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Re-tidy csma. 

git-svn-id: https://www.prismmodelchecker.org/svn/prism/prism/trunk@889 bbc10eb1-c90d-0410-af57-cb519fbb1720
master
Dave Parker 17 years ago
parent
bc758e3d7c
commit
3e0ba6cb5f
16 changed files with 99 additions and 228 deletions
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  1. 13
      prism-examples/csma/.autopp
  2. 11
      prism-examples/csma/.csmaN_K.nm.pp
  3. 18
      prism-examples/csma/auto
  4. 22
      prism-examples/csma/csma.pctl
  5. 26
      prism-examples/csma/csma2.pctl
  6. 9
      prism-examples/csma/csma2_2.nm
  7. 31
      prism-examples/csma/csma2_4.nm
  8. 17
      prism-examples/csma/csma2_6.nm
  9. 9
      prism-examples/csma/csma3_2.nm
  10. 13
      prism-examples/csma/csma3_4.nm
  11. 17
      prism-examples/csma/csma3_6.nm
  12. 34
      prism-examples/csma/csma4.pctl
  13. 35
      prism-examples/csma/csma4_2.nm
  14. 13
      prism-examples/csma/csma4_4.nm
  15. 17
      prism-examples/csma/csma4_6.nm
  16. 42
      prism-examples/csma/csma6.pctl

13
prism-examples/csma/.autopp
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@ -1,10 +1,9 @@
#!/bin/csh #!/bin/csh
foreach K ( 2 4 6 )
echo "Generating for K=$K"
prismpp .csmaK.pctl.pp $K >! csma$K.pctl
foreach N ( 2 3 4 )
echo " and N=$N"
prismpp .csmaK_N.nm.pp $N $K >! csma$K"_"$N.nm
end
foreach N ( 2 3 4 )
foreach K ( 2 4 6 )
echo "Generating for N=$N and K=$K"
prismpp .csmaN_K.nm.pp $N $K >! csma$N"_"$K.nm
end
end end

11
prism-examples/csma/.csmaK_N.nm.pp → prism-examples/csma/.csmaN_K.nm.pp
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@ -128,14 +128,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = #& i=1:N#s#i#=4#end#; label "all_delivered" = #& i=1:N#s#i#=4#end#;
label "one_delivered" = #| i=1:N#s#i#=4#end#; label "one_delivered" = #| i=1:N#s#i#=4#end#;
label "collision_max_backoff" = #| i=1:N#(cd#i#=K & s#i#=1 & b=2)#end#; label "collision_max_backoff" = #| i=1:N#(cd#i#=K & s#i#=1 & b=2)#end#;
#for i=1:K#
label "success_with_backoff_under_#i#" = #| j=1:N#(cd#j#<=#i# & s#j#=4)#end#;
#end#
#for i=1:K#
label "collisions_equal_#i#" = #| j=1:N#(cd#j#=#i#)#end#;
#end#
formula min_backoff_after_success = min(#, i=1:N#s#i#=4?cd#i#:K+1#end#);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

18
prism-examples/csma/auto
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@ -1,12 +1,12 @@
#!/bin/csh #!/bin/csh
prism csma2_2.nm csma2.pctl -s
prism csma2_3.nm csma2.pctl -s
prism csma2_4.nm csma2.pctl -s
prism csma4_2.nm csma4.pctl -s
prism csma4_3.nm csma4.pctl -s
#prism csma4_4.nm csma4.pctl -s
prism csma6_2.nm csma6.pctl -s
prism csma6_3.nm csma6.pctl -s
#prism csma6_4.nm csma6.pctl -s
prism csma2_2.nm csma.pctl -s
prism csma2_4.nm csma.pctl -s
prism csma2_6.nm csma.pctl -s
prism csma3_2.nm csma.pctl -s
prism csma3_4.nm csma.pctl -s
prism csma3_6.nm csma.pctl -s
prism csma4_2.nm csma.pctl -s
#prism csma4_4.nm csma.pctl -s
#prism csma4_6.nm csma.pctl -s

