Threshold Policy Research Articles

Strategic Behavior and Social Welfare Optimization in a Batch-service Queueing System with Threshold Policy

Strategic Behavior and Social Welfare Optimization in a Batch-service Queueing System with Threshold Policy

Simplicial epidemic model with a threshold policy

We establish a simplicial empty-susceptible–infected (ESI) model with consideration of threshold policy to depict the network-based epidemic transmission, where the underlying propagation structures are expanded from edges to higher-order structures. To address the epidemic evolution in an explicit network, we formulate the quenched mean-field probability evolution about each site, which is composed of non-smooth differential equations based on network topology. Remarkably, under the combined action of non-smooth and high-order structures, a tristable state is observed in empirical social networks, which is consistent with the coexistence of three stable equilibria by analysis of the mean-field system. Moreover, we find that a sliding mode exists in empirical social networks, which is also indicated by the theoretical analysis of the mean-field probability equations. Finally, the system is divided into the free subsystem without the threshold policy and control subsystem with the threshold policy. Both subsystems admit a stable disease-free equilibrium and a stable endemic equilibrium, as well as coexistence of a stable disease-free equilibrium and a stable pseudo equilibrium in the system, thereby admitting three types of the bistable state under the policy with different critical levels.

Mosquito suppression via Filippov incompatible insect technique

Mosquito-borne diseases persist as a global health challenge despite ongoing control efforts, necessitating the exploration of alternative control approaches. This research proposes a Filippov incompatible insect technique (IIT) model with a threshold policy control for suppressing mosquito population. The model implements biological and chemical control strategies only when wild mosquito density surpasses an economic threshold. The biological strategy involves releasing Wolbachia-infected male mosquitoes, offering advantages such as a shortened lifespan and disease blocking. Simultaneously, moderate insecticide and larvicide spraying serve as a chemical approach to expedite the control process. The model provides economic advantages by minimizing control costs and environmental benefits through the integration of biological strategies, thus reducing reliance on chemicals. By employing Filippov's convex method, we identify necessary conditions for the existence of sliding segments and determine the dynamics of the switching line. Theoretical analysis reveals the model's long-term dynamics, including sliding bifurcations, pseudo-equilibria, and their stability. The model exhibits boundary equilibrium bifurcations and transcritical bifurcations in both free and controlled systems. Varying threshold values significantly impact the control outcomes effectiveness. The main findings demonstrate that integrated strategies efficiently decrease the population density of wild mosquitoes.

A restless bandit approach for capacitated condition based maintenance scheduling

AbstractThis paper considers the maintenance scheduling problem of multiple non-identical machines deteriorating over time. The deterioration gradually decreases a machine’s performance, which results in revenue losses due to lower output quality. The maintenance cost is dependent on the degradation state, and the number of maintenance activities that can be carried out simultaneously is restricted by the number of maintenance workers. Our main goal is to propose a heuristic with low complexity that consistently produces solutions close to the optimal strategy for problems of real size. We cast the problem as a restless bandit problem and propose an index based heuristic (Whittle’s index policy) which can be computed efficiently. We also provide a lower bound that can be computed by linear programming. We numerically compare the performance of the index heuristic with alternative policies. In addition to achieving superior performance over failure-based and threshold policies, Whittle’s policy numerically converges to our lower bound when the number of machines is moderately high and/or maintenance workload is high.

Sampling for Remote Estimation of the Wiener Process over an Unreliable Channel

In this paper, we study a sampling problem where a source takes samples from a Wiener process and transmits them through a wireless channel to a remote estimator. Due to channel fading, interference, and potential collisions, the packet transmissions are unreliable and could take random time durations. Our objective is to devise an optimal causal sampling policy that minimizes the long-term average mean square estimation error. This optimal sampling problem is a recursive optimal stopping problem, which is generally quite difficult to solve. However, we prove that the optimal sampling strategy is, in fact, a simple threshold policy where a new sample is taken whenever the instantaneous estimation error exceeds a threshold. This threshold remains a constant value that does not vary over time. By exploring the structure properties of the recursive optimal stopping problem, a low-complexity iterative algorithm is developed to compute the optimal threshold. This work generalizes previous research by incorporating both transmission errors and random transmission times into remote estimation. Numerical simulations are provided to compare our optimal policy with the zero-wait and age-optimal policies.

