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*
| |