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// WLAN PROTOCOL (two stations)// discrete time model// gxn/jzs 20/02/02
mdp
// COLLISIONSconst int COL; // maximum number of collisions
// TIMING CONSTRAINTS// we have used the FHSS parameters// then scaled by the value of ASLOTTIMEconst int ASLOTTIME = 1;const int DIFS = 3; // due to scaling can be either 2 or 3 which is modelled by a non-deterministic choiceconst int VULN = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choiceconst int TRANS_TIME_MAX; // scaling upconst int TRANS_TIME_MIN = 4; // scaling downconst int ACK_TO = 6; const int ACK = 4; // due to scaling can be either 3 or 4 which is modelled by a non-deterministic choiceconst int SIFS = 1; // due to scaling can be either 0 or 1 which is modelled by a non-deterministic choice// maximum constant used in timing constraints + 1const int TIME_MAX = max(ACK_TO,TRANS_TIME_MAX)+1;
// CONTENTION WINDOW// CWMIN =15 & CWMAX =511// this means that MAX_BACKOFF IS 5const int MAX_BACKOFF = 5;
//-----------------------------------------------------------------//// THE MEDIUM/CHANNEL
// FORMULAE FOR THE CHANNEL// channel is busyformula busy = c1>0 | c2>0;// channel is freeformula free = c1=0 & c2=0;
module medium // number of collisions col : [0..COL]; // medium status c1 : [0..2]; c2 : [0..2]; // ci corresponds to messages associated with station i // 0 nothing being sent // 1 being sent correctly // 2 being sent garbled // begin sending message and nothing else currently being sent [send1] c1=0 & c2=0 -> (c1'=1); [send2] c2=0 & c1=0 -> (c2'=1); // begin sending message and something is already being sent // in this case both messages become garbled [send1] c1=0 & c2>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL)); [send2] c2=0 & c1>0 -> (c1'=2) & (c2'=2) & (col'=min(col+1,COL)); // finish sending message [finish1] c1>0 -> (c1'=0); [finish2] c2>0 -> (c2'=0);
endmodule
//-----------------------------------------------------------------//// STATION 1module station1 // clock for station 1 x1 : [0..TIME_MAX]; // local state s1 : [1..12]; // 1 sense // 2 wait until free before setting backoff // 3 wait for DIFS then set slot // 4 set backoff // 5 backoff // 6 wait until free in backoff // 7 wait for DIFS then resume backoff // 8 vulnerable // 9 transmit // 11 wait for SIFS and then ACK // 10 wait for ACT_TO // 12 done // BACKOFF // separate into slots slot1 : [0..31]; backoff1 : [0..15]; // BACKOFF COUNTER bc1 : [0..MAX_BACKOFF]; // SENSE // let time pass [time] s1=1 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX)); // ready to transmit [] s1=1 & (x1=DIFS | x1=DIFS-1) -> (s1'=8) & (x1'=0); // found channel busy so wait until free [] s1=1 & busy -> (s1'=2) & (x1'=0); // WAIT UNTIL FREE BEFORE SETTING BACKOFF // let time pass (no need for the clock x1 to change) [time] s1=2 & busy -> (s1'=2); // find that channel is free so check its free for DIFS before setting backoff [] s1=2 & free -> (s1'=3); // WAIT FOR DIFS THEN SET BACKOFF // let time pass [time] s1=3 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX)); // found channel busy so wait until free [] s1=3 & busy -> (s1'=2) & (x1'=0); // start backoff first uniformly choose slot // backoff counter 0 [] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=0 -> (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF)); // backoff counter 1 [] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=1 -> 1/2 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/2 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF)); // backoff counter 2 [] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=2 -> 1/4 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/4 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/4 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/4 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF)); // backoff counter 3 [] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=3 -> 1/8 : (s1'=4) & (x1'=0) & (slot1'=0) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=1) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=2) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=3) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=4) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=5) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=6) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/8 : (s1'=4) & (x1'=0) & (slot1'=7) & (bc1'=min(bc1+1,MAX_BACKOFF)); // backoff counter 4 [] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=4 -> 1/16 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/16 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF)); // backoff counter 5 [] s1=3 & (x1=DIFS | x1=DIFS-1) & bc1=5 -> 1/32 : (s1'=4) & (x1'=0) & (slot1'=0 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=1 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=2 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=3 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=4 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=5 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=6 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=7 