MU
9021   9031 LAM
9031   9021 MU
9031   9041 LAM
9041   9031 MU
9041   9051 LAM
9051   9041 MU
9051   9061 LAM
9061   9051 MU
9061   9071 LAM
9071   9061 MU
9071   9081 LAM
9081   9071 MU
9081   9091 LAM
9091   9081 MU
9091   9101 LAM
9101   9091 MU
9101   9111 LAM
9111   9101 MU
9111   9121 LAM
9121   9111 MU
9121   9131 LAM
9131   9121 MU
9131   9141 LAM
9141   9131 MU
9141   9151 LAM
9151   9141 MU
9151   9161 LAM
9161   9151 MU
9161   9171 LAM
9171   9161 MU
9171   9181 LAM
9181   9171 MU
9181   9191 LAM
9191   9181 MU
9191   9201 LAM
9201   9191 MU
9201   9211 LAM
9211   9201 MU
9211   9221 LAM
9221   9211 MU
9221   9231 LAM
9231   9221 MU
9231   9241 LAM
9241   9231 MU
9241   9251 LAM
9251   9241 MU
9251   9261 LAM
9261   9251 MU
9261   9271 LAM
9271   9261 MU
9271   9281 LAM
9281   9271 MU
9281   9291 LAM
9291   9281 MU
9291   9301 LAM
9301   9291 MU
9301   9311 LAM
9311   9301 MU
9311   9321 LAM
9321   9311 MU
9321   9331 LAM
9331   9321 MU
9331   9341 LAM
9341   9331 MU
9341   9351 LAM
9351   9341 MU
9351   9361 LAM
9361   9351 MU
9361   9371 LAM
9371   9361 MU
9371   9381 LAM
9381   9371 MU
9381   9391 LAM
9391   9381 MU
9391   9401 LAM
9401   9391 MU
9401   9411 LAM
9411   9401 MU
9411   9421 LAM
9421   9411 MU
9421   9431 LAM
9431   9421 MU
9431   9441 LAM
9441   9431 MU
9441   9451 LAM
9451   9441 MU
9451   9461 LAM
9461   9451 MU
9461   9471 LAM
9471   9461 MU
9471   9481 LAM
9481   9471 MU
9481   9491 LAM
9491   9481 MU
9491   9501 LAM
9501   9491 MU
9501   9511 LAM
9511   9501 MU
9511   9521 LAM
9521   9511 MU
9521   9531 LAM
9531   9521 MU
9531   9541 LAM
9541   9531 MU
9541   9551 LAM
9551   9541 MU
9551   9561 LAM
9561   9551 MU
9561   9571 LAM
9571   9561 MU
9571   9581 LAM
9581   9571 MU
9581   9591 LAM
9591   9581 MU
9591   9601 LAM
9601   9591 MU
9601   9611 LAM
9611   9601 MU
9611   9621 LAM
9621   9611 MU
9621   9631 LAM
9631   9621 MU
9631   9641 LAM
9641   9631 MU
9641   9651 LAM
9651   9641 MU
9651   9661 LAM
9661   9651 MU
9661   9671 LAM
9671   9661 MU
9671   9681 LAM
9681   9671 MU
9681   9691 LAM
9691   9681 MU
9691   9701 LAM
9701   9691 MU
9701   9711 LAM
9711   9701 MU
9711   9721 LAM
9721   9711 MU
9721   9731 LAM
9731   9721 MU
9731   9741 LAM
9741   9731 MU
9741   9751 LAM
9751   9741 MU
9751   9761 LAM
9761   9751 MU
9761   9771 LAM
9771   9761 MU
9771   9781 LAM
9781   9771 MU
9781   9791 LAM
9791   9781 MU
9791   9801 LAM
9801   9791 MU
9801   9811 LAM
9811   9801 MU
9811   9821 LAM
9821   9811 MU
9821   9831 LAM
9831   9821 MU
9831   9841 LAM
9841   9831 MU
9841   9851 LAM
9851   9841 MU
9851   9861 LAM
9861   9851 MU
9861   9871 LAM
9871   9861 MU
9871   9881 LAM
9881   9871 MU
9881   9891 LAM
9891   9881 MU
9891   9901 LAM
9901   9891 MU
9901   9911 LAM
9911   9901 MU
9911   9921 LAM
9921   9911 MU
9921   9931 LAM
9931   9921 MU
9931   9941 LAM
9941   9931 MU
9941   9951 LAM
9951   9941 MU
9951   9961 LAM
9961   9951 MU
9961   9971 LAM
9971   9961 MU
9971   9981 LAM
9981   9971 MU
9981   9991 LAM
9991   9981 MU
end

expr prob(mm1_999,01)
expr prob(mm1_999,9991)

