可分割負載是指足夠大且依賴性較低的數據類型，使其可被視為在分散式系統中能任意分割。可分割負載理論（DLT）研究此類負載的排程以提高系統性能。在該領域中，存在著許多的挑戰，包括時變系統上的排程以及確定時不變系統上具有起始成本的多輪排程的最佳輪數。
本文研究了可分割負載排程問題的兩個方面。首先，它解決了時變系統上可分割負載的排程問題。這包括改進以前單輪排程方法的計算時間並提出多輪排程的演算法。其次，它研究在具有起始成本的時不變系統上多輪可分割負載的排程。這包含了調整先前研究的演算法以適應具有前端處理器的系統，並提出一種新的排程演算法，該演算法可進一步轉換成矩陣運算。
為了評估所提出方法的有效性，將對時變系統的兩種場景進行數據測試，並比較時不變系統上多輪排程的性能。

Divisible load refers to a type of data that is sufficiently large and exhibits low dependency, making it arbitrarily divisible across a distributed system. Divisible Load Theory (DLT) is dedicated to studying the scheduling of such loads to enhance system performance. Within this field, there are notable challenges, including scheduling on time-varying systems and determining the optimal number of rounds for multi-round scheduling with start-up cost on time-invariant systems.
This thesis delves into two aspects of the divisible load scheduling problem. Firstly, it addresses the scheduling of divisible loads on time-varying systems. This includes improving the computation time of previous single-round scheduling approaches and proposing an algorithm for multi-round scheduling. Secondly, it focuses on scheduling multi-round divisible loads on time-invariant systems with start-up cost. To achieve this, the thesis aims to adapt the algorithm from previous research to accommodate systems with front-end processors and introduces a novel algorithm for scheduling, which can be further optimized through matrix operations.
To assess the effectiveness of the proposed methods, numerical tests will be conducted for two scenarios on time-varying systems and for comparing the performance of multi-round scheduling on time-invariant systems.

[1] Veeravalli Bharadwaj, Debasish Ghose, and V Mani. Multi-installment load distribution in tree networks with delays. IEEE Transactions on Aerospace and Electronic Systems, 31(2):555–567, 1995.
[2] Jacek B la˙zewicz and Maciej Drozdowski. Scheduling divisible jobs on hypercubes. Parallel computing, 21(12):1945–1956, 1995.
[3] Jacek B la˙zewicz, Maciej Drozdowski, Fr´ed´eric, and Denis Trystram. Scheduling a divisible task in a two-dimensional toroidal mesh. Discrete Applied Mathematics, 94(1-3):35–50, 1999.
[4] Yuan-Chieh Cheng and Thomas G Robertazzi. Distributed computation with communication delay (distributed intelligent sensor networks). IEEE transactions on aerospace and electronic systems, 24(6):700–712, 1988.
[5] Thomas E Carroll and Daniel Grosu. An incentive-based distributed mechanism for scheduling divisible loads in tree networks. Journal of Parallel and Distributed Computing, 72(3):389–401, 2012.
[6] Maciej Drozdowski and W lodzimierz G lazek. Scheduling divisible loads in a three-dimensional mesh of processors. Parallel Computing, 25(4):381–404, 1999.
[7] Maciej Drozdowski and Marcin Lawenda. Multi-installment divisible load processing in heterogeneous systems with limited memory. In Parallel Processing and Applied Mathematics: 6th International Conference, PPAM 2005, Pozna´n, Poland, September 11-14, 2005, Revised Selected Papers 6, pages 847–854. Springer, 2006.
[8] Keqin Li. Scheduling divisible tasks on heterogeneous linear arrays with applications to layered networks. In Parallel and Distributed Processing Symposium, International, volume 3, pages 0237b–0237b. IEEE Computer Society, 2002.
[9] Keqin Li. Improved methods for divisible load distribution on k-dimensional meshes using pipelined communications. IEEE Transactions on Parallel and Distributed Systems, 14(12):1250–1261, 2003.
[10] Thomas G Robertazzi. Processor equivalence for daisy chain load sharing processors. IEEE Transactions on Aerospace and Electronic Systems, 29(4):1216–1221, 1993.
[11] Jeeho Sohn and Thomas G Robertazzi. Optimal load sharing for a divisible job on bus networks. Technical report, Stony Brook, NY: State University of New York at Stony Brook, College of Engineering, 1992.
[12] Jeeho Sohn and Thomas G Robertazzi. Optimal time-varying load sharing for divisible loads. IEEE Transactions on Aerospace and Electronic Systems, 34(3):907–923, 1998.
[13] Amin Shokripour, Mohamed Othman, Hamidah Ibrahim, and Shamala Subramaniam. New method for scheduling heterogeneous multi-installment systems. Future Generation Computer Systems, 28(8):1205–1216, 2012.
[14] Fei Wu, Yang Cao, and Thomas Robertazzi. “Optimal divisible load scheduling for resource-sharing network”. In: arXiv preprint arXiv:1902.01898 (2019).
[15] Jingnan Yao and Bharadwaj Veeravalli. Design and performance analysis of divisible load scheduling strategies on arbitrary graphs. Cluster Computing, 7:191–207, 2004.
[16] Yang Yang, Krijn Van Der Raadt, and Henri Casanova. Multiround algorithms for scheduling divisible loads. IEEE Transactions on Parallel and Distributed Systems, 16(11):1092–1102, 2005.