Optimal Policy for Controlling Two-Server Queueing Systems with Jockeying

For the design of call admission control (CAC) policy in wireless networks, how to decrease the average system cost is a key issue. In this paper, we study the optimal admission policy for minimizing the system cost. By modeling the admission control problem into a Markov decision process (MDP) and analyzing the corresponding value function, we obtain some monotonicity properties of the optimal policy. These properties suggest that the optimal admission control policy for the bandwidth asymmetry wireless networks should have a threshold structure and the threshold specified for a class of calls may change with the system state. Due to the prohibitively high complexity for computing the thresholds in a system with large state space, we propose a heuristic CAC policy called call-rate- based dynamic threshold (CRDT) policy to approximate the theoretical optimal policy based on the insights we obtain from the modeling and the analytical study on the properties of the optimal policy. The CRDT policy is efficient and can be easily implemented. The numerical results show that the performance of average system cost of the proposed CRDT policy is close to that of the optimal policy from the MDP model and is better than that of some known existing CAC schemes, including those performing well in bandwidth asymmetry wireless networks.

This paper presents a hierarchical approach for controlling the spread of an epidemic disease. The approach consists of a three-layer architecture where a set of two-layer multiple social networks is governed by a (third) top-layer consisting of an optimal control policy. Each of the two-layer social networks is modeled by a microscopic Markov chain. On top of all the two-layer networks is an optimal control policy that has been developed by using an underlying Markov Decision Process (MDP) model. Mathematical models pertaining to the top-level MDP as well as two-layer microscopic Markov chains have been presented. Practical implementation methodology using the proposed models has also been discussed along with a numerical example. The results in the numerical example illustrate the control of an epidemic using the optimal policy. Directions for further research and characterization of the optimal policy have also been discussed with the help of the same numerical example.Article HighlightsAn optimal approach for controlling the spread of an epidemic infection.The approach is able to model the uncertainties involved in the problem.The approach is able to cater for the underlying social network.

Dynamic selling of quality-graded products under demand uncertainties

In this paper, We consider an uncertain Markov decision process (MDP) with a control cost and a linear temporal logic (LTL) control specification. We propose a reinforcement learning (RL) based method for design of an optimal control policy by which the controlled MDP satisfies the control specification with probability 1 and minimizes an expected discounted sum of the control costs. First, we construct a deterministic Rabin automaton (DRA) that accepts all and only infinite words satisfying the LTL control specification. Second, we construct a product MDP of the MDP and the DRA to represent a dynamic control policy that satisfies the control specification. Third, we modify the product MDP in order to apply RL to the design of an optimal control policy. The control action of the modified product MDP is a pair of a pattern and an action, where the pattern is a set of actions. Moreover, we introduce a reward that represents both the satisfaction of the control specification and the minimally restrictiveness of the pattern. Finally, we proposed an algorithm for design of an optimal control policy that consists of a sequential decision making of two steps. At the first decision making, we select a pattern that maximizes a discounted sum of the reward. At the second one, we select an action from the pattern selected at the first one such that it minimizes the expected discounted sum of the costs. Moreover, we consider an illustrative example to show that the proposed algorithm can obtain an optimal control policy.

Integrated production-delivery control policy for an unreliable manufacturing system and multiple retailers

Dynamic control of a closed two-stage queueing network for outfitting process in shipbuilding

We consider a finite-capacity single-server queuing system in which the problems of capacity design and service quality control are integrated. The amount of time spent on servicing a customer is used as a measure of the quality of service provided. The expected reward from servicing is assumed to be a nondecreasing function of the service duration, while a linear holding cost is assumed for customers waiting in the system. We maximize the long-run average return per unit time by optimally controlling the quality of service to be provided as a function of the workload facing the server for different waiting-room capacities. We show that the optimal control policy for a given capacity is monotone and also examine the effect of varying the system capacity on the optimal control policy. Furthermore, we analyze the design problem of selecting an optimal capacity by assuming that an optimal service control policy will be followed for each system capacity.

Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The objective function is then the expected discounted value of returns, over an infinite horizon. It gives the land or the forest value in a stochastic environment. In MDP models, the laws of motion between stand-price states are Markov chains. Faustmann's formula is a special case where the probability of movement from one state to another is equal to unity. MDP models apply whether the stand state is bare land, or any state with trees, be it even- or uneven-aged. Decisions change the transition probabilities between stand states through silvicultural interventions. Decisions that maximize land or forest value depend only on the stand-price state, independently of how it was reached. Furthermore, to each stand-price state corresponds one single best decision. The solution of the MDP gives simultaneously the best decision for each state, and the forest value (land plus trees), given the stand state and following the best policy. Numerical solutions use either successive approximation, or linear programming. Examples with deterministic and stochastic cases show in particular the convergence of the MDP model to Faustmann's formula when the future is assumed known with certainty. In this deterministic environment, Faustmann's rule is independent of the distribution of stands in the forest. FOR. SCI. 47(4):466–474.

