Anycast is a new communication service defined in IPv6 (Internet Protocol Version 6) [6]. An anycast message is the one that should be delivered to the 'nearest' member in a group of designated recipients. The ¡¥nearest¡¦ is not always the ¡¥best¡¦ member. In this paper, we propose a routing protocol for anycast message. It is composed of two subprotocols: the routing table establishment subprotocol and the packet forwarding subprotocol. In the routing table establishment subprotocol, we propose a mininum delay path method (MDP). We get a minimum delay path from router to destination by MDP. In the packet forwarding protocol, we propose a minimum delay and load balancing method (MDLB). We dispatch traffic load to a server with minimum delay and light load by MDLB. The performance has demonstrated the benefits of MDP and MDLB in reducing end-to-end delay and increasing throughput of network.

Dynamic Huffman compression algorithms operate on data-streams with a bounded symbol list. With these algorithms, the complete list of symbols must be contained in main memory or secondary storage. A horizontal format transaction database that is streaming can have a very large item list. Many nodes tax both the processing hardware primary memory size, and the processing time to dynamically maintain the tree. This research investigated Huffman compression of a transaction-streaming database with a very large symbol list, where each item in the transaction database schema’s item list is a symbol to compress. The constraint of a large symbol list is, in this research, equivalent to the constraint of a memory-limited machine. A large symbol set will result if each item in a large database item list is a symbol to compress in a database stream. In addition, database streams may have some temporal component spanning months or years. Finally, the horizontal format is the format most suited to a streaming transaction database because the transaction IDs are not known beforehand This research prototypes an algorithm that will compresses a transaction database stream. There are several advantages to the memory limited dynamic Huffman algorithm. Dynamic Huffman algorithms are single pass algorithms. In many instances a second pass over the data is not possible, such as with streaming databases. Previous dynamic Huffman algorithms are not memory limited, they are asymptotic to O(n), where n is the number of distinct item IDs. Memory is required to grow to fit the n items. The improvement of the new memory limited Dynamic Huffman algorithm is that it would have an O(k) asymptotic memory requirement; where k is the maximum number of nodes in the Huffman tree, k < n, and k is a user chosen constant. The new memory limited Dynamic Huffman algorithm compresses horizontally encoded transaction databases that do not contain long runs of 0’s or 1’s.

Digital Twins (DTs) are software representations of physical systems (PSs) that interact with other entities on behalf of their real-world counterparts. To ensure accurate representation and effective interaction, DTs must remain synchronized with their PSs through timely updates—a process known as DT synchronization. This thesis addresses key challenges related to DT synchronization to optimize performance metrics, including the synchronization period and Age of Information (AoI). In the first part, we address the challenge of optimally placing DTs on execution servers (ESs) to minimize both the data request-response delay experienced by applications and the synchronization period between PSs and their DTs, while satisfying communication and computation constraints. We formulate the DT placement problem in two ways. First, we model it as an integer quadratic program (IQP) aiming to minimize the maximum application response delay subject to maximum data age target constraints at the DTs and the application server. Due to the NP-completeness of the problem, we develop practical polynomial-time approximation algorithms that offer trade-offs between application latency and data age targets. Second, we tackle the Minimum Synchronization Period (MSP) problem by modeling it as a multi-commodity quickest flow evacuation problem, considering synchronization data and processing tasks as network flows with flow dependent edge delays. This innovative approach allows us to use well-established techniques from flow network theory to efficiently find the quickest flow solution. An unsplittable flow rounding procedure ensures that each DT is assigned to a single ES. Simulation results demonstrate the effectiveness of our proposed algorithms in both methods, compared to optimal solutions serving as lower bounds. In the second part, we address DT migration in vehicular systems, where maintaining acceptable AoI is challenging due to high mobility and frequent handoffs between cellular domains. We formulate the optimal initiation time for migrating a vehicle's DT as a Markov decision process, aiming to minimize the time-averaged AoI at the DT. An online optimal migration initiation algorithm is proposed using dynamic programming and optimal stopping problem. We also develop a more computationally intensive adaptive version of this algorithm, which recalculates the decision policy at each time step for improved performance. Additionally, we introduce a best-in-expectation algorithm that offers a balance between computational efficiency and AoI performance. These algorithms are compared with heuristic approaches, such as immediate migration and migration at handoff, as well as an offline algorithm providing a theoretical lower bound on the average AoI. Performance evaluations show that our proposed algorithms significantly enhance the efficiency of DT migrations while minimizing the time-averaged AoI compared to other methods. / Dissertation / Candidate in Philosophy / Digital Twins (DTs) are virtual replicas of real-world Physical Systems (PSs), such as mobile devices, vehicles, or smart cities. These digital counterparts are hosted by network servers. They mirror the state and behavior of their physical versions in real time, allowing them to interact with other devices or applications on behalf of their PSs. For a DT to effectively mirror and reflect any changes in its PS, it must consistently remain synchronized through timely updates, which consume the network resources. As a result, the placement of DTs on network servers affects the quality of the DTs. The problem becomes challenging when placing the DTs of a large number of PSs, and is further complicated when the PSs are mobile. This thesis tackles some key challenges towards optimal DT placements. \begin{enumerate} \item Optimizing Synchronization Timing and Placement: We investigate how to optimally place DTs within the network infrastructure to minimize synchronization delay. To achieve this, we develop algorithms that efficiently assign DTs to servers, balancing the need for timely updates, quick application responses, and the amount of network resources. \item Enhancing DT Migration in Vehicular Systems: Vehicles are constantly on the move. Therefor, the PS-DT synchronization delay varies with the PS locations, and at some point, it is better to migrate the DT to a different server. We develop algorithms that decide when to initiate the migration to minimize costs associated with the migration.