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							11 KiB
						
					
					
				| // 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; // 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
 |