*Example 12:
echo Example 12
bind
LAM 1.0
MU 1.2
end
format 8
markov mm5
0   1 LAM
1   0 MU
1   2 LAM
2   1 2*MU
2   3 LAM
3   2 3*MU
3   4 LAM
4   3 4*MU
4   5 LAM
5   4 5*MU
5   6 LAM
6   5 5*MU
6   7 LAM
7   6 5*MU
7   8 LAM
8   7 5*MU
8   9 LAM
9   8 5*MU
9   10 LAM
10   9 5*MU
10   11 LAM
11   10 5*MU
11   12 LAM
12   11 5*MU
12   13 LAM
13   12 5*MU
13   14 LAM
14   13 5*MU
14   15 LAM
15   14 5*MU
15   16 LAM
16   15 5*MU
16   17 LAM
17   16 5*MU
17   18 LAM
18   17 5*MU
18   19 LAM
19   18 5*MU
19   20 LAM
20   19 5*MU
20   21 LAM
21   20 5*MU
21   22 LAM
22   21 5*MU
22   23 LAM
23   22 5*MU
23   24 LAM
24   23 5*MU
24   25 LAM
25   24 5*MU
25   26 LAM
26   25 5*MU
26   27 LAM
27   26 5*MU
27   28 LAM
28   27 5*MU
28   29 LAM
29   28 5*MU
29   30 LAM
30   29 5*MU
30   31 LAM
31   30 5*MU
31   32 LAM
32   31 5*MU
32   33 LAM
33   32 5*MU
33   34 LAM
34   33 5*MU
34   35 LAM
35   34 5*MU
35   36 LAM
36   35 5*MU
36   37 LAM
37   36 5*MU
37   38 LAM
38   37 5*MU
38   39 LAM
39   38 5*MU
39   40 LAM
40   39 5*MU
40   41 LAM
41   40 5*MU
41   42 LAM
42   41 5*MU
42   43 LAM
43   42 5*MU
43   44 LAM
44   43 5*MU
44   45 LAM
45   44 5*MU
45   46 LAM
46   45 5*MU
46   47 LAM
47   46 5*MU
47   48 LAM
48   47 5*MU
48   49 LAM
49   48 5*MU
49   50 LAM
50   49 5*MU
50   51 LAM
51   50 5*MU
51   52 LAM
52   51 5*MU
52   53 LAM
53   52 5*MU
53   54 LAM
54   53 5*MU
54   55 LAM
55   54 5*MU
55   56 LAM
56   55 5*MU
56   57 LAM
57   56 5*MU
57   58 LAM
58   57 5*MU
58   59 LAM
59   58 5*MU
59   60 LAM
60   59 5*MU
60   61 LAM
61   60 5*MU
61   62 LAM
62   61 5*MU
62   63 LAM
63   62 5*MU
63   64 LAM
64   63 5*MU
64   65 LAM
65   64 5*MU
65   66 LAM
66   65 5*MU
66   67 LAM
67   66 5*MU
67   68 LAM
68   67 5*MU
68   69 LAM
69   68 5*MU
69   70 LAM
70   69 5*MU
70   71 LAM
71   70 5*MU
71   72 LAM
72   71 5*MU
72   73 LAM
73   72 5*MU
73   74 LAM
74   73 5*MU
74   75 LAM
75   74 5*MU
75   76 LAM
76   75 5*MU
76   77 LAM
77   76 5*MU
77   78 LAM
78   77 5*MU
78   79 LAM
79   78 5*MU
79   80 LAM
80   79 5*MU
80   81 LAM
81   80 5*MU
81   82 LAM
82   81 5*MU
82   83 LAM
83   82 5*MU
83   84 LAM
84   83 5*MU
84   85 LAM
85   84 5*MU
85   86 LAM
86   85 5*MU
86   87 LAM
87   86 5*MU
87   88 LAM
88   87 5*MU
88   89 LAM
89   88 5*MU
89   90 LAM
90   89 5*MU
90   91 LAM
91   90 5*MU
91   92 LAM
92   91 5*MU
92   93 LAM
93   92 5*MU
93   94 LAM
94   93 5*MU
94   95 LAM
95   94 5*MU
95   96 LAM
96   95 5*MU
96   97 LAM
97   96 5*MU
97   98 LAM
98   97 5*MU
98   99 LAM
99   98 5*MU
99   100 LAM
100   99 5*MU
end
expr prob(mm5,0)
expr LAM*prob(mm5,100)
bind 
LAM 3.0
end
expr prob(mm5,0)
expr LAM*prob(mm5,100)

