Note: A* means the powerset of set A.
| Model Acronym | State Space
S | Event Set
E | Time Set
T | Initialization-Function
s(0) = b | Clock-Function
c : S x E -> T | Transition-Function
d : S x E -> S |
| GSMP+SE | Countable | Finite | Uncountable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is arbitrarily distributed. | d : S x E* -> S*, since simultaneous events may occur, i.e., P(d(s1, {e}) = s2) = P(s1, {e}, s2). |
| GSMP-SE | Countable | Finite | Uncountable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is arbitrarily distributed. | d : S x E -> S*, since for a given state and event, several next states are possible, i.e., P(d(s1, e) = s2) = P(s1, e, s2). |
| SMP | Countable | Finite | Uncountable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is arbitrarily distributed. | P(d(s1, e) = s2) = P(s1, s2) where P is the transition probability matrix. This requires that the combination of s1 and s2 uniquely determines e. |
| QN | Countable (vector of place occupancies) | Finite | Uncountable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is arbitrarily distributed. | P(d(s1, e) = s2) = P(s1, s2) where P is the transition probability matrix. This requires that the combination of s1 and s2 uniquely determines e. |
| CTMC | Countable | Finite | Uncountable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is exponentially distributed. | P(d(s1, e) = s2) = P(s1, s2). |
| DTMC | Countable | Finite | Countable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is geometrically distributed. | P(d(s1, e) = s2) = P(s1, s2). |
| STA | Countable | Finite { symbols in alphabet } | Uncountable | P(s(0) = k) in [0, 1] | c(s, e) = t + f(e) where s = the current state, e is the next symbol in the input stream and f(e) is arbitrarily distributed. | P(d(s1, e) = s2) = P(s1, s2). |
| TA | Finite | Finite { symbols in alphabet } | Uncountable | s(0) = k for one k in S | c(s, e) = t + f(e) where s = the current state, e is the next symbol in the input stream and f(e) is deterministic. | d(s, e) = M[s, e] where M is the transition matrix. |
| DFA | Finite | Finite { symbols in alphabet } | Finite {1,..., n} where n is the number of symbols in the input | s(0) = k for one k in S | c(s, e) = t + 1 where s = the current state and e is the next symbol in the input stream. | d(s, e) = M[s, e]. |
| EG | Uncountable | Finite | Uncountable | s(0) = k for one k in S | c(s, e) = t + f(e) where s = the current state, e is a candidate next event and f(e) is arbitrarily distributed. | d : S x E -> S* |