Zero-wait Policy Research Articles

Unifying AoI Minimization and Remote Estimation—Optimal Sensor/Controller Coordination With Random Two-Way Delay

The ubiquitous usage of communication networks in modern sensing and control applications has kindled new interests on the timing coordination between sensors and controllers, i.e., how to use the “waiting time” to improve the system performance. Contrary to the common belief that a zero-wait policy is optimal, Sun <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> showed that a controller can strictly improve the data freshness, the so-called Age-of-Information (AoI), by postponing transmission in order to lengthen the duration of staying in a good state. The optimal waiting policy for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sensor</i> side was later characterized in the context of remote estimation. Instead of focusing on the sensor and controller sides separately, this work develops the jointly optimal sensor/controller waiting policy in a Wiener-process system. This work generalizes the above two important results in the sense that not only do we consider joint sensor/controller designs (as opposed to sensor-only or controller-only schemes), but we also assume random delay in both the forward and feedback directions (as opposed to random delay in only one direction). In addition to provable optimality, extensive simulation is used to verify the performance of the proposed scheme.

Optimal sampling policy of multi‐dimensional wiener processes with random delivery time

A sampling problem for remote monitoring and estimation of the multi-dimensional Wiener process through a channel with random delivery time under the constraint of maximum sampling frequency is considered. The authors study the optimal sampling policy that minimizes the mean square error. It is showed that the threshold policy is optimal and the near closed-form expressions of the optimal threshold and the corresponding mean square error are given. A bisection method is proposed to search the numerical solutions. The results provide a general framework for remote estimation and sampling, including the special cases that the dimension of Wiener source is one and that the delivery time of the channel tends to zero. Simulation results show that even though there is no constraint on the maximum sampling frequency, age-optimal policy, periodic sampling policy and zero-wait policy are far from optimal.

Analysis on Computation-Intensive Status Update in Mobile Edge Computing

In status update scenarios, the freshness of information is measured in terms of age-of-information (AoI), which essentially reflects the timeliness for real-time applications to transmit status update messages to a remote controller. For some applications, computational expensive and time consuming data processing is inevitable for status information of messages to be displayed. Mobile edge servers are equipped with adequate computation resources and they are placed close to users. Thus, mobile edge computing (MEC) can be a promising technology to reduce AoI for computation-intensive messages. In this paper, we study the AoI for computation-intensive messages with MEC, and consider three computing schemes: local computing, remote computing at the MEC server, and partial computing, i.e., some part of computing tasks are performed locally, and the rest is executed at the MEC server. Zero-wait policy is adopted in all three schemes. Specifically, in local computing, a new message is generated immediately after the previous one is revealed by computing. While in remote computing and partial computing, a new message is generated once the previous one is received by the remote MEC server. With infinite queue size and exponentially distributed transmission time, closed-form average AoI for exponentially distributed computing time is derived for the three computing schemes. For deterministic computing time, the average AoI is analyzed numerically. Simulation results show that by carefully partitioning the computing tasks, the average AoI in partial computing is the smallest compared to local computing and remote computing. The results also indicate numerically the conditions on which remote computing attains smaller average AoI compared with local computing.

Optimal Policies for Status Update Generation in an IoT Device With Heterogeneous Traffic

A large body of applications that involve monitoring, decision making, and forecasting require timely status updates for their efficient operation. Age of Information (AoI) is a newly proposed metric that effectively captures this requirement. Recent research on the subject has derived AoI optimal policies for the generation of status updates and AoI optimal packet queueing disciplines. Unlike previous research, we focus on low-end devices that typically support monitoring applications in the context of the Internet of Things. We acknowledge that these devices host a diverse set of applications some of which are AoI sensitive while others are not. Furthermore, due to their limited computational resources, they typically utilize a simple first-in–first-out (FIFO) queueing discipline. We consider the problem of optimally controlling the status update generation process for a system with a source–destination pair that communicates via a wireless link, whereby the source node is composed of a FIFO queue and serves two applications, one that is AoI sensitive and one that is not. We formulate this problem as a dynamic programming problem and utilize the framework of Markov decision processes to derive the optimal policy for the generation of status update packets. Due to the lack of comparable methods in the literature, we compare the derived optimal policies against baseline policies such as the zero-wait policy. Results indicate that the baseline policy fails to capture the complex system dynamics that determine the relationship between the frequency of status update generation and the resulting queueing delay and thus perform poorly. To the best of our knowledge, the derived optimal policy does not exhibit a simple structure; thus, we utilized the baseline policies, whose operation is intuitive, to gain insight into the inner workings of the optimal policy.

Is the Zero-Wait Policy Always Optimum for Information Freshness (Peak Age) or Throughput?

The zero-wait (ZW) policy is widely held to achieve maximum information “freshness,” i.e., to achieve minimum peak age (PA) and maximum throughput, for real-time Internet-of-Things applications. In this letter, it was shown through a series of experiments that the ZW policy is not necessarily the optimum policy for freshness or throughput in all real-world scenarios. First, the effect of delay on the ZW policy was shown on a local area network (LAN). Afterward, the server was located on the Internet, and it was shown that the ZW policy incurred a two-fold PA and throughput performance degradation compared with continuously sending status updates.

Update or Wait: How to Keep Your Data Fresh

In this paper, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information, or simply age, which is defined as how old the freshest received update is, since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semi-Markov decision problem with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if: 1) the age penalty function grows quickly with respect to the age; 2) the packet transmission times over the channel are positively correlated over time; or 3) the packet transmission times are highly random (e.g., following a heavy-tail distribution).

New MILP Models for Scheduling of Multiproduct Batch Plants under Zero-Wait Policy

This paper presents a new mixed-integer linear programming (MILP) model in which makespan is minimized for the multiproduct batch plants. In particular, the zero-wait (ZW) scheduling with transfer and setup times is analyzed. Not only idle times between the successive products but also heads and tails are used to select a possible production sequence with the minimum makespan. To determine the suitable head and tail, new binary variables are defined and aggregated to the assignment constraints of traveling salesman problems (TSPs). Although the number of binary variables increases, the mathematical formulation can yield a very compact MILP model. The effectiveness of the proposed model is demonstrated through several examples. The proposed model is extended to solve the scheduling problems for productions with single product campaigns (SPCs) and mixed product campaigns (MPCs) explained by Birewar and Grossmann (Ind. Eng. Chem. Res. 1989b, 28, 1333). The solutions by the proposed method are compared with the solutions obtained from the rigorous solution method by Birewar and Grossmann. The proposed model is formulated as a compact size and leads to a significant reduction in solution times.

Completion times and optimal scheduling for serial multi-product processes with transfer and set-up times in zero-wait policy

Calculation of completion times and optimal scheduling for serial multi-product, multi-unit problems have been studied for the different types of intermediate storage options. In this study, a set of simple recurrence relations for serial multi-product multi-batch processes in ZW policy is suggested, which calculates completion times with or without non-zero transfer times and non-zero sequence dependent set-up times of the last unit ( j = M) for each product ( i = 1, 2, … N). An algorithm is also proposed which calculates completion times of each unit ( j = 1, 2, …, M - 1) for a given product i, not recursively but independently in ZW policy. For the case of zero transfer times and zero sequence dependent set-up times, a mixed-integer linear programming (MILP) formulation is developed, and for the case of non-zero transfer times and non-zero sequence dependent set-up times, a mixed-integer nonlinear programming (MINLP) formulation is developed for optimal scheduling in ZW policy using newly proposed algorithm which calculates completion times of each product at each stage.