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// 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 // gxn/dxp/jzs 02/05/03
// model is an mdp mdp
// reset or noreset model const bool reset=false;
//-------------------------------------------------------------
// we suppose that // - the abstract hosts have already picked their addresses // and always defend their addresses // - the concrete host never picks the same ip address twice // (this can happen only with a verys small probability)
// under these assumptions we do not need message types because: // 1) since messages to the concrete host will never be a probe, // this host will react to all messages in the same way // 2) since the abstract hosts always defend their addresses, // all messages from the host will get an arp reply if the ip matches
// following from the above assumptions we require only three abstract IP addresses // (0,1 and 2) which correspond to the following sets of IP addresses:
// 0 - the IP addresses of the abstract hosts which the concrete host // previously tried to configure // 1 - an IP address of an abstract host which the concrete host is // currently trying to configure // 2 - a fresh IP address which the concrete host is currently trying to configure
// if the host picks an address that is being used it may end up picking another ip address // in which case there may still be messages corresponding to the old ip address // to be sent both from and to the host which the host should now disregard // (since it will never pick the same ip address)
// to deal with this situation: when a host picks a new ip address we reconfigure the // messages that are still be be sent or are being sent by changing the ip address to 0 // (an old ip address of the host)
// all the messages from the abstract hosts for the 'old' address (in fact the // set of old addresses since it may have started again more than once) // can arrive in any order since they are equivalent to the host - it ignores then all
// also the messages for the old and new address will come from different hosts // (the ones with that ip address) which we model by allowing them to arrive in any order // i.e. not neccessarily in the order they where sent
//-------------------------------------------------------------
//------------------------------------------------------------- // VARIABLES //const int N; // number of abstract hosts const int K=7; // number of probes to send const double loss; // probability of message loss
// PROBABILITIES const double old; //=N/65024; // 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 DEFEND = 10;
const int TIME_MAX_X = 60; // max value of clock x const int TIME_MAX_Y = 10; // max value of clock y const int TIME_MAX_Z = 1; // max value of clock z
// OTHER CONSTANTS const int MAXCOLL = 10; // maximum number of collisions before long wait // size of buffers for other hosts const int B0 = 20; // buffer size for one abstract host const int B1 = 8; // buffer sizes for all abstract hosts
//------------------------------------------------------------- // ENVIRONMENT - models: medium, output buffer of concrete host and all other hosts module environment // buffer of concrete host b_ip7 : [0..2]; // ip address of message in buffer position 8 b_ip6 : [0..2]; // ip address of message in buffer position 7 b_ip5 : [0..2]; // ip address of message in buffer position 6 b_ip4 : [0..2]; // ip address of message in buffer position 5 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..8]; // 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'=0) // message being set & (n'=(reset)?0:n) // concrete buffer (remove this update to get NO_RESET model) & (b_ip7'=0) & (b_ip6'=0) & (b_ip5'=0) & (b_ip4'=0) & (b_ip3'=0) & (b_ip2'=0) & (b_ip1'=0) & (b_ip0'=0); // note: prevent anything else from happening when reconfiguration needs to take place // time passage (only if no messages to send or sending a message) [time] l>0 & b=0 & n=0 & n0=0 & n1=0 -> (b'=b); // cannot send a message [time] l>0 & b>0 & z<1 -> (z'=min(z+1,TIME_MAX_Z)); // sending a message // get messages to be sent (so message has same ip address as host) [send] l>0 & n=0 -> (b_ip0'=ip) & (n'=n+1); [send] l>0 & n=1 -> (b_ip1'=ip) & (n'=n+1); [send] l>0 & n=2 -> (b_ip2'=ip) & (n'=n+1); [send] l>0 & n=3 -> (b_ip3'=ip) & (n'=n+1); [send] l>0 & n=4 -> (b_ip4'=ip) & (n'=n+1); [send] l>0 & n=5 -> (b_ip5'=ip) & (n'=n+1); [send] l>0 & n=6 -> (b_ip6'=ip) & (n'=n+1); [send] l>0 & n=7 -> (b_ip7'=ip) & (n'=n+1); [send] l>0 & n=8 -> (n'=n); // buffer full so lose message // start sending message from host [] l>0 & b=0 & n>0 -> (1-loss) : (b'=1) & (ip_mess'=b_ip0) & (n'=n-1) & (b_ip7'=0) & (b_ip6'=b_ip7) & (b_ip5'=b_ip6) & (b_ip4'=b_ip5) & (b_ip3'=b_ip4) & (b_ip2'=b_ip3) & (b_ip1'=b_ip2) & (b_ip0'=b_ip1) // send message + loss : (n'=n-1) & (b_ip7'=0) & (b_ip6'=b_ip7) & (b_ip5'=b_ip6) & (b_ip4'=b_ip5) & (b_ip3'=b_ip4) & (b_ip2'=b_ip3) & (b_ip1'=b_ip2) & (b_ip0'=b_ip1); // lose message // start sending message to host [] l>0 & b=0 & n0>0 -> (1-loss) : (b'=2) & (ip_mess'=0) & (n0'=n0-1) + loss : (n0'=n0-1); // different ip [] l>0 & 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 [] l>0 & b=1 & ip_mess=0 -> (b'=0) & (z'=0) & (n0'=min(n0+1,B0)) & (ip_mess'=0); [] l>0 & b=1 & ip_mess=1 -> (b'=0) & (z'=0) & (n1'=min(n1+1,B1)) & (ip_mess'=0); [] l>0 & b=1 & ip_mess=2 -> (b'=0) & (z'=0) & (ip_mess'=0); // finish sending message to host [rec] l>0 & b=2 -> (b'=0) & (z'=0) & (ip_mess'=0); endmodule
//------------------------------------------------------------- // CONCRETE HOST module 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) [rec] (l=1) -> 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 [send] l=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 [rec] l=2 & ip_mess!=ip -> (l'=l); // get a message with matching ip: reconfigure [rec] l=2 & ip_mess=ip -> (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 [rec] l=3 & mess=0 & ip_mess=ip & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0); // receive message and same ip: defer [rec] l=3 & mess=0 & ip_mess=ip & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0); // receive message and different ip [rec] l=3 & mess=0 & ip_mess!=ip -> (l'=l); // send probe reply or message for defence [send] l=3 & mess=1 -> (mess'=0); // send first gratuitous arp message [send] l=3 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1); // send second gratuitous arp message (move to use) [send] l=3 & 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 -> 1 : true; endmodule
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