* Example 13:
echo Example 13:

format 8

markov cycletime
3 2 3*lam
2 3 mu
2 F 2*lam
end
2 1.0
end

bind
lam 0.0001
mu 1.0
end

expr 1/mean (cycletime), 6*mu*(lam/(lam+mu))*(lam/(lam+mu))*(mu/(lam+mu))

* Example 14:
echo Example 14:
* irreducible chain, using algorithm from phase-type chains to
* find transient probability function for states.
* make sure value (evaluation of the funcons at t) and tvalue
* (use uniformization algorithm to find transient proaility)
* give the same answer.

markov m readprobs
1 2 10
2 1 4
end
1 1
end

phnew
cdf (m,1)
cdf (m,2)
expr prob (m,1), prob(m,2)

loop t,0,1,.2
    expr value(t;m,1), tvalue (t;m,1), value(t;m,2), tvalue (t;m,2)
end

* Example 15:
echo Example 15:
format 8
* Running a HARP-like model.
* We use the behavioral decomp with moments fehm (only the first moment)
* Near coincident fault rate is lam
var c1 1-mom*lam/3600
var n mom*lam/3600

bind
* epsilon is used to control errors in computations
*epsilon 0.00000000000000001
lam .0001
mu .00001
mom .36
end

expr c1,n
expr 2*lam*c1,2*lam*n

markov 3st
2 1 2*lam*c1
2 fncf 2*lam*n
1 0 mu
end
2 1
end

cdf(3st)
expr mean(3st)
* We compute the failure prob in two diffeernt ways;
* value computes using the eigenvalue approach
* while tvalue computes it using the randomization(uniformization)
loop i,-5,5,1
bind t 10^i
expr value(t;3st), tvalue(t;3st)
end

*Example 16:
echo Example 16:
* This a reliability model of a TMR system with
* a spare. First we use the spdag (graph) model
* See Figure 8.24 (p. 406) 
* of Trivedi's book

format 8

* lam is the failure rate of an active unit and
* mu is the failure rate of a spare
* c is the coverage probability

graph phasetype(lam,mu,c)
31 30
31 Z
30 20
end
exit 31 prob
prob 31 30 (3*lam*c+mu)/(3*lam+mu)
dist  31 exp(3*lam+mu)
dist  30 exp(3*lam)
dist  20 exp(2*lam)
dist  Z  zero
end


* Now solve the same problem using a Markov model
* This is a special case of the model in Figure 8.23
* in Trivedi's book (p. 405)

markov markovian(lam,mu,c)
31 30 3*lam*c+mu
31 F  3*lam*(1-c)
30 20 3*lam
20 F 2*lam
end
31 1.0
end

* df is the dormancy factor: mu/lam
bind df 0.0
expr df
cdf(phasetype;1.0,df,0.9)
cdf(markovian;1.0,df,0.9)
cdf(phasetype;0.0001,df*0.0001,0.9)
cdf(markovian;0.0001,df*0.0001,0.9)
cdf(phasetype;1000,df*1000,0.9)
cdf(markovian;1000,df*1000,0.9)

bind df 0.5
expr df
cdf(phasetype;1.0,df,0.9)
cdf(markovian;1.0,df,0.9)
cdf(phasetype;0.0001,df*0.0001,0.9)
cdf(markovian;0.0001,df*0.0001,0.9)
cdf(phasetype;1000,df*1000,0.9)
cdf(markovian;1000,df*1000,0.9)