Reduction of energy consumption has attracted much attention of the researchers and practitioners in the field of sustainable manufacturing. However, the issue of integrated optimal production and energy control for sustainable manufacturing systems has not yet been investigated sufficiently. In this paper, we study such a problem for a single machine and single product-type manufacturing system, with the objective of minimizing the sum of production cost and energy consumption cost. To solve this problem, a Markov decision process model is developed, based on which, we obtain the integrated optimal production and energy control policy by the policy iteration method. Furthermore, we reveal the structural characteristics of optimal control policy and analyze the influence of system parameters on it by comparing different cases.

Invisible stock loss often occurs in inventory management systems, which is usually caused by quality deterioration, theft, and misplacement and makes inventory record inaccurate. Inaccurate inventory record will bring significant negative impact on the performance of inventory control and leads to severe stock-out. To eliminate this negative impact, in this paper, we develop a Markov decision process (MDP) model for an inventory control system with invisible stock loss, inaccurate record, and replenishment lead-time. Based on the MDP model, a robust inventory control policy is constructed by using the policy iteration technique. From numerical experiments, we find that the robust policy still has a reorder point/order-up-to level structure i.e., an (s, S) structure, and can significantly reduce the impact of inventory inaccuracy.

In the coronavirus epidemic, many Chinese hospitals have established buffer zones to prevent the spread and transmission of the virus. The buffer zone is a monitored and separate area where the patients who need hospitalizations after the quick treatments in the emergency department can temporarily wait for the Covid-19 test and receive some healthcare services to stabilize their conditions. Because the beds in the buffer zones are limited, the managers face the patient admission control problem for the buffer zone. This management and control problem is challenging since the patient arrivals are uncertain, and the patients’ conditions are different. In this paper, we build the infinite- and finite-horizon Markov decision process (MDP) models for this problem. We use the uniformization method to discretize the patient flow. We propose various iteration algorithms to solve the MDP models and obtain the optimal and threshold policies. Numerical experiments validate the advantages of the policies obtained by the algorithms in this paper over the current policies of hospitals. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The ongoing COVID-19 pandemic has been causing enormous damage to people’s health, jobs, and well-being. COVID-19 has affected almost all countries globally and has changed the operation mode of the healthcare system, especially the hospitals. The hospitals are the frontlines of healthcare service and the battle with the COVID-19 pandemic. This article is motivated by our collaborations with hospitals in Shanghai, China. In China, many hospitals establish buffer zones: a monitored area where the patients who need hospitalizations after the quick treatments in the emergency department can temporarily wait for the Covid-19 test and receive some healthcare services to stabilize their conditions. Because the zone’s capacity is limited, the managers must make dynamic patient admission control decisions according to multiple factors, such as patients’ health conditions and the usage of beds in the zone. We propose two MDP models to solve this complex problem. Several iteration algorithms are designed to solve the MDP models and obtain the optimal and threshold policies. Based on hospitals’ real-life data, we show the methods presented in this paper can help hospital managers make more reasonable decisions. Although we focus on the hospital’s buffer zone in China, the methodology and approach for this problem can be extended to other practical hospital management scenarios in the coronavirus pandemic. For example, For example, some hospitals have admission control problems for coronavirus patients due to hospital capacity limitations. The hospital has to decide if a patient is accepted as an inpatient or suggested to home quarantine. In such a case, the admission control problem can also be solved by the methodologies in the paper.

Towards enhanced threat modelling and analysis using a Markov Decision Process

In this paper, an application of Markov Decision Processes (MDP) for modeling selected marketing process is presented. The process is converted into MDP model, where states of the MDP are determined by a configuration of state vector. Elements of the state vector represent most important attributes of the customer in the modeled process. Movement between the states is determined by actions of the customer. In constructed MDP model, individual states with assigned initial reward values then represent consequences of action chosen by the customer resulting in either incresing or reducing the revenue following moving into these states. Value iteration method is then used for computation of the expected final rewards for each state. Based on provided realistic data, customer behavior is analyzed and the best course of action is proposed. Model suitability for future predictions of desired action outcome rate is discussed as well.

Linear programming formulation for non-stationary, finite-horizon Markov decision process models

Dynamic production control in parallel processing systems under process queue time constraints