Scheduling algorithms for procrastinators

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.

Adaptive policies for multi-mode project scheduling under uncertainty

In this paper, we study the delay optimal scheduling policy for a multi-state wireless fading channel, by taking bursty packet arrivals and automatic repeat request-based packet transmission into account. In our system, the average delay each packet experiences includes the time it waits in the queue and the time it may take to retransmit due to packet delivery failure. To reduce the average delay, we propose a joint channel-aware and queue-aware stochastic scheduling policy to determine whether and with which probability the source should transmit based on channel and buffer states, subject to an average power constraint at the transmitter. To find the optimal scheduling probabilities, we formulate a non-linear power-constrained delay minimization problem with the aid of controlled Markov decision processes. The optimization problem is then converted into an equivalent linear programming problem by introducing new variables from the steady-state probabilities of the underlying Markov chain and transmission probabilities. By analyzing its property, we derive the structure of the optimal solution, and exploit it to obtain the optimal probabilities analytically. It is found that the optimal scheduling policy has a double threshold structure, and can significantly reduce the average delay.

Age of Information (AoI) has attracted much attention recently due to its capability of characterizing the freshness of information in Industrial Internet of Things (IIoT). To improve the information freshness over a fading channel shared by multiple users, efficient scheduling methods are highly desired for IIoT. In this paper, we are interested in a cross-layer scheduling policy, in which power and rate-adaptive transmissions are enabled in the physical layer. More specifically, we adopt a probabilistic scheduling method to minimize AoI while satisfying an average power constraint. The optimization of the probabilistic scheduling policy is formulated as a Constrained Markov Decision Process (CMDP), the dimension of which grows exponentially with the number of users and the buffer size. To overcome the prohibitive computational cost, we reveal the threshold-based structure of the AoI-optimal scheduling. Then we conceive a low complexity iterative algorithm that gives us the optimal freshness-aware scheduling policy.

This work studies the power optimal dynamic scheduling problem in multi-channel multi-user wireless access networks. Users have quality-of-service (QoS) requirements on the minimum rates with statistical delay guarantees. Only one user is allowed to transmit over a channel in a given time slot. This work considers two scenarios: homogeneous and heterogeneous users. For the former scenario, the optimal scheduling policy can be derived, and an online scheduling algorithm for the optimal policy is proposed using online time-averaging without requiring a-priori known fading statistics. For the latter scenario, the optimal scheduling problem is combinatorially hard; hence, even when the fading statistics are available, computing the optimal policy is intractable. Consequently, this work develops a sub-optimal online scheduling algorithm with linear complexity which does not require a-priori known fading statistics. Moreover, the scheduling algorithm satisfies the QoS constraints for the users. Illustrative results demonstrate the performance of the proposed scheduling algorithms in various settings.

Opportunistic scheduling provides an important capability of resource management for wireless systems by taking advantage of multiuser diversity, allowing delay variation in delivering data packets. Our opportunistic scheduling aims at maximizing the utility which is usually expressed as a function of user throughput. In this paper we derive an off-line optimal scheduling policy by optimization theory, and show that the policy is also optimal in opportunistic scheduling. We extend the scheduling policy by adding QoS requirements for each user. To do so, we classify opportunistic schedulers according to QoS constraints. Their optimalities are also proved through mathematical analysis. To obtain optimal scheduling policy, the parameters related to QoS should be computed, so we propose a practical algorithm for parameter adaptation and verify its performance through simulations. The results confirm that our considered opportunistic schedulers show good fairness performance and guarantee each user's QoS without any difficulty in implementation.

The time needed to complete a software development project is hard to estimate in practice. In addition to the uncertainty about the duration of the individual development steps, software projects often suffer from unexpected rework and delays. As a result, project scheduling remains a difficult task for the managers of software projects. In this paper, we compute optimal scheduling strategies for a set of sample software projects. The computations are based on a stochastic Markov decision model for software projects which focuses on capturing the feedback between concurrent development activities. The optimal strategies are computed using a variant of the value iteration algorithm from stochastic dynamic programming. Since the underlying process model is stochastic, the strategies are stochastically optimal, that is, they minimize the expected project duration. The ultimate goal of this research is to develop guidelines for managers how to schedule their software projects under uncertainty in the best possible way. The sample projects are similar, but differ in certain characteristics of the project or product, such as the strength of the coupling between the components or the degree of specialization of the teams on the tasks. By using a set of related projects, we can study how the project characteristics influence the optimal scheduling decisions in a project. In addition to computing the optimal scheduling policies for the sample projects, we use extensive simulations to compare the performance of the optimal policy against the so-called list policies for each given setting. List policies are a simple, but commonly used class of scheduling policies. For our sample projects, we find that the best list policy in general is not optimal. The performance gap is the larger the higher the degree of specialization of the teams is. On the other hand, the stronger the coupling between the components, the smaller is the improvement which the optimal policy achieves over the best list policy.

Infomercial call centers answer calls in an order that reduces the number of abandoned calls to minimize lost revenue. We study a multi-class queuing system with a single server and customer abandonment, motivated by the case of infomercial call centers. We fully characterize the structure of the server’s optimal scheduling policy that minimizes the long-run average customer abandonment cost. We show that the optimal service policy is a static priority policy. We derive sufficient conditions under which the so-called b μ –rule is optimal. Under the b μ –rule, it is optimal to give priority to the customer type that has a higher service rate ( μ ) and higher abandonment cost (b), i.e., higher index b μ . We numerically test the robustness of our proposed policy in more general settings, including multi-server infomercial call centers.

