Digital Twins are softwarized mirrors of physical systems. They can represent their corresponding physical counterparts in real-world applications and reflect the behavior of the latter under different scenarios with decent accuracy. In this thesis, we consider the case where an application requests data from multiple digital twins, each representing a physical system. The digital twins are hosted on execution servers located between the application and the set of physical devices. Each digital twin has to be periodically updated by its physical system and uses a portion of the execution server’s computing resource to refresh itself. Due to the scarcity of computation resources of the execution servers, in this thesis, we have tackled the problem of optimal digital twin placement onto a limited set of execution servers. We are aiming at minimizing the latency of the digital twins’ responses to the application’s requests while keeping the age of information of served data below a certain threshold. We first formulate the problem as an integer quadratic program (IQP) and then transform it into a semidefinite program (SDP). We prove that the problem is NP-complete and propose polynomial-time approximation algorithms that solve the problem with different trade-offs between the accommodation of the application’s request latency and the achievement of data age targets. / Thesis / Master of Applied Science (MASc)

Many automotive systems are real-time systems, which means that not only correct operationsbut also appropriate timings are their main requirements. Considering the in uence that end-to-end delay might have on the performance of the systems, the calculation of it is of necessity.Abundant techniques have actually been proposed, and some of them have already been applied intopractical systems. In spite of this, some further work still needs to be done. The target of thisthesis is to evaluate and compare two end-to-end timing analysis methods from dierent aspectssuch as data age, consumption time, and then decide which method is a prior choice for end-to-end timing analysis. The experiments can be divided into three blocks, system generation andend-to-end delay calculation by two methods respectively. The experiments focus on two kinds ofperformance parameters, data age and the consumption time that these two methods cost duringtheir execution. By changing the system generating parameters like task number and periods, thechanges of performances of the two methods are analyzed. The performances of the two dierentmethods are also compared when they are applied into the same automotive systems. According tothe results of the experiments, the second method can calculate more accurate data age and consumeless time than the rst method does.

Many automotive systems are real-time systems, which means that not only correct operationsbut also appropriate timings are their main requirements. Considering the in uence that end-to-end delay might have on the performance of the systems, the calculation of it is of necessity.Abundant techniques have actually been proposed, and some of them have already been applied intopractical systems. In spite of this, some further work still needs to be done. The target of thisthesis is to evaluate and compare two end-to-end timing analysis methods from dierent aspectssuch as data age, consumption time, and then decide which method is a prior choice for end-to-end timing analysis. The experiments can be divided into three blocks, system generation andend-to-end delay calculation by two methods respectively. The experiments focus on two kinds ofperformance parameters, data age and the consumption time that these two methods cost duringtheir execution. By changing the system generating parameters like task number and periods, thechanges of performances of the two methods are analyzed. The performances of the two dierentmethods are also compared when they are applied into the same automotive systems. According tothe results of the experiments, the second method can calculate more accurate data age and consumeless time than the rst method does.