Robotics and Automation in Construction 2012 Part 6

Tham khảo tài liệu 'robotics and automation in construction 2012 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Risk and Reliability Analysis of Flexible Construction Robotized Systems 143 completion of t tn - nth completed timed transition Mn - Stable marking reached at the firing of tn Sn - Completion time of tn Tn - Holding time of marking Mn-1 V t n - Number of instances of t among t1 . tn. The dynamic behaviour of an SPN can be explained in the following way at the initial marking Mo set rn t X t 1 V t e Tt M0 and set V t 0 0 V t e Tt. All other parameters tn 1 Tn 1 sn 1 V t n 1 Mn 1 rn 1 can be determined recursively as usually done in discrete event simulation. Recursive equations are given in Zhou Twiss 1998 . The following routing mechanism is used in GSMP Mn 1 0 Mn tn 1 U tn 1 V tn 1 n 1 4 Where 0 is a mapping so that P 0 M t U M P M M t . Following the approach given in Hopkins 2002 we suppose that the distributions of firing times depend on a parameter 0. In perturbation analysis the following results hold Watson Desrochers 1994 where the performance measures under consideration are of the form g M1 t1 T1 . Mn tn in and a shorthand notation g 0 is used a For each 0 g 0 is . continuously differentiable at 0 and the infinitesimal perturbation indicator is dg 9 y gg . dr de ỔT de 1 1 1 b If d e g 0 d0 exists the following perturbation estimator is unbiased ÈO ẳfl 1 l Gl 6 1 1 1 k 1 f ftk 1 Lk tk 1 _ 7 k Ftk 1 Lk tk 1 yk _ Ftk 1 Lk tk 1 yk min rk t Vt e T Mk - tk 1 8 Tk dLk tk 1 _ dx tk 1 9 Lk t is the age of time transition t at Sk Gk gpp k - gDNP k. The sample path M1 0 t1 0 T1 0 . . Mn 0 tn 0 Tn 0 is the nominal path denoted by NP. The gDNP k is the performance measure of the kth degenerated nominal path denoted by DNPk. It is identical to NP except for the sojourn time of the k 1 th stable marking in DNPk. gpp k is the performance measure of a so-called kth perturbed path denoted by PPk. It is identical to DNPk up to time sk. At this instant the order of transition tk and tk 1 is reversed . the firing of tk 1 completes just before that of tk in

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