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.
139 lines
4.8 KiB
139 lines
4.8 KiB
// CSMA/CD protocol - probabilistic version of kronos model adapted to model a single station
|
|
// gxn/dxp 04/12/01
|
|
|
|
pta
|
|
|
|
// note made changes since cannot have strict inequalities
|
|
// in digital clocks approach and suppose a station only sends one message
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
// actual parameters
|
|
const int bmax; // exponential backoff limit
|
|
const int slot=2*sigma; // length of slot
|
|
const int sigma=26;
|
|
const int lambda=808;
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
// the bus
|
|
module bus
|
|
|
|
b : [0..2];
|
|
// b=0 - idle
|
|
// b=1 - active
|
|
// b=2 - collision
|
|
|
|
// clock of bus
|
|
y : clock;
|
|
|
|
invariant
|
|
(b=0 => true) &
|
|
(b=1 => true) &
|
|
(b=2 => y<=sigma)
|
|
endinvariant
|
|
|
|
// station starts sending
|
|
[send1] (b=0) -> (b'=1) & (y'=0); // no message being sent
|
|
[send2] (b=0) -> (b'=1) & (y'=0); // no message being sent
|
|
|
|
[send1] (b=1) & (y<sigma) -> (b'=2) & (y'=0); // message being sent (move to collision)
|
|
[send2] (b=1) & (y<sigma) -> (b'=2) & (y'=0); // message being sent (move to collision)
|
|
|
|
// message being sent
|
|
[busy1] (b=1) & (y>=sigma) -> (b'=1);
|
|
[busy2] (b=1) & (y>=sigma) -> (b'=1);
|
|
|
|
// station finishes
|
|
[end1] (b=1) -> (b'=0) & (y'=0);
|
|
[end2] (b=1) -> (b'=0) & (y'=0);
|
|
|
|
// collision detected
|
|
[cd] (b=2) & (y<=sigma) -> (b'=0) & (y'=0);
|
|
|
|
endmodule
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
// model of first sender
|
|
module station1
|
|
|
|
// LOCAL STATE
|
|
s1 : [0..4];
|
|
// s1=0 - initial state
|
|
// s1=1 - transmit
|
|
// s1=2 - collision (set backoff)
|
|
// s1=3 - wait (bus busy)
|
|
// s1=4 -done (since sending only one message)
|
|
// LOCAL CLOCK
|
|
x1 : clock;
|
|
// COLLISION COUNTER
|
|
cd1 : [0..bmax];
|
|
|
|
invariant
|
|
(s1=0 => x1=0) &
|
|
(s1=1 => x1<=lambda) &
|
|
(s1=2 => x1=0) &
|
|
(s1=3 => x1<=pow(2, cd1)*slot) &
|
|
(s1=4 => true)
|
|
endinvariant
|
|
|
|
// start sending
|
|
[send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending
|
|
[busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // detects channel is busy so go into backoff
|
|
|
|
// transmitting
|
|
[end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished
|
|
[cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // collision detected
|
|
|
|
// set backoff (no time can pass in this state)
|
|
// first retransmission
|
|
[] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (x1'=0*slot)
|
|
+ 1/2 : (s1'=3) & (x1'=1*slot);
|
|
// second retransmission
|
|
[] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (x1'=0*slot)
|
|
+ 1/4 : (s1'=3) & (x1'=1*slot)
|
|
+ 1/4 : (s1'=3) & (x1'=2*slot)
|
|
+ 1/4 : (s1'=3) & (x1'=3*slot);
|
|
// thrid retransmission
|
|
[] s1=2 & cd1=3 -> 1/8 : (s1'=3) & (x1'=0*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=1*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=2*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=3*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=4*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=5*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=6*slot)
|
|
+ 1/8 : (s1'=3) & (x1'=7*slot);
|
|
// fourth retransmission
|
|
[] s1=2 & cd1=4 -> 1/16 : (s1'=3) & (x1'=0*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=1*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=2*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=3*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=4*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=5*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=6*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=7*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=8*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=9*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=10*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=11*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=12*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=13*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=14*slot)
|
|
+ 1/16 : (s1'=3) & (x1'=15*slot);
|
|
|
|
// finished backoff
|
|
[send1] (s1=3) & (x1=pow(2, cd1)*slot) -> (s1'=1) & (x1'=0); // channel free
|
|
[busy1] (s1=3) & (x1=pow(2, cd1)*slot) -> (s1'=2) & (x1'=0) & (cd1'=min(bmax,cd1+1)); // channel busy
|
|
|
|
// once finished nothing matters
|
|
[done] (s1=4) -> true;
|
|
|
|
endmodule
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
|
|
// construct further stations through renaming
|
|
module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule
|
|
|
|
//----------------------------------------------------------------------------------------------------------------------------
|
|
// LABELS
|
|
|
|
label "done" = s1=4 & s2=4;
|