// IPv4: PTA model with digitial clocks // one concrete host attempting to choose an ip address // when a number of (abstract) hosts have already got ip addresses // no reset model // gxn/dxp/jzs 02/05/03 mdp // reward structure rewards "time" [time] true : 1; endrewards //------------------------------------------------------------- // VARIABLES const int N=20; // number of abstract hosts const int K; // number of probes to send const double loss = 0.1; // probability of message loss // PROBABILITIES //const double old = N/65024; // probability pick an ip address being used const double old = 1/4; // probability pick an ip address being used const double new = (1-old); // probability pick a new ip address // TIMING CONSTANTS const int CONSEC = 2; // time interval between sending consecutive probles const int TRANSTIME = 1; // upper bound on transmission time delay const int LONGWAIT = 60; // minimum time delay after a high number of address collisions const int TIME_MAX_X = 60; // max value of clock x const int TIME_MAX_Z = 1; // max value of clock z // OTHER CONSTANTS const int MAXCOLL = 10; // maximum number of collisions before long wait const int B0 = 4; // buffer size for one abstract host const int B1 = 4; // buffer sizes for all abstract hosts //------------------------------------------------------------- // ENVIRONMENT - models: medium, output buffer of concrete host and all other hosts // ENVIRONMENT - models: medium, output buffer of concrete host and all other hosts module environment // buffer of concrete host b_ip3 : [0..2]; // ip address of message in buffer position 4 b_ip2 : [0..2]; // ip address of message in buffer position 3 b_ip1 : [0..2]; // ip address of message in buffer position 2 b_ip0 : [0..2]; // ip address of message in buffer position 1 n : [0..4]; // number of places in the buffer used (from host) // messages to be sent from abstract hosts to concrete host n0 : [0..B0]; // number of messages which do not have the host's current ip address n1 : [0..B1]; // number of messages which have the host's current ip address b : [0..2]; // local state // 0 - idle // 1 - sending message from concrete host // 2 - sending message from abstract host z : [0..1]; // clock of environment (needed for the time to send a message) ip_mess : [0..2]; // ip in the current message being sent // 0 - different from concrete host // 1 - same as the concrete host and in use // 2 - same as the concrete host and not in use // RESET/RECONFIG: when host is about to choose new ip address // suppose that the host cannot choose the same ip address // (since happens with very small probability). // Therefore all messages will have a different ip address, // i.e. all n1 messages become n0 ones. // Note this include any message currently being sent (ip is set to zero 0) [reset] true -> (n1'=0) & (n0'=min(B0,n0+n1)) // abstract buffers & (ip_mess'=(ip_mess=2)?2:0) // message being set & (b_ip3'=(b_ip3=2)?2:0) & (b_ip2'=(b_ip2=2)?2:0) & (b_ip1'=(b_ip1=2)?2:0) & (b_ip0'=(b_ip0=2)?2:0); // time passage (only if no messages to send or sending a message) [time] b=0 & n=0 & n0=0 & n1=0 -> (b'=b); // cannot send a message [time] b>0 & z<1 -> (z'=min(z+1,TIME_MAX_Z)); // sending a message // get messages to be sent // message has ip address 1 [send1] n=0 -> (b_ip0'=1) & (n'=n+1); [send1] n=1 -> (b_ip1'=1) & (n'=n+1); [send1] n=2 -> (b_ip2'=1) & (n'=n+1); [send1] n=3 -> (b_ip3'=1) & (n'=n+1); [send1] n=4 -> (n'=n); // buffer full so lose message // message has ip address 2 [send2] n=0 -> (b_ip0'=2) & (n'=n+1); [send2] n=1 -> (b_ip1'=2) & (n'=n+1); [send2] n=2 -> (b_ip2'=2) & (n'=n+1); [send2] n=3 -> (b_ip3'=2) & (n'=n+1); [send2] n=4 -> (n'=n); // buffer full so lose message // start sending message from host [env] b=0 & n>0 -> (1-loss) : (b'=1) & (ip_mess'=b_ip0) & (n'=n-1) & (b_ip3'=0) & (b_ip2'=b_ip3) & (b_ip1'=b_ip2) & (b_ip0'=b_ip1) // send message + loss : (n'=n-1) & (b_ip3'=0) & (b_ip2'=b_ip3) & (b_ip1'=b_ip2) & (b_ip0'=b_ip1); // lose message // start sending message to host [env] b=0 & n0>0 -> (1-loss) : (b'=2) & (ip_mess'=0) & (n0'=n0-1) + loss : (n0'=n0-1); // different ip [env] b=0 & n1>0 -> (1-loss) : (b'=2) & (ip_mess'=1) & (n1'=n1-1) + loss : (n1'=n1-1); // same ip // finish sending message from host [env] b=1 & ip_mess=0 -> (b'=0) & (z'=0) & (n0'=min(n0+1,B0)) & (ip_mess'=0); [env] b=1 & ip_mess=1 -> (b'=0) & (z'=0) & (n1'=min(n1+1,B1)) & (ip_mess'=0); [env] b=1 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); // finish sending message to host [rec0] b=2 & ip_mess=0 -> (b'=0) & (z'=0) & (ip_mess'=0); [rec1] b=2 & ip_mess=1 -> (b'=0) & (z'=0) & (ip_mess'=0); endmodule //------------------------------------------------------------- // CONCRETE HOST module host0 x : [0..TIME_MAX_X]; // first 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 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) [host] 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)); [host] 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 [host] 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 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)); // receive message and same ip: always defer [rec1] l=3 & mess=0 & ip=1 -> (l'=0) & (probes'=0) & (x'=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) & (probes'=0); [send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (probes'=0); // USE (only interested in reaching this state so do not need to add anything here) [host] l=4 -> true; endmodule