22
prism-examples/csma/csma.pctl
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@ -0,0 +1,22 @@
const int k;
// expected time for all messages to be sent
R{"time"}min=?[ F "all_delivered" ]
R{"time"}max=?[ F "all_delivered" ]
// expected time for one message to be sent
Rmin=?[ F "one_delivered" ]
Rmax=?[ F "one_delivered" ]
// message of any station eventually delivered before k backoffs
Pmin=?[ F min_backoff_after_success<=k ]
Pmax=?[ F min_backoff_after_success<=k ]
// probability all sent successfully before a collision with max backoff
Pmin=?[ !"collision_max_backoff" U "all_delivered" ]
Pmax=?[ !"collision_max_backoff" U "all_delivered" ]
// probability some station suffers at least k collisions
Pmin=?[ F max_collisions>=k ]
Pmax=?[ F max_collisions>=k ]

26
prism-examples/csma/csma2.pctl
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@ -1,26 +0,0 @@
// expected time for all messages to be sent
R{"time"}min=?[ F "all_delivered" ]
R{"time"}max=?[ F "all_delivered" ]
// expected time for one message to be sent
Rmin=?[ F "one_delivered" ]
Rmax=?[ F "one_delivered" ]
// message of any station eventually delivered before i backoffs
Pmin=?[ F "success_with_backoff_under_1" ]
Pmax=?[ F "success_with_backoff_under_1" ]
Pmin=?[ F "success_with_backoff_under_2" ]
Pmax=?[ F "success_with_backoff_under_2" ]
// probability all sent successfully before a collision with max backoff
Pmin=?[ !"collision_max_backoff" U "all_delivered" ]
Pmax=?[ !"collision_max_backoff" U "all_delivered" ]
// probability a station suffers i collisions
Pmin=?[ F "collisions_equal_1" ]
Pmax=?[ F "collisions_equal_1" ]
Pmin=?[ F "collisions_equal_2" ]
Pmax=?[ F "collisions_equal_2" ]

9
prism-examples/csma/csma2_2.nm
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@ -118,12 +118,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4; label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4; label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

