Dynamic Queue Research Articles

The role of EV fast charging in the urban context: An agent-based model approach

Using an agent-based simulation approach, this paper investigates the role of fast-charging infrastructure in urban environments. The simulation model tracks the spatial and temporal behaviours of electric vehicles (EVs), facilitating a comprehensive analysis of the deployment of charging infrastructure. Notably, the model incorporates non-parametric queuing dynamics, information-sharing regarding waiting times, and diverse agent characteristics, deepening insights into the subject matter. Drawing on a large-scale implementation in the municipalities of Frederiksberg and Copenhagen, the study advocates for adopting fast chargers by demonstrating several key points. Firstly, information-sharing significantly reduces waiting times, particularly within the fast-charging network, with potential reductions of up to 30% during peak demand periods. Secondly, larger fast-charging clusters comprising 10–14 outlets outperform smaller clusters, primarily due to reduced waiting times and enhanced prediction accuracy of waiting times, which is a consequence of the information-sharing. Thirdly, placement strategies based on unserved demand metrics yield superior outcomes than those solely driven by observed demand patterns. By effectively monitoring both observed and unmet demand, these strategies tend to better optimize charging infrastructure placement. These insights, which emerge from the sophisticated and heterogeneous nature of the simulation framework, highlight the value of information and unserved demand in this field.

Modelling and numerical simulation of sequencing strategies for connected and autonomous vehicles at signal-free intersections

The signal-free intersections employ connected and automated vehicle technology to manage vehicles passing through the intersection. Due to conflicting traffic flows in opposition directions, a proper sequencing of Connected and Autonomous Vehicles (CAVs) at signal-free intersections becomes critical to impacting intersection traffic performance. Based on an examination of CAV queueing rules under the most common sequencing strategies of First-Come-First-Serve (FCFS) and Longest-Queue-First (LQF), commonly employed as benchmarks for evaluating diverse innovative approaches to signal-free intersections, we propose a Dynamic-Queue-Service (DQS) strategy that is tailored to accommodate high traffic demand. To explicitly elucidate the impact of diverse traffic demand in conflicting directions on the queue uncertainty and stochasticity of CAVs, as well as to investigate how various sequencing strategies influence the equity of CAV traffic at signal-free intersections with regard to CAV queueing dynamics under different strategies, we have developed a double-input traffic queueing model and derived a range of metrics, including the queue length, delay, conditional queue length, and variance of queue length. In addition, for the three strategies, we performed a series of numerical simulations to investigate the queueing process of CAVs at signal-free intersections. Numerical results show that under different levels of traffic demand in the conflicting directions, the FCFS, LQF, and DQS strategies output diverse traffic queueing performances, and the DQS strategy is confirmed to be well-suited for the situation of high traffic demand in both conflicting directions.

Modeling and evaluating the impact of variable bus lane on isolated signal intersection performance

Dedicated Bus Lane (DBL) is a typical strategy to ensure priority for public transportation. However, when the frequency of bus departures is low, the DBL often remains vacant, reducing the efficiency of traffic utilization. Variable bus lane (VBL) strategy allows for the provision of service to social vehicles in specific scenarios, aiming to alleviate traffic congestion and improve emission efficiency at intersections. To analyze the impact of this strategy on dynamic queuing behavior and traffic efficiency at an isolated intersection, this paper proposes a multidimensional stochastic queuing model. The model incorporates various factors such as traffic demand, signal timing, bus arrival time, and the length of the variable area at intersections. By examining the steady-state distribution of queue length and calculating performance indicators, the effectiveness of VBL in improving intersection performance is evaluated. Numerical simulations have demonstrated that the proposed model accurately describes the vehicle queuing process at intersections under different conditions. Theoretical analysis confirms that the implementation of VBL strategy can effectively improve traffic efficiency at intersections and minimize the queue length of vehicles.

Optimizing Restaurant Queue Management: A Simulation-Based Approach Using Arena Software