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=8 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=9 ) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=10) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=11) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=12) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=13) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=14) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=15) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=16) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=17) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=18) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=19) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=20) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=21) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=22) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=23) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=24) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=25) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=26) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=27) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=28) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=29) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=30) & (bc1'=min(bc1+1,MAX_BACKOFF)) + 1/32 : (s1'=4) & (x1'=0) & (slot1'=31) & (bc1'=min(bc1+1,MAX_BACKOFF)); // SET BACKOFF (no time can pass) // chosen slot now set backoff [] s1=4 -> 1/16 : (s1'=5) & (backoff1'=0 ) + 1/16 : (s1'=5) & (backoff1'=1 ) + 1/16 : (s1'=5) & (backoff1'=2 ) + 1/16 : (s1'=5) & (backoff1'=3 ) + 1/16 : (s1'=5) & (backoff1'=4 ) + 1/16 : (s1'=5) & (backoff1'=5 ) + 1/16 : (s1'=5) & (backoff1'=6 ) + 1/16 : (s1'=5) & (backoff1'=7 ) + 1/16 : (s1'=5) & (backoff1'=8 ) + 1/16 : (s1'=5) & (backoff1'=9 ) + 1/16 : (s1'=5) & (backoff1'=10) + 1/16 : (s1'=5) & (backoff1'=11) + 1/16 : (s1'=5) & (backoff1'=12) + 1/16 : (s1'=5) & (backoff1'=13) + 1/16 : (s1'=5) & (backoff1'=14) + 1/16 : (s1'=5) & (backoff1'=15); // BACKOFF // let time pass [time] s1=5 & x1<ASLOTTIME & free -> (x1'=min(x1+1,TIME_MAX)); // decrement backoff [] s1=5 & x1=ASLOTTIME & backoff1>0 -> (s1'=5) & (x1'=0) & (backoff1'=backoff1-1); [] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1>0 -> (s1'=5) & (x1'=0) & (backoff1'=15) & (slot1'=slot1-1); // finish backoff [] s1=5 & x1=ASLOTTIME & backoff1=0 & slot1=0 -> (s1'=8) & (x1'=0); // found channel busy [] s1=5 & busy -> (s1'=6) & (x1'=0); // WAIT UNTIL FREE IN BACKOFF // let time pass (no need for the clock x1 to change) [time] s1=6 & busy -> (s1'=6); // find that channel is free [] s1=6 & free -> (s1'=7); // WAIT FOR DIFS THEN RESUME BACKOFF // let time pass [time] s1=7 & x1<DIFS & free -> (x1'=min(x1+1,TIME_MAX)); // resume backoff (start again from previous backoff) [] s1=7 & (x1=DIFS | x1=DIFS-1) -> (s1'=5) & (x1'=0); // found channel busy [] s1=7 & busy -> (s1'=6) & (x1'=0); // VULNERABLE // let time pass [time] s1=8 & x1<VULN -> (x1'=min(x1+1,TIME_MAX)); // move to transmit [send1] s1=8 & (x1=VULN | x1=VULN-1) -> (s1'=9) & (x1'=0); // TRANSMIT // let time pass [time] s1=9 & x1<TRANS_TIME_MAX -> (x1'=min(x1+1,TIME_MAX)); // finish transmission successful [finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=1 -> (s1'=10) & (x1'=0); // finish transmission garbled [finish1] s1=9 & x1>=TRANS_TIME_MIN & c1=2 -> (s1'=11) & (x1'=0); // WAIT FOR SIFS THEN WAIT FOR ACK // WAIT FOR SIFS i.e. c1=0 // check channel and busy: go into backoff [] s1=10 & c1=0 & x1=0 & busy -> (s1'=2); // check channel and free: let time pass [time] s1=10 & c1=0 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX)); // let time pass // following guard is always false as SIFS=1 // [time] s1=10 & c1=0 & x1>0 & x1<SIFS -> (x1'=min(x1+1,TIME_MAX)); // ack is sent after SIFS (since SIFS-1=0 add condition that channel is free) [send1] s1=10 & c1=0 & (x1=SIFS | (x1=SIFS-1 & free)) -> (s1'=10) & (x1'=0); // WAIT FOR ACK i.e. c1=1 // let time pass [time] s1=10 & c1=1 & x1<ACK -> (x1'=min(x1+1,TIME_MAX)); // get acknowledgement so packet sent correctly and move to done [finish1] s1=10 & c1=1 & (x1=ACK | x1=ACK-1) -> (s1'=12) & (x1'=0) & (bc1'=0); // WAIT FOR ACK_TO // check channel and busy: go into backoff [] s1=11 & x1=0 & busy -> (s1'=2); // check channel and free: let time pass [time] s1=11 & x1=0 & free -> (x1'=min(x1+1,TIME_MAX)); // let time pass [time] s1=11 & x1>0 & x1<ACK_TO -> (x1'=min(x1+1,TIME_MAX)); // no acknowledgement (go to backoff waiting DIFS first) [] s1=11 & x1=ACK_TO -> (s1'=3) & (x1'=0); // DONE [time] s1=12 -> (s1'=12);endmodule
// ---------------------------------------------------------------------------- //// STATION 2 (rename STATION 1)module station2=station1[x1=x2, s1=s2, s2=s1, c1=c2, c2=c1, slot1=slot2, backoff1=backoff2, bc1=bc2, send1=send2, finish1=finish2] endmodule// ---------------------------------------------------------------------------- //
label "twoCollisions" = col=2;label "fourCollisions" = col=4;label "sixCollisions" = col=6;
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