31
prism-examples/csma/csma2_4.nm
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@ -7,8 +7,8 @@ mdp
// in digital clocks approach and suppose a station only sends one message // in digital clocks approach and suppose a station only sends one message
// actual parameters // actual parameters
const int N = 4; // number of processes
const int K = 2; // exponential backoff limit
const int N = 2; // number of processes
const int K = 4; // exponential backoff limit
const int slot = 2*sigma; // length of slot const int slot = 2*sigma; // length of slot
const int M = floor(pow(2, K))-1 ; // max number of slots to wait const int M = floor(pow(2, K))-1 ; // max number of slots to wait
//const int lambda=782; //const int lambda=782;
@ -34,26 +34,18 @@ module bus
// a sender sends (ok - no other message being sent) // a sender sends (ok - no other message being sent)
[send1] (b=0) -> (b'=1); [send1] (b=0) -> (b'=1);
[send2] (b=0) -> (b'=1); [send2] (b=0) -> (b'=1);
[send3] (b=0) -> (b'=1);
[send4] (b=0) -> (b'=1);
// a sender sends (bus busy - collision) // a sender sends (bus busy - collision)
[send1] (b=1|b=2) & (y1<sigma) -> (b'=2); [send1] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send2] (b=1|b=2) & (y1<sigma) -> (b'=2); [send2] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send3] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send4] (b=1|b=2) & (y1<sigma) -> (b'=2);
// finish sending // finish sending
[end1] (b=1) -> (b'=0) & (y1'=0); [end1] (b=1) -> (b'=0) & (y1'=0);
[end2] (b=1) -> (b'=0) & (y1'=0); [end2] (b=1) -> (b'=0) & (y1'=0);
[end3] (b=1) -> (b'=0) & (y1'=0);
[end4] (b=1) -> (b'=0) & (y1'=0);
// bus busy // bus busy
[busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b); [busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b); [busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy3] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy4] (b=1|b=2) & (y1>=sigma) -> (b'=b);
// collision detected // collision detected
[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0); [cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0);
@ -100,6 +92,8 @@ module station1
// probability depends on which transmission this is (cd1) // probability depends on which transmission this is (cd1)
[] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ; [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ;
[] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ; [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ;
[] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (bc1'=0) + 1/8 : (s1'=3) & (bc1'=1) + 1/8 : (s1'=3) & (bc1'=2) + 1/8 : (s1'=3) & (bc1'=3) + 1/8 : (s1'=3) & (bc1'=4) + 1/8 : (s1'=3) & (bc1'=5) + 1/8 : (s1'=3) & (bc1'=6) + 1/8 : (s1'=3) & (bc1'=7) ;
[] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (bc1'=0) + 1/16 : (s1'=3) & (bc1'=1) + 1/16 : (s1'=3) & (bc1'=2) + 1/16 : (s1'=3) & (bc1'=3) + 1/16 : (s1'=3) & (bc1'=4) + 1/16 : (s1'=3) & (bc1'=5) + 1/16 : (s1'=3) & (bc1'=6) + 1/16 : (s1'=3) & (bc1'=7) + 1/16 : (s1'=3) & (bc1'=8) + 1/16 : (s1'=3) & (bc1'=9) + 1/16 : (s1'=3) & (bc1'=10) + 1/16 : (s1'=3) & (bc1'=11) + 1/16 : (s1'=3) & (bc1'=12) + 1/16 : (s1'=3) & (bc1'=13) + 1/16 : (s1'=3) & (bc1'=14) + 1/16 : (s1'=3) & (bc1'=15) ;
// wait until backoff counter reaches 0 then send again // wait until backoff counter reaches 0 then send again
[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot) [time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot)
@ -116,8 +110,6 @@ endmodule
// construct further stations through renaming // construct further stations through renaming
module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule
module station3=station1[s1=s3,x1=x3,cd1=cd3,bc1=bc3,send1=send3,busy1=busy3,end1=end3] endmodule
module station4=station1[s1=s4,x1=x4,cd1=cd4,bc1=bc4,send1=send4,busy1=busy4,end1=end4] endmodule
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
@ -128,12 +120,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
label "all_delivered" = s1=4&s2=4&s3=4&s4=4;
label "one_delivered" = s1=4|s2=4|s3=4|s4=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2)|(cd4=K & s4=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4)|(cd3<=1 & s3=4)|(cd4<=1 & s4=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4)|(cd3<=2 & s3=4)|(cd4<=2 & s4=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1)|(cd3=1)|(cd4=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2)|(cd3=2)|(cd4=2);
// labels/formulae
label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

17
prism-examples/csma/csma6_2.nm → prism-examples/csma/csma2_6.nm
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@ -122,20 +122,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4; label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4; label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4);
label "success_with_backoff_under_3" = (cd1<=3 & s1=4)|(cd2<=3 & s2=4);
label "success_with_backoff_under_4" = (cd1<=4 & s1=4)|(cd2<=4 & s2=4);
label "success_with_backoff_under_5" = (cd1<=5 & s1=4)|(cd2<=5 & s2=4);
label "success_with_backoff_under_6" = (cd1<=6 & s1=4)|(cd2<=6 & s2=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2);
label "collisions_equal_3" = (cd1=3)|(cd2=3);
label "collisions_equal_4" = (cd1=4)|(cd2=4);
label "collisions_equal_5" = (cd1=5)|(cd2=5);
label "collisions_equal_6" = (cd1=6)|(cd2=6);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

