No abstract

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.iii I would like to express my gratitude to my supervisors, Professors Dongmei Zhao, George Karakostas, and Terence D. Todd who guided me throughout my graduate studies. I am also grateful to Dr. Douglas Down for his valuable comments as part of the examining committee. Finally, I would also like to thank my friends and family for their love and support.