Minimum Age TDMA Scheduling

Abstract

We consider a transmission scheduling problem in which multiple systems receive update information through a shared Time Division Multiple Access (TDMA) channel. To provide timely delivery of update information, the problem asks for a schedule that minimizes the overall age of information. We call this problem the Min-Age problem. This problem is first studied by He et al. [IEEE Trans. Inform. Theory, 2018], who identified several special cases where the problem can be solved optimally in polynomial time. Our contribution is threefold. First, we introduce a new job scheduling problem called the Min-WCS problem, and we prove that, for any constant r ≥ 1, every r-approximation algorithm for the Min-WCS problem can be transformed into an r-approximation algorithm for the Min-Age problem. Second, we give a randomized 2.733-approximation algorithm and a dynamic-programming-based exact algorithm for the Min-WCS problem. Finally, we prove that the Min-Age problem is NP-hard. I. INTRODUCTIONWe consider systems whose states change upon reception of update messages. Such systems include, for example, web caches [2], intelligent vehicles [3], and real-time databases [4]. The timely delivery of update messages is often critical to the smooth and secure functioning of the system. Moreover, since any given update is likely dependent on previous updates, the update messages should not be delivered out of order. In most cases, the system does not have exclusive access to a communication channel. Instead, it must share the channel with other systems. Hence, the transmission schedule plays a crucial role in determining the performance of the systems that share the channel.can be obtained by sorting the sender-receiver pairs according to the number of messages to be sent to the receiver [14]. However, even if the channel is TDMA-based, it remained open whether the problem can be solved optimally in polynomial time. In this paper, we therefore focus on TDMA channels. In the remainder of this paper, we refer to this scheduling problem on a TDMA channel as the Min-Age problem.In this paper, we cast the Min-Age problem as a job scheduling problem called the Min-WCS problem.The Min-WCS problem has a simple formulation inspired by a geometric interpretation of the Min-Age problem. The simplicity of the formulation also facilitates algorithm design. As we will see in Section VII, 1 The sender may serve as a relay or hub for the system and thus may not be responsible for generating update messages. 2 The buffer may be a logical one that stores the inputs to a scheduler. 3 one may solve variants of the Min-Age problem by modifying the geometric interpretation and then solving the corresponding job scheduling problem. Job scheduling has been studied for decades. In fact, the Min-WCS problem is a special case of singlemachine scheduling with a non-linear objective function under precedence constraints, which has been studied by Schulz and Verschae [15] and Carrasco et al. [16]. Specifically, for any > 0, the algorithm proposed by Schulz and...

Age of Information Optimization for Multiple VLC/RF IoT Sensor Networks

“…Similar to data rate and delay, AoI is also impacted by the presence of multiple sensors, which must be properly allocated or scheduled. Considering this issue, resource allocation schemes aimed at minimizing the AoI in time-division multiple access (TDMA) and frequency-division multiple access (FDMA) systems are studied in [31] and [32]. In [33], the authors optimize the AoI in orthogonal and nonorthogonal multiple access methods and compare the results.…”