478 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 8, NO. 2, FEBRUARY 2021 Joint Algorithm of Message Fragmentation and No- Wait Scheduling for Time-Sensitive Networks Xi Jin, Member, IEEE, Changqing Xia, Member, IEEE, Nan Guan, and Peng Zeng Abstract—Time-sensitive networks (TSNs) support not only end-to-end delay constraints in hard real-time industrial traditional best-effort communications but also deterministic systems. communications, which send each packet at a deterministic time so that the data transmissions of networked control systems can In networked control systems, TSNs have been adopted [1]– be precisely scheduled to guarantee hard real-time constraints. [3]. Deterministic communications contain control commands No-wait scheduling is suitable for such TSNs and generates the and critical sensing data, and the other data adopts best-effort schedules of deterministic communications with the minimal communications [4]. Deterministic communications and best- network resources so that all of the remaining resources can be effort communications have different objectives. The real-time used to improve the throughput of best-effort communications. performance of deterministic communications is the most However, due to inappropriate message fragmentation, the real- time performance of no-wait scheduling algorithms is reduced. important. Before they start to transmit, their deterministic Therefore, in this paper, joint algorithms of message schedules must be generated so that the transmission process fragmentation and no-wait scheduling are proposed. First, a can be controlled to guarantee hard real-time constraints. For specification for the joint problem based on optimization modulo best-effort communications, there is no strict constraint. Their theories is proposed so that off-the-shelf solvers can be used to schedules do not need to be generated in advance, and networks find optimal solutions. Second, to improve the scalability of our algorithm, the worst-case delay of messages is analyzed, and then, just try to transmit them as soon as possible. In a TSN switch, based on the analysis, a heuristic algorithm is proposed to the two kinds of communications share a fixed number of construct low-delay schedules. Finally, we conduct extensive test output queues. Deterministic communications must be assigned cases to evaluate our proposed algorithms. The evaluation results dedicated queues, while best-effort communications require indicate that, compared to existing algorithms, the proposed joint more queues to improve network throughput [5]. Therefore, algorithm improves schedulability by up to 50 . % determining how to assign and utilize the queues are the key to Index Terms—Message fragmentation, networked control system, improving network performance. real-time scheduling, time sensitive network. This paper focuses on store-and-forward switching, because compared to cut-through switching, store-and-forward I. Introduction switching is supported by more off-the-shelf TSN products. IME-SENSITIVE networks (TSNs) are an emerging For example, CISCO IE 4000 [6] and NXP SJA1105 [7] Tindustrial network technology based on Ethernet networks support only store-and-forward switching, while no off-the- and extend a set of IEEE standards to improve the shelf TSN product supports only cut-through switching. In controllability of industrial networks. Thus, in addition to store-and-forward networks, no-wait scheduling is an best-effort communications supported by Ethernet networks, effective method to make a performance trade-off between TSNs also support deterministic communications that have deterministic communications and best-effort communications been widely considered as an effective solution to guarantee [8]. Under no-wait scheduling, once a network switch receives Manuscript received May 25, 2020; revised June 15, 2020; accepted June a packet, it sends the packet immediately, i.e., only one queue 24, 2020. This work was partially supported by National Key Research and is needed to cache the scheduled packets. Thus, when a no- Development Program of China (2018YFB1700200), National Natural Science Foundation of China (61972389, 61903356, 61803368, U1908212), wait scheduling algorithm is used to generate schedules for Youth Innovation Promotion Association of the Chinese Academy of deterministic communications, except the occupied queue, all Sciences, National Science and Technology Major Project of the other queues can be used by best-effort (2017ZX02101007-004), Liaoning Provincial Natural Science Foundation of China (2020-MS-034, 2019-YQ-09), and China Postdoctoral Science communications. Therefore, no-wait scheduling algorithms Foundation (2019M661156). Recommended by Associate Editor Zidong not only generate