The dynamics and near‐optimal controls of a dengue model with threshold policy

In this paper, a piecewise smooth dengue model with threshold policy is developed, and the impacts of different control measures on the spread of dengue fever are also investigated. The number of dengue infections is used as a threshold level to determine whether to implement control, and control measures are triggered only if the number of infected individuals exceeds . Using the Routh–Hurwitz criterion, the dynamic behaviors of the free system and control system are studied. Then, the existence of the sliding mode is verified, and the sliding dynamics are analyzed by using the Utkin equivalent control method. It is shown that model solutions eventually converge to one of two endemic equilibria or the sliding equilibrium depending on . In addition, by using Ekeland's principle and maximum principle, the sufficient and necessary conditions for near‐optimal controls of this model are obtained. Finally, numerical simulations are carried out to explain and supplement the theoretical results.

The effects of threshold policies on individual effort in uncertain outcomes

There are situations where the rewards associated with an outcome differ based on whether a certain threshold is exceeded. This paper examines how the threshold affects individual effort levels and the performance distribution. When performance uncertainty is small, only individuals near the threshold increase their effort. In contrast, large performance uncertainty increases the likelihood of exceeding the threshold, motivating more people to exert costly efforts. Consequently, the distribution can be either unimodal or bimodal. These findings suggest that examiners can effectively enhance the overall performance of an assessed population by appropriately setting the threshold and managing score uncertainty.

Admission Control in Multi-server Systems Under Binary Reward Structure

We study a multi-server queueing system where a customer is satisfied (and generates a unit revenue) if their queueing time is at most a given constant. If the queueing time of the admitted customer exceeds this constant, the customer gets served, but is unsatisfied and generates no revenue. Such queueing systems arise in the context of modeling service systems where excessive delays are of concern. A key challenge is how to design an admission control policy to maximize the number of satisfied customers per unit time in the long run, assuming that we can observe the number of customers in the system at any time. We call this the binary reward structure system and show that a threshold-type admission policy is optimal. The optimal threshold policy has to be computed numerically. Hence we propose a square-root admission policy to approximate the optimal admission control policy, and compare the performance of these two policies. We derive an analytical upper bound on the performance of optimal admission control policy by deriving an optimal admission policy assuming we have full information over the queueing time of the admitted customers. This is equivalent to a queueing system where customers abandon the queue (i.e., leave without service) if their queueing time exceeds the given constant. We demonstrate that the optimal policy that includes customer abandonment, or alternatively, the optimal policy under full information, the optimal threshold policy, and the square-root admission policy, all exhibit identical performance in the asymptotic regions of the parameter space. Our numerical results indicate that the worst optimality gap of the square-root admission policy is within 3.9% of the optimal revenue, and implementing the square-root admission policy in the observable queueing system leads to a revenue loss that is at most 5.6% of the maximum possible revenue rate in the full information system. We also compare the binary reward structure with the more common linear reward structure where the system incurs holding cost per unit queueing time per customer. In addition, we also show that the analysis based on queueing time is applicable to the system time as well.

Equilibrium balking behavior of customers and regulation measures in a multi-server queue with threshold policy

ABSTRACT The equilibrium balking behavior of customers and some effective regulation measures in a multi-server queueing system with a threshold policy are mostly investigated in this paper. We consider four information levels: entirely visible, nearly visible, nearly invisible and entirely invisible. For each case, we compare the equilibrium and socially optimal balking strategies of customers, formulate pricing strategy and analyze the revenue of the system manager. It is found that no matter what information level, there always exist the optimal thresholds that maximize the optimal social welfare and the system manager’s revenue, respectively. Moreover, how much information the customers know has influence on the optimal social welfare. Such findings can provide guidance for the social planner to formulate pricing strategies, make appropriate threshold policies and decide what information should be disclosed to customers to improve the optimal social welfare.