bind df 1.0
expr df
cdf(phasetype;1.0,df,0.9)
cdf(markovian;1.0,df,0.9)
cdf(phasetype;0.0001,df*0.0001,0.9)
cdf(markovian;0.0001,df*0.0001,0.9)
cdf(phasetype;1000,df*1000,0.9)
cdf(markovian;1000,df*1000,0.9)

loop c,0.9,1.0,.1
  loop i,0,10,5
    bind df 0.1*i
    * mean time to failure
    expr mean(phasetype;.0001,df*.0001,c)
    expr mean(markovian;.0001,df*.0001,c)
    * fail prob at time 10 hours
    expr value(10;phasetype;0.0001,df*.0001,c)
    expr value(10;markovian;0.0001,df*.0001,c)
    expr tvalue(10;markovian;0.0001,df*.0001,c)
  end
end

*Example 17:
echo Example 17:
* Now consider a reliability model of a multiprocessor
* with two diffrent approaches
* Approach 1: 
* a block diagram model of a system with
* 16 processors, 16 memories and a switch.

format 8

  bind 
  lambda 0.0001
  mu    0.005
  gamma  0.001
  end

block procs
comp processor exp(lambda)
* req is the minimum number of procs needed for system to remain operational
kofn procs req,16, processor
end

block mems
comp memory exp(mu)
* req is the minimum number of mems needed for system to remain operational
kofn mems req, 16 , memory
end

block sys1
comp switch exp(gamma)
comp procs  cdf(procs)
comp mems   cdf(mems)
series TOP switch procs mems
end