9
prism-examples/csma/csma2_3.nm → prism-examples/csma/csma3_2.nm
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@ -123,12 +123,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4&s3=4; label "all_delivered" = s1=4&s2=4&s3=4;
label "one_delivered" = s1=4|s2=4|s3=4; label "one_delivered" = s1=4|s2=4|s3=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4)|(cd3<=1 & s3=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4)|(cd3<=2 & s3=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1)|(cd3=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2)|(cd3=2);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1,s3=4?cd3:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

13
prism-examples/csma/csma4_3.nm → prism-examples/csma/csma3_4.nm
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@ -125,16 +125,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4&s3=4; label "all_delivered" = s1=4&s2=4&s3=4;
label "one_delivered" = s1=4|s2=4|s3=4; label "one_delivered" = s1=4|s2=4|s3=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4)|(cd3<=1 & s3=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4)|(cd3<=2 & s3=4);
label "success_with_backoff_under_3" = (cd1<=3 & s1=4)|(cd2<=3 & s2=4)|(cd3<=3 & s3=4);
label "success_with_backoff_under_4" = (cd1<=4 & s1=4)|(cd2<=4 & s2=4)|(cd3<=4 & s3=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1)|(cd3=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2)|(cd3=2);
label "collisions_equal_3" = (cd1=3)|(cd2=3)|(cd3=3);
label "collisions_equal_4" = (cd1=4)|(cd2=4)|(cd3=4);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1,s3=4?cd3:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

17
prism-examples/csma/csma6_3.nm → prism-examples/csma/csma3_6.nm
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@ -127,20 +127,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4&s3=4; label "all_delivered" = s1=4&s2=4&s3=4;
label "one_delivered" = s1=4|s2=4|s3=4; label "one_delivered" = s1=4|s2=4|s3=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4)|(cd3<=1 & s3=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4)|(cd3<=2 & s3=4);
label "success_with_backoff_under_3" = (cd1<=3 & s1=4)|(cd2<=3 & s2=4)|(cd3<=3 & s3=4);
label "success_with_backoff_under_4" = (cd1<=4 & s1=4)|(cd2<=4 & s2=4)|(cd3<=4 & s3=4);
label "success_with_backoff_under_5" = (cd1<=5 & s1=4)|(cd2<=5 & s2=4)|(cd3<=5 & s3=4);
label "success_with_backoff_under_6" = (cd1<=6 & s1=4)|(cd2<=6 & s2=4)|(cd3<=6 & s3=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1)|(cd3=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2)|(cd3=2);
label "collisions_equal_3" = (cd1=3)|(cd2=3)|(cd3=3);
label "collisions_equal_4" = (cd1=4)|(cd2=4)|(cd3=4);
label "collisions_equal_5" = (cd1=5)|(cd2=5)|(cd3=5);
label "collisions_equal_6" = (cd1=6)|(cd2=6)|(cd3=6);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1,s3=4?cd3:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

34
prism-examples/csma/csma4.pctl
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@ -1,34 +0,0 @@
// expected time for all messages to be sent
R{"time"}min=?[ F "all_delivered" ]
R{"time"}max=?[ F "all_delivered" ]
// expected time for one message to be sent
Rmin=?[ F "one_delivered" ]
Rmax=?[ F "one_delivered" ]
// message of any station eventually delivered before i backoffs
Pmin=?[ F "success_with_backoff_under_1" ]
Pmax=?[ F "success_with_backoff_under_1" ]
Pmin=?[ F "success_with_backoff_under_2" ]
Pmax=?[ F "success_with_backoff_under_2" ]
Pmin=?[ F "success_with_backoff_under_3" ]
Pmax=?[ F "success_with_backoff_under_3" ]
Pmin=?[ F "success_with_backoff_under_4" ]
Pmax=?[ F "success_with_backoff_under_4" ]
// probability all sent successfully before a collision with max backoff
Pmin=?[ !"collision_max_backoff" U "all_delivered" ]
Pmax=?[ !"collision_max_backoff" U "all_delivered" ]
// probability a station suffers i collisions
Pmin=?[ F "collisions_equal_1" ]
Pmax=?[ F "collisions_equal_1" ]
Pmin=?[ F "collisions_equal_2" ]
Pmax=?[ F "collisions_equal_2" ]
Pmin=?[ F "collisions_equal_3" ]
Pmax=?[ F "collisions_equal_3" ]
Pmin=?[ F "collisions_equal_4" ]
Pmax=?[ F "collisions_equal_4" ]