The Impact of The Parliamentary Threshold Policy On Small Parties: The Failure of The Partai Persatuan Pembangunan To Meet The Parliamentary Threshold In The 2024 Election

The implementation of the parliamentary threshold policy poses significant challenges for small parties or new parties to gain representation in the legislature. This case study examines the impact of the parliamentary threshold policy on small parties, focusing on the failure of the Partai Persatuan Pembangunan (PPP) to meet the parliamentary threshold in the 2024 elections. The research highlights that small parties face difficulties in reaching the threshold, which results in their failure to gain seats in parliament. This situation affects political pluralism by limiting the diversity of political views represented in the legislature, potentially reducing inclusive and fair representation for different groups of voters. Furthermore, it underscores the importance of a mature political system in addressing the challenges of democracy, accommodating diverse political views, including from small parties, to ensure fair and inclusive representation for all citizens. In this research, the method used is normative qualitative, which describes information obtained from legal standards, theories, and legal principles and rules related to the core of the problem by collecting data through interviews. Parliamentary thresholds in fact put pressure on small parties to remain in parliament as the threshold numbers get higher. Thresholds that aim to simplify parties turn out to be a barrier to the represented and the represented, as well as political dissatisfaction and undermine the legitimacy of the political system.

Implications of unobservable promotion on distribution channel strategies in a retail platform

Besides distribution services, retail platforms are beginning to provide unobservable promotion services to enhance traffic and demand. Thus, suppliers are incentive to consider the impact of platform promotion on distribution channel strategies. Hence, considering a retail platform supply chain in which the supplier uses an outcome-based contract to incentivize the retail platform’s hidden promotion effort, this paper investigates the implications of unobservable platform promotion on the supplier’s distribution channel strategies. We develop a Stackelberg game model to examine the equilibrium outcomes of reselling and agency selling under unobservable promotion action and find that the retail platform may volunteer to promote in both channels when the market potential difference is large. Interestingly, voluntary promotion may motivate the supplier to increase the wholesale price. Furthermore, we derive conditions under which the supplier prefers reselling and agency selling. When the market potential difference is small, the distribution channel strategy is a threshold policy of the commission rate, below which agency selling is preferred, and reselling is preferred otherwise. It is counterintuitive that when the market potential difference is large, the commission rate will not influence the preference of channel selection and the reselling channel is always preferred by the supplier. Interestingly, the impact of platform promotion on the threshold of distribution channel strategies is non-monotonic in the increment probability of high market potential and market potential difference. Specifically, platform promotion induces the upstream supplier to select the reselling channel suppose the increment probability of high market potential is moderate, while induces the supplier to select the agency selling (reselling) channel when the market potential difference is moderate (large) suppose the increment probability of high market potential is high. Moreover, we find that enhancing the increment probability of high market potential benefits the supplier more, but only moderate increment probability of high market potential makes the retail platform better off.

Problematika Sistem Presidential Threshold Ditinjau dari Maqāṣid al-Syarī’ah

The presidential threshold is a threshold requirement for a political party or a coalition of political parties supporting a presidential and vice-presidential candidate pair using the percentage of the DPR seat acquisition or the national valid vote acquisition in the DPR general election. The presence of this presidential threshold is a barrier to the right to equal opportunity in government. This research aims to evaluate the various rights that have been violated by the presidential threshold policy from the perspective of human rights and maqashid sharia as a new view of the efforts to reform a just law. This research includes normative research with statutory and legal policy approaches. The results and discussion of this research are that the general election law related to the presidential threshold has been tested by the Constitutional Court. However, the Court always rejects the application because it is of the opinion that the presidential threshold is an open authority of the legislator based on the delegation of Article 6A Paragraph (5) of the 1945 Constitution. The rejection resulted in disappointment for the Indonesian people because it was considered to limit the right to become a leader. In the perspective of Maqāṣid syarī'ah, the presidential threshold policy has also violated hifdzu 'aql. Therefore, in the future, fair legal reform efforts must be realized, namely by amending Article 6A Paragraph (2) related to presidential requirements to clearly regulate and close the loopholes of interpretation by the legislators and moral development of constitutional judges so that they really fight for the rights of citizens with a further view of the constitution.

