Placement of Social Digital Twins at the Edge for Beyond 5G IoT Networks

As the fifth-generation (5G) and beyond (5G+/6G) networks move forward, and a wide variety of new advanced Internet of Things (IoT) applications are offered, effective methodologies for discovering time-relevant information, services, and resources are being demanded. To this end, computing-, storage-, and battery-constrained IoT devices are progressively augmented via digital twins (DTs) hosted on edge servers. According to recent research results, a further feature these devices may acquire is social behavior; this latter offers enormous possibilities for fast and trustworthy service discovery, although it requires new orchestration policies of DTs at the network edge. This work addresses the dynamic placement of DTs with social capabilities (Social Digital Twins, SDTs) at the edge, by providing an optimal solution under IoT device mobility and by accounting for edge network deployment specifics, types of devices, and their social peculiarities. The optimization problem is formulated as a particular case of the quadratic assignment problem (QAP); also, an approximation algorithm is proposed and two relaxation techniques are applied to reduce computation complexity. Results show that the proposed placement policy ensures a latency among SDTs up to 1.4 times lower than the one obtainable with a traditional proximity-based only placement, while still guaranteeing appropriate proximity between physical devices and their virtual counterparts. Moreover, the proposed heuristic closely approximates the optimal solution while guaranteeing the lowest computational time.