35
prism-examples/csma/csma4_2.nm
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@ -7,8 +7,8 @@ mdp
// in digital clocks approach and suppose a station only sends one message // in digital clocks approach and suppose a station only sends one message
// actual parameters // actual parameters
const int N = 2; // number of processes
const int K = 4; // exponential backoff limit
const int N = 4; // number of processes
const int K = 2; // exponential backoff limit
const int slot = 2*sigma; // length of slot const int slot = 2*sigma; // length of slot
const int M = floor(pow(2, K))-1 ; // max number of slots to wait const int M = floor(pow(2, K))-1 ; // max number of slots to wait
//const int lambda=782; //const int lambda=782;
@ -34,18 +34,26 @@ module bus
// a sender sends (ok - no other message being sent) // a sender sends (ok - no other message being sent)
[send1] (b=0) -> (b'=1); [send1] (b=0) -> (b'=1);
[send2] (b=0) -> (b'=1); [send2] (b=0) -> (b'=1);
[send3] (b=0) -> (b'=1);
[send4] (b=0) -> (b'=1);
// a sender sends (bus busy - collision) // a sender sends (bus busy - collision)
[send1] (b=1|b=2) & (y1<sigma) -> (b'=2); [send1] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send2] (b=1|b=2) & (y1<sigma) -> (b'=2); [send2] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send3] (b=1|b=2) & (y1<sigma) -> (b'=2);
[send4] (b=1|b=2) & (y1<sigma) -> (b'=2);
// finish sending // finish sending
[end1] (b=1) -> (b'=0) & (y1'=0); [end1] (b=1) -> (b'=0) & (y1'=0);
[end2] (b=1) -> (b'=0) & (y1'=0); [end2] (b=1) -> (b'=0) & (y1'=0);
[end3] (b=1) -> (b'=0) & (y1'=0);
[end4] (b=1) -> (b'=0) & (y1'=0);
// bus busy // bus busy
[busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b); [busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b); [busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy3] (b=1|b=2) & (y1>=sigma) -> (b'=b);
[busy4] (b=1|b=2) & (y1>=sigma) -> (b'=b);
// collision detected // collision detected
[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0); [cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0);
@ -92,8 +100,6 @@ module station1
// probability depends on which transmission this is (cd1) // probability depends on which transmission this is (cd1)
[] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ; [] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ;
[] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ; [] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ;
[] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (bc1'=0) + 1/8 : (s1'=3) & (bc1'=1) + 1/8 : (s1'=3) & (bc1'=2) + 1/8 : (s1'=3) & (bc1'=3) + 1/8 : (s1'=3) & (bc1'=4) + 1/8 : (s1'=3) & (bc1'=5) + 1/8 : (s1'=3) & (bc1'=6) + 1/8 : (s1'=3) & (bc1'=7) ;
[] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (bc1'=0) + 1/16 : (s1'=3) & (bc1'=1) + 1/16 : (s1'=3) & (bc1'=2) + 1/16 : (s1'=3) & (bc1'=3) + 1/16 : (s1'=3) & (bc1'=4) + 1/16 : (s1'=3) & (bc1'=5) + 1/16 : (s1'=3) & (bc1'=6) + 1/16 : (s1'=3) & (bc1'=7) + 1/16 : (s1'=3) & (bc1'=8) + 1/16 : (s1'=3) & (bc1'=9) + 1/16 : (s1'=3) & (bc1'=10) + 1/16 : (s1'=3) & (bc1'=11) + 1/16 : (s1'=3) & (bc1'=12) + 1/16 : (s1'=3) & (bc1'=13) + 1/16 : (s1'=3) & (bc1'=14) + 1/16 : (s1'=3) & (bc1'=15) ;
// wait until backoff counter reaches 0 then send again // wait until backoff counter reaches 0 then send again
[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot) [time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot)
@ -110,6 +116,8 @@ endmodule
// construct further stations through renaming // construct further stations through renaming
module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule
module station3=station1[s1=s3,x1=x3,cd1=cd3,bc1=bc3,send1=send3,busy1=busy3,end1=end3] endmodule
module station4=station1[s1=s4,x1=x4,cd1=cd4,bc1=bc4,send1=send4,busy1=busy4,end1=end4] endmodule
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
@ -120,16 +128,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4);
label "success_with_backoff_under_3" = (cd1<=3 & s1=4)|(cd2<=3 & s2=4);
label "success_with_backoff_under_4" = (cd1<=4 & s1=4)|(cd2<=4 & s2=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2);
label "collisions_equal_3" = (cd1=3)|(cd2=3);
label "collisions_equal_4" = (cd1=4)|(cd2=4);
// labels/formulae
label "all_delivered" = s1=4&s2=4&s3=4&s4=4;
label "one_delivered" = s1=4|s2=4|s3=4|s4=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2)|(cd4=K & s4=1 & b=2);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1,s3=4?cd3:K+1,s4=4?cd4:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

