Because of the piece-wise time reliant inter-arrival time of a Cm(t)(t)/Ck/s lining up form, we can compose the transition matrix as granted in formula (4.18)
The stable state probabilities may not live because the transition rate matrix changes. Nonetheless, we would like to assessment certain mean assesses founded upon the probabilities of each state over time horizon. Letbe an assessment founded upon the state likelihood vector, and letbe the mean of the assessment over time granted by formula (4.19).
Many benchmark lining up form assesses are linear with esteem to the state likelihood vector, accordingly, it is adequate to assess the mean state likelihood vectorfor each time period and assess an mean assess with formula (4.20).
In this part, we will talk about how to calculatefor each time period. Equation (4.21) displays how to assess the state likelihood vector over time, which can be incorporated numerically utilising the numbers solver software.
At a granted time, an adequately little and represent likelihood state vectors of two distinct state spaces which lead to a important assessment complication. Consequently, we redefine by two distinct vectors. For each time let and be the state likelihood vectors at time in state spaces affiliated with time span and, respectively. We then redefineand as and to farther identify notation, as shown in formula (4.22).
An algorithm to assess the likelihood vector for each time periodis granted by the next steps.
Step 1: Let and suppose is given.
Step 2: Find and using integration.
Step 3: If, then task into the state space of time span to find and proceed to step 2.
The algorithm supposes that is granted even though such a state vector may not have existed. We implicitly presumed that might be some time very early in the forenoon before most planes ...