|
|
// IPv4: PTA model with digitial clocks// multi-objective model of the host// gxn/dxp 28/09/09
mdp
//-------------------------------------------------------------// VARIABLESconst int N=20; // number of abstract hostsconst int K=4; // number of probes to send
// PROBABILITIESconst double old = N/65024; // probability pick an ip address being used//const double old = 0.5; // probability pick an ip address being usedconst double new = (1-old); // probability pick a new ip address
// TIMING CONSTANTSconst int CONSEC = 2; // time interval between sending consecutive probles const int TRANSTIME = 1; // upper bound on transmission time delayconst int LONGWAIT = 60; // minimum time delay after a high number of address collisionsconst int DEFEND = 10;
const int TIME_MAX_X = 60; // max value of clock xconst int TIME_MAX_Y = 10; // max value of clock yconst int TIME_MAX_Z = 1; // max value of clock z
// OTHER CONSTANTSconst int MAXCOLL = 10; // maximum number of collisions before long waitconst int M=1; // time between sending and receiving a message
//-------------------------------------------------------------// CONCRETE HOSTmodule host0 x : [0..TIME_MAX_X]; // first clock of the host y : [0..TIME_MAX_Y]; // second clock of the host coll : [0..MAXCOLL]; // number of address collisions probes : [0..K]; // counter (number of probes sent) mess : [0..1]; // need to send a message or not defend : [0..1]; // defend (if =1, try to defend IP address) ip : [1..2]; // ip address (1 - in use & 2 - fresh) l : [0..4] init 1; // location // 0 : RECONFIGURE // 1 : RANDOM // 2 : WAITSP // 3 : WAITSG // 4 : USE // RECONFIGURE [reset] l=0 -> (l'=1); // RANDOM (choose IP address) [rec0] (l=1) -> true; // get message (ignore since have no ip address) [rec1] (l=1) -> true; // get message (ignore since have no ip address) // small number of collisions (choose straight away) [] l=1 & coll<MAXCOLL -> 1/3*old : (l'=2) & (ip'=1) & (x'=0) + 1/3*old : (l'=2) & (ip'=1) & (x'=1) + 1/3*old : (l'=2) & (ip'=1) & (x'=2) + 1/3*new : (l'=2) & (ip'=2) & (x'=0) + 1/3*new : (l'=2) & (ip'=2) & (x'=1) + 1/3*new : (l'=2) & (ip'=2) & (x'=2); // large number of collisions: (wait for LONGWAIT) [time] l=1 & coll=MAXCOLL & x<LONGWAIT -> (x'=min(x+1,TIME_MAX_X)); [] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0) + 1/3*old : (l'=2) & (ip'=1) & (x'=1) + 1/3*old : (l'=2) & (ip'=1) & (x'=2) + 1/3*new : (l'=2) & (ip'=2) & (x'=0) + 1/3*new : (l'=2) & (ip'=2) & (x'=1) + 1/3*new : (l'=2) & (ip'=2) & (x'=2); // WAITSP // let time pass [time] l=2 & x<2 -> (x'=min(x+1,2)); // send probe [send1] l=2 & ip=1 & x=2 & probes<K -> (x'=0) & (probes'=probes+1); [send2] l=2 & ip=2 & x=2 & probes<K -> (x'=0) & (probes'=probes+1); // sent K probes and waited 2 seconds [] l=2 & x=2 & probes=K -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0); // get message and ip does not match: ignore [rec0] l=2 & ip!=0 -> (l'=l); [rec1] l=2 & ip!=1 -> (l'=l); // get a message with matching ip: reconfigure [rec1] l=2 & ip=1 -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0); // WAITSG (sends two gratuitious arp probes) // time passage [time] l=3 & mess=0 & defend=0 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)); [time] l=3 & mess=0 & defend=1 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)) & (y'=min(y+1,DEFEND)); // receive message and same ip: defend [rec1] l=3 & mess=0 & ip=1 & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); // receive message and same ip: defer [rec1] l=3 & mess=0 & ip=1 & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); // receive message and different ip [rec0] l=3 & mess=0 & ip!=0 -> (l'=l); [rec1] l=3 & mess=0 & ip!=1 -> (l'=l); // send probe reply or message for defence [send1] l=3 & ip=1 & mess=1 -> (mess'=0); [send2] l=3 & ip=2 & mess=1 -> (mess'=0); // send first gratuitous arp message [send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1); [send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1); // send second gratuitous arp message (move to use) [send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); [send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0); // USE (only interested in reaching this state so do not need to add anything here) [] l=4 -> true; endmodule
//-------------------------------------------------------------// error automaton for the environment assumption// do not get a reply when K probes are sent
module env_error4
env : [0..1]; // 0 active and 1 done k : [0..4]; // counts the number of messages sent c1 : [0..M+1]; // time since first message c2 : [0..M+1]; // time since second message c3 : [0..M+1]; // time since third message c4 : [0..M+1]; // time since fourth message error : [0..1];
// message with new ip address arrives so done [send2] error=0 & env=0 -> (env'=1); // message with old ip address arrives so count [send1] error=0 & env=0 -> (k'=min(k+1,K)); // time passgae so update relevant clocks [time] error=0 & env=0 & k=0 -> true; [time] error=0 & env=0 & k=1 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)); [time] error=0 & env=0 & k=2 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)); [time] error=0 & env=0 & k=3 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)) & (c3'=min(c3+1,M+1)); [time] error=0 & env=0 & k=4 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)) & (c3'=min(c3+1,M+1)) & (c4'=min(c4+1,M+1)); // all clocks reached their bound so an error [time] error=0 & env=0 & min(c1,c2,c3,c4)=M -> (error'=1); // send a reply (then done) [rec1] error=0 & env=0 & k>0 & min(c1,c2,c3,c4)<=M -> (env'=1); // finished so any action can be performed [time] error=1 | env=1 -> true; [send1] error=1 | env=1 -> true; [send2] error=1 | env=1 -> true; [send2] error=1 | env=1 -> true; [rec1] error=1 | env=1 -> true;
endmodule
|
