Digital Twin Placement for Minimum Application Request Delay With Data Age Targets

Abstract

Digital twins (DTs) are virtual implementations of physical systems (PSs) and can represent the states of the PSs in realtime. In order to update the DTs with changes in their corresponding PSs, the PSs should regularly send their state information data to the DTs. Each DT must be assigned to an execution server (ES) that processes the forwarded data from its corresponding PS. The output is then made available to applications that are operating at an Internet cloud server. In this article, we consider the problem of DT placement such that the maximum data request–response delay experienced by the application over all PSs is minimized, subject to maximum data age target constraints at the DTs and the application server. The problem is first formulated as an integer quadratic program (IQP) and then transformed into a semidefinite program (SDP). The problem is NP-complete. Since exact polynomial solutions are unavailable, several practical polynomial-time approximation algorithms are introduced. The algorithms are designed to give solutions with different tradeoffs between the accommodation of the application input timing latency and the achievement of data age targets.