Exact Characterization of the Jointly Optimal Restocking and Auditing Policy in Inventory Systems with Record Inaccuracy

We present a continuous-time stochastic model of an inventory system with record inaccuracy. In this formulation, demand is modeled by a point process and is observable only when it leads to sales. In addition to demand that can reduce the stock, an unobservable stochastic loss process can also reduce the stock. The retailer’s goal is to identify the restocking and auditing policy that minimizes the expected discounted cost of carrying a product over an infinite horizon. We analytically characterize the optimal restocking and jointly optimal auditing policy. We prove that the optimal restocking policy is a threshold policy. Our proof of this result is based on a coupling argument that is valid for any demand and loss model. Unlike the optimal restocking policy, the jointly optimal auditing policy is not of threshold type. We show that a complete proof of this statement cannot be obtained by solely resorting to the first-order stochastic dominance property of the Bayesian shelf stock distribution induced by the demand and loss process. Instead, our characterization of the jointly optimal auditing policy is based on proving that the dynamics of the shelf stock distribution constitute a (strictly) sign-regular kernel. To our knowledge, this is the first paper that characterizes the optimal policy of a complex control problem by establishing sign regularity of its underlying Markovian dynamics. Our theoretical results lead to a fast algorithm for computing the exact jointly optimal auditing/restocking policy over the problem’s entire state space. This enables comparative statics analysis, which allows us to determine how inventory record inaccuracy affects the economic significance of various cost drivers. This, in turn, allows us to determine when or, better, under what conditions auditing can be an effective tool for reducing the total cost.

Relay node selection scheme and deep sleep period for power management in energy‐harvesting wireless sensor networks

SummaryThis paper presents Relay node selection scheme and Deep sleep period for power management in Energy Harvesting Wireless Sensor Networks (RD‐EHWSN), a new energy‐saving scheme founded on asynchronous duty cycling. RD‐EHWSN reduces sensor node energy consumption and guarantees equilibrium energy use between sensor nodes in WSN with the energy harvesting capacity by adjusting these sensor nodes duty cycles more drastically and deeply by according to the estimated value of its residual energy on the basis of future‐presented harvested energy, and this is done through the use of a new proposed energy threshold policy. RD‐EHWSN also grips the benefit of transmitter initiated using the low power listening (LPL) technique with short preamble messages and uses a new relay node selection procedure to achieve the load balancing in WSN. We implemented RD‐EHWSN by using OMNeT++/MiXiM. For evaluation, we compared it with PS‐EHWSN, under multiple concurrent multihop traffic flows scenarios and scenarios in which nodes can harvest different energy harvesting rate. In all experiments, RD‐EHWSN significantly outperformed the PS‐EHWSN scheme; the results of simulation demonstrate that our scheme enhances the general yielding of WSN thru lessening the energy consumption and the mean latency, as well as raising the packet delivery ratio and the throughput. Moreover, RD‐EHWSN improves the WSN lifetime and ensures it operates in good condition in the case where the energy harvesting rate is lower by comparing it with the PS‐EHWSN scheme.

Impact of natural resource rents on well-being in sub-Saharan Africa: The role of human capital

This study contributes to the resource curse literature in diverse means. First, using a non-monetary welfare measure, the study investigates the validity of the resource curse hypothesis in sub-Saharan Africa (SSA). Secondly, the paper examines the impact of natural resource rents on human welfare through the human capital channel and finally investigates the minimum human capital score to avert the resource curse in SSA. The empirical analysis conducted using the system Generalized Method of Moment (GMM) econometric approach on a panel of 32 SSA countries spanning the period 2004–2019, demonstrates that resource rents have a dumping effect on human progress. However, investing in human capital may avert the negative repercussions emanating from the natural resource-welfare link. Further, the study revealed the minimum threshold level for human capital score and tertiary school enrollment rate as 2.40 units and 23.21 %, respectively, necessary to avert the prosperity curse. To increase human prosperity, policymakers are recommended to increase investment in education in order to increase tertiary school enrollment above the estimated threshold and institute policies that will increase the average years the productive unit spent in schooling.