* Alternative is a markov model
 
markov mark readprobs 
  577     543        16*lambda         
  577     575        16*mu             
  577   580        gamma          
  543     509        15*lambda         
  543     541        16*mu             
  543   580        gamma          
  575     541        16*lambda         
  575     573        15*mu             
  575   580        gamma          
  509     475        14*lambda         
  509     507        16*mu             
  509   580        gamma          
  541     507        15*lambda         
  541     539        15*mu             
  541   580        gamma          
  573     539        16*lambda         
  573     571        14*mu             
  573   580        gamma          
  475     441        13*lambda         
  475     473        16*mu             
  475   580        gamma          
  507     473        14*lambda         
  507     505        15*mu             
  507   580        gamma          
  539     505        15*lambda         
  539     537        14*mu             
  539   580        gamma          
  571     537        16*lambda         
  571     569        13*mu             
  571   580        gamma          
  441     407        12*lambda         
  441     439        16*mu             
  441   580        gamma          
  473     439        13*lambda         
  473     471        15*mu             
  473   580        gamma          
  505     471        14*lambda         
  505     503        14*mu             
  505   580        gamma          
  537     503        15*lambda         
  537     535        13*mu             
  537   580        gamma          
  569     535        16*lambda         
  569     567        12*mu             
  569   580        gamma          
  407     373        11*lambda         
  407     405        16*mu             
  407   580        gamma          
  439     405        12*lambda         
  439     437        15*mu             
  439   580        gamma          
  471     437        13*lambda         
  471     469        14*mu             
  471   580        gamma          
  503     469        14*lambda         
  503     501        13*mu             
  503   580        gamma          
  535     501        15*lambda         
  535     533        12*mu             
  535   580        gamma          
  567     533        16*lambda         
  567     565        11*mu             
  567   580        gamma          
  373     339        10*lambda         
  373     371        16*mu             
  373   580        gamma          
  405     371        11*lambda         
  405     403        15*mu             
  405   580        gamma          
  437     403        12*lambda         
  437     435        14*mu             
  437   580        gamma          
  469     435        13*lambda         
  469     467        13*mu             
  469   580        gamma          
  501     467        14*lambda         
  501     499        12*mu             
  501   580        gamma          
  533     499        15*lambda         
  533     531        11*mu             
  533   580        gamma          
  565     531        16*lambda         
  565     563        10*mu             
  565   580        gamma          
  339     305        9*lambda         
  339     337        16*mu             
  339   580        gamma          
  371     337        10*lambda         
  371     369        15*mu             
  371   580        gamma          
  403     369        11*lambda         
  403     401        14*mu             
  403   580        gamma          
  435     401        12*lambda         
  435     433        13*mu             
  435   580        gamma          
  467     433        13*lambda         
  467     465        12*mu             
  467   580        gamma          
  499     465        14*lambda         
  499     497        11*mu             
  499   580        gamma          
  531     497        15*lambda         
  531     529        10*mu             
  531   580        gamma          
  563     529        16*lambda         
  563     561        9*mu             
  563   580        gamma          
  305     271        8*lambda         
  305     303        16*mu             
  305   580        gamma          
  337     303        9*lambda         
  337     335        15*mu             
  337   580        gamma          
  369     335        10*lambda         
  369     367        14*mu             
  369   580        gamma          
  401     367        11*lambda         
  401     399        13*mu             
  401   580        gamma          
  433     399        12*lambda         
  433     431        12*mu             
  433   580        gamma          
  465     431        13*lambda         
  465     463        11*mu             
  465   580        gamma          
  497     463        14*lambda         
  497     495        10*mu             
  497   580        gamma          
  529     495        15*lambda         
  529     527        9*mu             
  529   580        gamma          
  561     527        16*lambda         
  561     559        8*mu             
  561   580        gamma          
  271   578        7*lambda         
  271     269        16*mu             
  271   580        gamma          
  303     269        8*lambda         
  303     301        15*mu             
  303   580        gamma          
  335     301        9*lambda         
  335     333        14*mu             
  335   580        gamma          
  367     333        10*lambda         
  367     365        13*mu             
  367   580        gamma          
  399     365        11*lambda         
  399     397        12*mu             
  399   580        gamma          
  431     397        12*lambda         
  431     429        11*mu             
  431   580        gamma          
  463     429        13*lambda         
  463     461        10*mu             
  463   580        gamma          
  495     461        14*lambda         
  495     493        9*mu             
  495   580        gamma          
  527     493        15*lambda         
  527     525        8*mu             
  527   580        gamma          
  559     525        16*lambda         
  559   579        7*mu             
  559   580        gamma          
  269   578        7*lambda         
  269     267        15*mu             
  269   580        gamma          
  301     267        8*lambda         
  301     299        14*mu             
  301   580        gamma          
  333     299        9*lambda         
  333     331        13*mu             
  333   580        gamma          
  365     331        10*lambda         
  365     363        12*mu             
  365   580        gamma          
  397     363        11*lambda         
  397     395        11*mu             
  397   580        gamma          
  429     395        12*lambda         
  429     427        10*mu             
  429   580        gamma          
  461     427        13*lambda         
  461     459        9*mu             
  461   580        gamma          
  493     459        14*lambda         
  493     491        8*mu             
  493   580        gamma          
  525     491        15*lambda         
  525   579        7*mu             
  525   580        gamma          
  267   578        7*lambda         
  267     265        14*mu             
  267   580        gamma          
  299     265        8*lambda         
  299     297        13*mu             
  299   580        gamma          
  331     297        9*lambda         
  331     329        12*mu             
  331   580        gamma          
  363     329        10*lambda         
  363     361        11*mu             
  363   580        gamma          
  395     361        11*lambda         
  395     393        10*mu             
  395   580        gamma          
  427     393        12*lambda         
  427     425        9*mu             
  427   580        gamma          
  459     425        13*lambda         
  459     457        8*mu             
  459   580        gamma          
  491     457        14*lambda         
  491   579        7*mu             
  491   580        gamma          
  265   578        7*lambda         
  265     263        13*mu             
  265   580        gamma          
  297     263        8*lambda         
  297     295        12*mu             
  297   580        gamma          
  329     295        9*lambda         
  329     327        11*mu             
  329   580        gamma          
  361     327        10*lambda         
  361     359        10*mu             
  361   580        gamma          
  393     359        11*lambda         
  393     391        9*mu             
  393   580        gamma          
  425     391        12*lambda         
  425     423        8*mu             
  425   580        gamma          
  457     423        13*lambda         
  457   579        7*mu             
  457   580        gamma          
  263   578        7*lambda         
  263     261        12*mu             
  263   580        gamma          
  295     261        8*lambda         
  295     293        11*mu             
  295   580        gamma          
  327     293        9*lambda         
  327     325        10*mu             
  327   580        gamma          
  359     325        10*lambda         
  359     357        9*mu             
  359   580        gamma          
  391     357        11*lambda         
  391     389        8*mu             
  391   580        gamma          
  423     389        12*lambda         
  423   579        7*mu             
  423   580        gamma          
  261   578        7*lambda         
  261     259        11*mu             
  261   580        gamma          
  293     259        8*lambda         
  293     291        10*mu             
  293   580        gamma          
  325     291        9*lambda         
  325     323        9*mu             
  325   580        gamma          
  357     323        10*lambda         
  357     355        8*mu             
  357   580        gamma          
  389     355        11*lambda         
  389   579        7*mu             
  389   580        gamma          
  259   578        7*lambda         
  259     257        10*mu             
  259   580        gamma          
  291     257        8*lambda         
  291     289        9*mu             
  291   580        gamma          
  323     289        9*lambda         
  323     321        8*mu             
  323   580        gamma          
  355     321        10*lambda         
  355   579        7*mu             
  355   580        gamma          
  257   578        7*lambda         
  257     255        9*mu             
  257   580        gamma          
  289     255        8*lambda         
  289     287        8*mu             
  289   580        gamma          
  321     287        9*lambda         
  321   579        7*mu             
  321   580        gamma          
  255   578        7*lambda         
  255     253        8*mu             
  255   580        gamma          
  287     253        8*lambda         
  287   579        7*mu             
  287   580        gamma          
  253   578        7*lambda         
  253   579        7*mu             
  253   580        gamma          
  end
  577 1.0
  end