13
prism-examples/csma/csma4_4.nm
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@ -130,16 +130,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4&s3=4&s4=4; label "all_delivered" = s1=4&s2=4&s3=4&s4=4;
label "one_delivered" = s1=4|s2=4|s3=4|s4=4; label "one_delivered" = s1=4|s2=4|s3=4|s4=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2)|(cd4=K & s4=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2)|(cd4=K & s4=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4)|(cd3<=1 & s3=4)|(cd4<=1 & s4=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4)|(cd3<=2 & s3=4)|(cd4<=2 & s4=4);
label "success_with_backoff_under_3" = (cd1<=3 & s1=4)|(cd2<=3 & s2=4)|(cd3<=3 & s3=4)|(cd4<=3 & s4=4);
label "success_with_backoff_under_4" = (cd1<=4 & s1=4)|(cd2<=4 & s2=4)|(cd3<=4 & s3=4)|(cd4<=4 & s4=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1)|(cd3=1)|(cd4=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2)|(cd3=2)|(cd4=2);
label "collisions_equal_3" = (cd1=3)|(cd2=3)|(cd3=3)|(cd4=3);
label "collisions_equal_4" = (cd1=4)|(cd2=4)|(cd3=4)|(cd4=4);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1,s3=4?cd3:K+1,s4=4?cd4:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

