You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
132 lines
5.3 KiB
132 lines
5.3 KiB
// CSMA/CD protocol - probabilistic version of kronos model (3 stations)
|
|
// gxn/dxp 04/12/01
|
|
|
|
mdp
|
|
|
|
// note made changes since cannot have strict inequalities
|
|
// in digital clocks approach and suppose a station only sends one message
|
|
|
|
// simplified parameters scaled
|
|
const int sigma=1; // time for messages to propagate along the bus
|
|
const int lambda=30; // time to send a message
|
|
|
|
// actual parameters
|
|
const int N = 3; // number of processes
|
|
const int K = 4; // exponential backoff limit
|
|
const int slot = 2*sigma; // length of slot
|
|
const int M = 15; // max number of slots to wait
|
|
//const int lambda=782;
|
|
//const int sigma=26;
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
// the bus
|
|
module bus
|
|
|
|
b : [0..2];
|
|
// b=0 - idle
|
|
// b=1 - active
|
|
// b=2 - collision
|
|
|
|
// clocks of bus
|
|
y1 : [0..sigma+1]; // time since first send (used find time until channel sensed busy)
|
|
y2 : [0..sigma+1]; // time since second send (used to find time until collision detected)
|
|
|
|
// a sender sends (ok - no other message being sent)
|
|
[send1] (b=0) -> (b'=1);
|
|
[send2] (b=0) -> (b'=1);
|
|
[send3] (b=0) -> (b'=1);
|
|
|
|
// a sender sends (bus busy - collision)
|
|
[send1] (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);
|
|
|
|
// finish sending
|
|
[end1] (b=1) -> (b'=0) & (y1'=0);
|
|
[end2] (b=1) -> (b'=0) & (y1'=0);
|
|
[end3] (b=1) -> (b'=0) & (y1'=0);
|
|
|
|
// bus busy
|
|
[busy1] (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);
|
|
|
|
// collision detected
|
|
[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0);
|
|
|
|
// time passage
|
|
[time] (b=0) -> (y1'=0); // value of y1/y2 does not matter in state 0
|
|
[time] (b=1) -> (y1'=min(y1+1,sigma+1)); // no invariant in state 1
|
|
[time] (b=2) & (y2<sigma) -> (y1'=min(y1+1,sigma+1)) & (y2'=min(y2+1,sigma+1)); // invariant in state 2 (time until collision detected)
|
|
|
|
endmodule
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
// model of first sender
|
|
module station1
|
|
|
|
// LOCAL STATE
|
|
s1 : [0..5];
|
|
// s1=0 - initial state
|
|
// s1=1 - transmit
|
|
// s1=2 - collision (set backoff)
|
|
// s1=3 - wait (bus busy)
|
|
// s1=4 - successfully sent
|
|
|
|
// LOCAL CLOCK
|
|
x1 : [0..max(lambda,slot)];
|
|
|
|
// BACKOFF COUNTER (number of slots to wait)
|
|
bc1 : [0..M];
|
|
|
|
// COLLISION COUNTER
|
|
cd1 : [0..K];
|
|
|
|
// start sending
|
|
[send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending
|
|
[busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff
|
|
|
|
// transmitting
|
|
[time] (s1=1) & (x1<lambda) -> (x1'=min(x1+1,lambda)); // let time pass
|
|
[end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished
|
|
[cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected (increment backoff counter)
|
|
[cd] !(s1=1) -> (s1'=s1); // add loop for collision detection when not important
|
|
|
|
// set backoff (no time can pass in this state)
|
|
// 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=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
|
|
[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot)
|
|
[time] (s1=3) & (x1=slot) & (bc1>0) -> (x1'=1) & (bc1'=bc1-1); // let time pass (move slots)
|
|
[send1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=1) & (x1'=0); // finished backoff (bus appears free)
|
|
[busy1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // finished backoff (bus busy)
|
|
|
|
// once finished nothing matters
|
|
[time] (s1>=4) -> (x1'=0);
|
|
|
|
endmodule
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
|
|
// construct further stations through renaming
|
|
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
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
|
|
// reward structure for expected time
|
|
rewards "time"
|
|
[time] true : 1;
|
|
endrewards
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
|
|
// labels/formulae
|
|
label "all_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);
|
|
|