// 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=4; // 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