Semi-Markov Processes

Description

Definition

Examples

References

 

 

 

Description:

Semi-Markov Process models are GSMP models in which event set (and thus a clock set) consists of a single entry, i.e. we can eliminate event set altogether.  Events now do not compete with each other and a single clock is measuring interevent times.

Formal Definition:

A Semi-Markov Process model is a 5-tuple

                        (X, Γ,  p, p0, F )

X – is a countable  set of states

Γ(x) – is a set of active events defined for all x ∈X, with Γ(x) a subset of E,

p(x1; x) – is a state transition probability, defined for all x, x1 ∈X, reflecting probability of going from state x to state x1.

p0(x) – is the pmf P[X0=x], x∈X, of the initial state X0.

F– is a clock distribution functions.

Examples:

References:

  1. K.Kant, Introduction to computer system performance evaluation, McGraw-Hill, 1992.