Several manufacturing industries try to reduce transportation waste using automated material handling systems, which can enhance the transportation of raw materials from one location to another in the production line of a manufacturing area. The issue with transportation and job flow is a critical factor in a production line because some production stations need to wait for the work-in-progress to be delivered. Automated guided vehicle (AGV) transportation needs a setup of traffic control over a factory’s physical infrastructure and simulation. Doing so can help showcase and evaluate possible deficiencies that can be improved in the real job flow scenario of the production line. The design of experiment plays a huge role in finding and explaining variations of information under conditions that are regularly put as a hypothesis to reflect or describe the variation. A simulation model is implemented by adopting simplified AGV parameters. The model development follows the structure of system specification → machine specification → AGV specification → discrete-event simulation model → experimental design → analysis of performance indicators (PIs). To precisely reflect an alternative for evaluating aforementioned issues, this study proposes the model stated above and an analysis that is based on the PIs. Analysis of variance (ANOVA) results are chosen to analyze different factors affecting the PIs. Using the factorial ANOVA test results, this study uses one-way and two-way interactions to compare the relationship between job flow time, AGVs, AGV utilization, number of AGVs, and average waiting time.

The increasing demand for data services has given rise to efficient utilization of available resources (e.g., energy) in modern wireless communication. In order to address the energy requirements a wireless powered communication network (WPCN) with separate energy source (ES) and access point (AP) is considered in this work. The transmitters here adopt harvest-then-transmit (HTT) protocol for transmission to AP. An optimal dynamic time allocation and scheduling policy is considered which maximizes the throughput of the system. The throughput maximization problem formulated is convex in nature and solved using convex optimization techniques. The fairness of proposed policy is compared with max-min policy which use harvest-or-transmit (HOT) protocol in terms of Jain's fairness index. Simulation results highlights the trade-off between throughput and fairness and show that the proposed policy is more reliable for the overcrowded scenario.

The scheduling at an ATM access point is modelled as a stochastic control problem and an optimal scheduling policy is obtained for equalising the input buffer contents in the case of two inputs with unequal arrival rates. The optimal policy is work conserving, and it serves the longer queue when the queue lengths are unequal and serves the queue with the larger arrival rate when the queue lengths are equal. In the case of 0-1 arrival processes, some sample path wise results are obtained.

The problem addressed in this study is that of determining how to allocate the workstation processing and buffering capacity in a capacitated re-entrant line to the job instances competing for it, in order to maximize its long-run/steady-state throughput, while maintaining the logical correctness of the underlying material flow, i.e., deadlock-free operations. An approximation scheme for the optimal policy that is based on neuro-dynamic programming theory is proposed, and its performance is assessed through a numerical experiment. The derived results indicate that the proposed method holds considerable promise for providing a viable, computationally efficient approach to the problem and highlight directions for further investigation. Note to Practitioners-Sequencing and scheduling problems arising in the context of contemporary manufacturing environments are known to be extremely hard. For this reason, in most practical situations, these problems have been resolved through the application of a number of heuristics-i.e., rules of thumb that are expected to provide reasonable performance. Things are complicated even further in the automated versions of these environments, since the applied sequencing and scheduling logic must guarantee, in addition to good performance, logically correct and smooth operation. Both the logical and the performance-oriented control problem of flexibly automated production systems can be-and have been-addressed through formal systems theory. However, a challenging remaining problem is the approximation of the derived optimal policies in a way that will maintain near optimality, and at the same time, it will be computationally tractable in the context of the real-world applications. Our past work has addressed this approximation problem primarily with respect to the optimal logical control policy. The work presented in this paper undertakes the complementary problem of approximating the optimal scheduling policy. To this end, we employ some recently emerged results from a field known as neuro-dynamic programming (which is essentially a systematic approximation framework for dynamic programming). Our results indicate that the proposed approximation framework holds considerable promise toward developing a systematic analytical methodology for deriving near-optimal and logically correct scheduling policies for flexibly automated production systems. More specifically, it is shown that, when applied to some prototypical problems concerning the scheduling of re-entrant lines with finite buffering capacity at their workstations, the proposed approximation framework: 1) effectively integrates past results concerning the logical control of these environments and 2) the obtained performance is consistently superior to the performance provided by the typically used heuristics.

A two-phased approach to setting due-dates in single machine job shops

In this paper, we investigate the transmission completion time minimization problem in a two-user additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature. The harvested energy is modeled to arrive at the transmitters randomly. In this paper, under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. The transmitter has a fixed number of packets to be delivered to each receiver. Our goal is to minimize the time by which all of the packets for both users are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates intended for both users. We first analyze the structural properties of the optimal transmission policy. We prove that the optimal total transmit power has the same structure as the optimal single-user transmit power. We also prove that there exists a cut-off power level for the stronger user. If the optimal total transmit power is lower than this level, all transmit power is allocated to the stronger user, and when the optimal total transmit power is larger than this level, all transmit power above this level is allocated to the weaker user. Based on these structural properties of the optimal policy, we propose an algorithm that yields the globally optimal off-line scheduling policy.

The study investigates whether the location at which the order review and release (ORR) strategy is applied in a hybrid of job shop and flow shop influences its performance. Five different ORR strategies were applied at two different locations of the simulated shop in conjunction with four dispatching rules used at two shop utilisation levels and two due date tightness levels. The shop performance was evaluated by several job due date and shop related measures, including both mean and variability statistics. The results confirm that the effectiveness of an ORR strategy can be enhanced by controlling the location of its application. Furthermore, the ORR strategies based on the backward infinite loading (BIL) criterion outperformed those based on the modified infinite loading (MIL) criterion. With regard to the dispatching rule performance, the due date (EDD) rule yielded the best results on most of the variability measures, while the shortest processing time (SPT) rule did better on the mean measures.