Quantitative assessment methods and measures of logistic synchronization

Vladimir Tregubov

Abstract


Synchronization covers a wide range of phenomena in different spheres, but there is not a single standard approach to its measure and each sphere requires additional research for development of various indicators for reflecting the degree of synchronization between interacting subsystems. The article discusses different approaches to estimating the degree of synchronization in logistics processes. We presented some different methods of synchronization indicators based on different ideas about measure it.

The first method is a cross-correlation which uses synchronization as a coordinated, consistent occurrence of events. External influence creates strong links and lead to fast synchronization in logistics process, and the degree of cross-correlation reflects a degree of synchronization between the elements of the logistic process. If there are weak links, a spectral analysis can be used for estimation the capture of the base frequency a subsystem by the base frequency of the second subsystem. This is manifested through clock synchronization, and in terms of dynamics it is represented as an instantaneous phase capture of cyclic process by an instantaneous phase of the second one.  For quantitative estimation is proposed a coherence function which can have values in the range from zero to one, while zero is for those frequencies when the phases of the two signals in all cases take independent values. Then it is necessary to normalize the full spectral power of the process. this allows to obtain a generalized quantitative characteristic of synchronization for all processes.  We also proposed to use the quantity of information for quantitative evaluation of synchronization in logistics. This approach is based on the analysis of information links, which determine the possibility to determine the state of the first subsystem by the state of the second subsystems. If the state of the first subsystem unambiguously determines by the second one, we can say about their full synchronization and the degree of synchronization is equal to one. On the other hand, when the state of one of the subsystems weakly affects the state of the second one, it indicates a low synchronization.


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References


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