schedules for deterministic communications Wang. (Corresponding author: Xi Jin.) on the dedicated queue, but also improve the performance of Citation: X. Jin, C. Q. Xia, N. Guan, and P. Zeng, “Joint algorithm of message fragmentation and no-wait scheduling for time-sensitive networks,” best-effort communications. IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 478–490, Feb. 2021. However, when no-wait scheduling algorithms are adopted, X. Jin, C. Q. Xia, and P. Zeng are with Key Laboratory of Networked the following issue should be considered. On the IP layer, a Control Systems, Chinese Academy of Sciences, Shenyang 110016, and with Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang large message from the TCP layer must be fragmented into 110016, China, and also with Institutes for Robotics and Intelligent several smaller pieces. Each piece and its added packet header Manufacturing, Chinese Academy of Sciences, Shenyang 110169, China (e- constitute a complete packet. These packets are then mail: [email protected]; [email protected]; [email protected]). transmitted separately and reassembled at destination devices. N. Guan is with Department of Computing, Hong Kong Polytechnic University, Hong Kong, China (e-mail: [email protected]). In this process, fragmentation algorithms will affect the Digital Object Identifier 10.1109/JAS.2021.1003844 transmission delay because smaller packets have higher JIN et al.: JOINT ALGORITHM OF MESSAGE FRAGMENTATION AND NO-WAIT SCHEDULING FOR TIME-SENSITIVE NETWORKS 479 parallelism. For example, in Fig. 1, a message of 1620 bytes two corollaries are proposed on how to construct low-delay must be fragmented into two pieces. In traditional Ethernet transmissions. fragmentation, the length of the first packet is equal to the Third, based on the two corollaries, a joint algorithm is maximum segment size (MSS) plus a packet header, and the proposed that uses packets from large to small to construct remaining part is contained in the second packet. Since no- schedules under hard real-time constraints. Thus, the proposed wait scheduling algorithms do not allow a time interval joint algorithm strikes a balance between saving resources and between two consecutive hops of a packet, the second packet temporality. Extensive test cases were run to evaluate the joint is postponed by the first packet and cannot be transmitted algorithm. The evaluation results demonstrate that, compared earlier. In another fragmentation, to reduce the long delay, the to existing algorithms, the proposed joint algorithm improves message can be fragmented into two pieces of 810 bytes each. schedulability by up to 50% and increases a small number of Although the number of packets is unchanged, the delay is packets. reduced by approximately one-third. Message fragmentation The rest of this paper is organized as follows: Section II exists in TSNs [5]. However, there is currently no work that reviews two categories of related work, including message considers message fragmentation algorithms and no-wait fragmentation and real-time scheduling algorithms. Section III scheduling algorithms together. This has led to some details the system model and problem. Section IV formulates optimizable solution spaces being ignored. the problem as an OMT specification. Section V proposes a heuristic algorithm to improve scalability of our algorithms. 1620 bytes Section VI evaluates the proposed algorithms based on A message extensive test cases. Section VII concludes the paper. The network A B C D II. Related Work 1460 bytes 160 bytes Much research has been proposed to improve the real-time MSS performance of industrial networks, e.g., real-time scheduling Traditional A−B B−C [9], resource allocation [10] and data recovery [11]. In this fragmentation Header C−D paper, we only focus on the real-time scheduling problem of 810 bytes 810 bytes industrial TSNs. The work in [5] formulates the basic A new A−B fragmentation B−C scheduling problem of TSNs as a specification, and then uses C−D Time an off-the-shelf solver to calculate schedules. Then, the work No-wait scheduling Reduced delay in [12] introduces the capacity limitation of TSN switches into the basic problem so that the proposed scheduling algorithms Fig. 1. Effect of message fragmentation on no-wait scheduling. can be adopted in actual systems. Based on the above work, the work in [13] proposes a loose scheduling algorithm to Therefore, in this paper, a joint algorithm is proposed that transmit massive data packets using limited switch resources. fragments deterministic messages into packets of optimized In addition to the classical scheduling problem, some sizes and schedules the packets under hard real-time extended problems have been considered. The work in [14] constraints