Impact of Channel Co-opetition and Taxes on a Multinational Firm’s Resilient Local Production Decision

Relevance: In this article, we focus on the decision of a multinational firm (MNF) on production strategies under the influence of national culture. The national culture of a country can result in a high preference for openness or self-reliance, and such a preference changes over time. The related government policies have a strong impact on the MNF’s decision whether to produce overseas and sell products in the domestic market or produce locally for domestic selling. Theory and methodology: We build a game-theoretical model comprising an MNF and a local retailer to investigate the MNF’s preference for production strategies with the consideration of the influence of national culture. Practice of the research: We find that when the factory establishment variable cost is low and the fixed cost is in a moderate range, the MNF’s preference over production strategies switches twice from local production to overseas production and then back to local production, as the channel substitutability increases. Interestingly, when the factory establishment variable cost is low and the fixed cost is high, the MNF’s preference is heavily dependent upon the tax disparity, exhibiting a threshold policy based on the channel substitutability. Our findings provide important insights for the MNFs into utilizing the national-culture-oriented tax policies and channel substitutability when establishing factories in foreign countries. We also reveal that the preferential local manufacturing policies originated from a high cultural preference for self-reliance may not attract more MNFs, which negatively impacts the policy effectiveness.

Fixed-time adaptive event-triggered control for multiagent systems with full-state constraints

This paper investigates the fixed-time adaptive event-triggered control problem for a class of nonlinear multiagent systems with full-state constraints. The problem of full-state constraints is solved for multiagent systems by utilising a one-to-one nonlinear mapping. The design conditions of the controllers are more easily satisfied than the existing barrier Lyapunov functions strategy. A fixed-time adaptive control scheme is proposed for unconstrained systems that are converted from constrained systems. In contract with the existing finite-time control schemes that rely on the initial states, this restriction condition can be removed in this paper. An improved event-triggered mechanism with an adaptable switching threshold is designed to provide flexible switching between fixed threshold and variable threshold policies, resulting in reduced execution and sampling. It is proved via the Lyapunov stability method that all signals of the closed-loop systems are semi-global practical fixed-time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results.

It’s Showtime: Live-Streaming E-commerce and Optimal Promotion Insertion Policy

Live-streaming e-commerce has gained tremendous success as a new form of business model over the past few years. Nevertheless, there has been scarce research examining the effect of exogenous stimulus-driven factors (i.e., social cues such as promotion coupons) on the profit of the live-streaming platform. We model the continuous evolvement of the aggregate viewer involvement level with geometric Brownian motion and investigate the optimal timing and depth of promotion insertion policy. Our findings reveal that the optimal promotion insertion policy for the live-streaming room is a threshold policy that consists of a start-to-promote threshold and an involvement target when the trend of the aggregate involvement level is not large and the promotion cost is not high. Under some scenarios, the promotion planning process is constrained by various business rules, such as the promotion depth being limited by a discrete set (e.g., integral multiples of [Formula: see text]). Although this problem involves more complex constraints, we analytically show that a variation of the abovementioned threshold policy is the optimal strategy among all feasible policies, i.e., when the aggregate viewer involvement drops below a certain level ([Formula: see text]), the live-streaming host promotes with the depth of the least integral multiple of [Formula: see text] to raise the viewer involvement level above [Formula: see text]. Finally, to examine the effectiveness of our proposed policy, we compare it with prevalent industry practices. The result shows that the proposed promotion insertion policy outperforms prevailing ones significantly in generating profit for the live-streaming room.

Learning-Based Optimal Admission Control in a Single-Server Queuing System

We consider a long-term average profit–maximizing admission control problem in an M/M/1 queuing system with unknown service and arrival rates. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue length of the system. Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24] shows that, if all the parameters of the model are known, then it is optimal to use a static threshold policy: admit if the queue length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full-information model of Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24]. We show that the algorithm achieves an O(1) regret when all optimal thresholds with full information are nonzero and achieves an [Formula: see text] regret for any specified [Formula: see text] in the case that an optimal threshold with full information is 0 (i.e., an optimal policy is to reject all arrivals), where N is the number of arrivals. Funding: A. Cohen is partially supported by the National Science Foundation [Grant DMS-2006305]. V. Subramanian is supported in part by the NSF [Grants CCF-2008130, ECCS-2038416, CNS-1955777, and CMMI-2240981].

On the Almost Threshold Policy for Multisourcing under Uncertain Supplies

On the Almost Threshold Policy for Multisourcing under Uncertain Supplies