  bind req 7


* Compare Markov model results with those from RBD.
  loop t,0,10,1
    expr tvalue(t;mark), tvalue(t;sys1)
  end
  loop t,10,100,10
    expr tvalue(t;mark), tvalue(t;sys1)
  end
  loop t,100,1000,100
    expr tvalue(t;mark), tvalue(t;sys1)
  end
  loop t,1000,10000,1000
    expr tvalue(t;mark), tvalue(t;sys1)
  end

*Example 18:
echo Example 18:

* Model of an isdn protocol in which voice packets arrive at rate lam1
* and data packets arrive at lam2; respective service rates are mu1 and mu2
* Voice packets are not buffered while the total number data packets in
* the system is limited to 10.
* For a reference see Tom Robertazzi's book: Computer Networks and Systems,
* 1990
markov isdn10 readprobs 
00 10 lam2
10 20 lam2
20 30 lam2
30 40 lam2
40 50 lam2
50 60 lam2
60 70 lam2
70 80 lam2
80 90 lam2
90 100 lam2
100 90 mu2
90 80 mu2
80 70 mu2
70 60 mu2
60 50 mu2
50 40 mu2
40 30 mu2
30 20 mu2
20 10 mu2
10 00 mu2
00 01 lam1
01 00 mu1
01 11 lam2
11 21 lam2
21 31 lam2
31 41 lam2
41 51 lam2
51 61 lam2
61 71 lam2
71 81 lam2
81 91 lam2
91 101 lam2
101 100 mu1
91 90 mu1
81 80 mu1
71 70 mu1
61 60 mu1
51 50 mu1
41 40 mu1
31 30 mu1
21 20 mu1
11 10 mu1
* Assign to state i0 a reward rate equal to the number of data packets in the
* the system in that state
reward
00 0
10 1
20 2
30 3
40 4
50 5
60 6
70 7
80 8
90 9
100 10
end
00 1.0
end

bind
lam1 1.0
mu1 10.0
lam2 2.0
mu2  20.0
end

echo Steady state rejection prob for data packets
expr prob(isdn10,100)+prob(isdn10,101)

echo Steady state rejection prob for voice packets
expr 1.0 - prob(isdn10,00)

echo Transient rejection probabilities 
loop t,0.1,1,0.1
expr tvalue(t;isdn10,100) + tvalue(t;isdn10,101)
expr 1.0 - tvalue(t;isdn10,00)

end

echo Compute the channel idle prob at time t
loop t,0,10,1
expr tvalue (t;isdn10,00)
end

echo Compute the channel idle prob at steady state
expr prob(isdn10,00)


echo Compute the steady state average queulength of data packets
expr exrss(isdn10)
var tput1 lam1*prob(isdn10,00)
var tput2 lam2*(1.0 - prob(isdn10,100) -prob(isdn10,101))
var resp1 prob(isdn10,01)/tput1
var resp2 exrss(isdn10)/tput2

echo thruputs of voice and data packets
expr tput1, tput2
echo mean response times of voice and data packets
expr resp1, resp2
end