17
prism-examples/csma/csma6_4.nm → prism-examples/csma/csma4_6.nm
View File

@ -132,20 +132,11 @@ endrewards
//---------------------------------------------------------------------------------------------------------------------------- //----------------------------------------------------------------------------------------------------------------------------
// labels/formulae
label "all_delivered" = s1=4&s2=4&s3=4&s4=4; label "all_delivered" = s1=4&s2=4&s3=4&s4=4;
label "one_delivered" = s1=4|s2=4|s3=4|s4=4; label "one_delivered" = s1=4|s2=4|s3=4|s4=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2)|(cd4=K & s4=1 & b=2); label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2)|(cd3=K & s3=1 & b=2)|(cd4=K & s4=1 & b=2);
label "success_with_backoff_under_1" = (cd1<=1 & s1=4)|(cd2<=1 & s2=4)|(cd3<=1 & s3=4)|(cd4<=1 & s4=4);
label "success_with_backoff_under_2" = (cd1<=2 & s1=4)|(cd2<=2 & s2=4)|(cd3<=2 & s3=4)|(cd4<=2 & s4=4);
label "success_with_backoff_under_3" = (cd1<=3 & s1=4)|(cd2<=3 & s2=4)|(cd3<=3 & s3=4)|(cd4<=3 & s4=4);
label "success_with_backoff_under_4" = (cd1<=4 & s1=4)|(cd2<=4 & s2=4)|(cd3<=4 & s3=4)|(cd4<=4 & s4=4);
label "success_with_backoff_under_5" = (cd1<=5 & s1=4)|(cd2<=5 & s2=4)|(cd3<=5 & s3=4)|(cd4<=5 & s4=4);
label "success_with_backoff_under_6" = (cd1<=6 & s1=4)|(cd2<=6 & s2=4)|(cd3<=6 & s3=4)|(cd4<=6 & s4=4);
label "collisions_equal_1" = (cd1=1)|(cd2=1)|(cd3=1)|(cd4=1);
label "collisions_equal_2" = (cd1=2)|(cd2=2)|(cd3=2)|(cd4=2);
label "collisions_equal_3" = (cd1=3)|(cd2=3)|(cd3=3)|(cd4=3);
label "collisions_equal_4" = (cd1=4)|(cd2=4)|(cd3=4)|(cd4=4);
label "collisions_equal_5" = (cd1=5)|(cd2=5)|(cd3=5)|(cd4=5);
label "collisions_equal_6" = (cd1=6)|(cd2=6)|(cd3=6)|(cd4=6);
formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1,s3=4?cd3:K+1,s4=4?cd4:K+1);
formula min_collisions = min(cd1,cd2,cd3,cd4);
formula max_collisions = max(cd1,cd2,cd3,cd4);

42
prism-examples/csma/csma6.pctl
View File

@ -1,42 +0,0 @@
// expected time for all messages to be sent
R{"time"}min=?[ F "all_delivered" ]
R{"time"}max=?[ F "all_delivered" ]
// expected time for one message to be sent
Rmin=?[ F "one_delivered" ]
Rmax=?[ F "one_delivered" ]
// message of any station eventually delivered before i backoffs
Pmin=?[ F "success_with_backoff_under_1" ]
Pmax=?[ F "success_with_backoff_under_1" ]
Pmin=?[ F "success_with_backoff_under_2" ]
Pmax=?[ F "success_with_backoff_under_2" ]
Pmin=?[ F "success_with_backoff_under_3" ]
Pmax=?[ F "success_with_backoff_under_3" ]
Pmin=?[ F "success_with_backoff_under_4" ]
Pmax=?[ F "success_with_backoff_under_4" ]
Pmin=?[ F "success_with_backoff_under_5" ]
Pmax=?[ F "success_with_backoff_under_5" ]
Pmin=?[ F "success_with_backoff_under_6" ]
Pmax=?[ F "success_with_backoff_under_6" ]
// probability all sent successfully before a collision with max backoff
Pmin=?[ !"collision_max_backoff" U "all_delivered" ]
Pmax=?[ !"collision_max_backoff" U "all_delivered" ]
// probability a station suffers i collisions
Pmin=?[ F "collisions_equal_1" ]
Pmax=?[ F "collisions_equal_1" ]
Pmin=?[ F "collisions_equal_2" ]
Pmax=?[ F "collisions_equal_2" ]
Pmin=?[ F "collisions_equal_3" ]
Pmax=?[ F "collisions_equal_3" ]
Pmin=?[ F "collisions_equal_4" ]
Pmax=?[ F "collisions_equal_4" ]
Pmin=?[ F "collisions_equal_5" ]
Pmax=?[ F "collisions_equal_5" ]
Pmin=?[ F "collisions_equal_6" ]
Pmax=?[ F "collisions_equal_6" ]
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