Examining the effectiveness of models in terms of utilization and waiting time is one of the anticipated benefits of analyzing queuing systems. This study uses Arena simulation software to examine the queue system of a particular restaurant. The primary objective is to assess and enhance the restaurant’s service efficiency through the modelling of customer arrivals, service procedures, and queue dynamics. Data on customer arrivals and service times were collected for the restaurant’s current system. The necessary expressions were developed from the observed data using the input analyzer. A conceptual model of the original queuing system was created, and two alternative Arena models were developed to reduce customer waiting times in the restaurant. The developed models were run to evaluate their performance. During a 24-hour simulation study, the average waiting time in the overall model was found to be 24.49 minutes, with a maximum of 48.69 minutes. The waiting time for server 1 was 25.30 minutes, for server 2 was 23.27 minutes, for server 3 was 25.11 minutes, and for server 4 was 22.30 minutes. The number of customers in line at server 1 was 12.65, at server 2 was 6.98, at server 3 was 8.29, and at server 4 was 8.25. Resource utilization was 57% for server 1, 35% for server 2, 27% for server 3, and 15% for server 4. By decreasing the queuing length and average waiting time in the restaurant, customer satisfaction can be increased, leading to a reduction in time wasted. The findings indicate significant potential for improving overall service quality and reducing client wait times. This research provides valuable insights for restaurant managers seeking to enhance customer satisfaction and operational efficiency.

Subtype-Aware Dynamic Unsupervised Domain Adaptation.

Unsupervised domain adaptation (UDA) has been successfully applied to transfer knowledge from a labeled source domain to target domains without their labels. Recently introduced transferable prototypical networks (TPNs) further address class-wise conditional alignment. In TPN, while the closeness of class centers between source and target domains is explicitly enforced in a latent space, the underlying fine-grained subtype structure and the cross-domain within-class compactness have not been fully investigated. To counter this, we propose a new approach to adaptively perform a fine-grained subtype-aware alignment to improve the performance in the target domain without the subtype label in both domains. The insight of our approach is that the unlabeled subtypes in a class have the local proximity within a subtype while exhibiting disparate characteristics because of different conditional and label shifts. Specifically, we propose to simultaneously enforce subtype-wise compactness and class-wise separation, by utilizing intermediate pseudo-labels. In addition, we systematically investigate various scenarios with and without prior knowledge of subtype numbers and propose to exploit the underlying subtype structure. Furthermore, a dynamic queue framework is developed to evolve the subtype cluster centroids steadily using an alternative processing scheme. Experimental results, carried out with multiview congenital heart disease data and VisDA and DomainNet, show the effectiveness and validity of our subtype-aware UDA, compared with state-of-the-art UDA methods.

Deep attentive survival analysis in limit order books: estimating fill probabilities with convolutional-transformers

One of the key decisions in execution strategies is the choice between a passive (liquidity providing) or an aggressive (liquidity taking) order to execute a trade in a limit order book (LOB). Essential to this choice is the fill probability of a passive limit order placed in the LOB. This paper proposes a deep learning method to estimate the filltimes of limit orders posted in different levels of the LOB. We develop a novel model for survival analysis that maps time-varying features of the LOB to the distribution of filltimes of limit orders. Our method is based on a convolutional-Transformer encoder and a monotonic neural network decoder. We use proper scoring rules to compare our method with other approaches in survival analysis, and perform an interpretability analysis to understand the informativeness of features used to compute fill probabilities. Our method significantly outperforms those typically used in survival analysis literature. Finally, we carry out a statistical analysis of the fill probability of orders placed in the order book (e.g. within the bid-ask spread) for assets with different queue dynamics and trading activity.

USER: Unified Semantic Enhancement With Momentum Contrast for Image-Text Retrieval.

As a fundamental and challenging task in bridging language and vision domains, Image-Text Retrieval (ITR) aims at searching for the target instances that are semantically relevant to the given query from the other modality, and its key challenge is to measure the semantic similarity across different modalities. Although significant progress has been achieved, existing approaches typically suffer from two major limitations: (1) It hurts the accuracy of the representation by directly exploiting the bottom-up attention based region-level features where each region is equally treated. (2) It limits the scale of negative sample pairs by employing the mini-batch based end-to-end training mechanism. To address these limitations, we propose a Unified Semantic Enhancement Momentum Contrastive Learning (USER) method for ITR. Specifically, we delicately design two simple but effective Global representation based Semantic Enhancement (GSE) modules. One learns the global representation via the self-attention algorithm, noted as Self-Guided Enhancement (SGE) module. The other module benefits from the pre-trained CLIP module, which provides a novel scheme to exploit and transfer the knowledge from an off-the-shelf model, noted as CLIP-Guided Enhancement (CGE) module. Moreover, we incorporate the training mechanism of MoCo into ITR, in which two dynamic queues are employed to enrich and enlarge the scale of negative sample pairs. Meanwhile, a Unified Training Objective (UTO) is developed to learn from mini-batch based and dynamic queue based samples. Extensive experiments on the benchmark MSCOCO and Flickr30K datasets demonstrate the superiority of both retrieval accuracy and inference efficiency. For instance, compared with the existing best method NAAF, the metric R@1 of our USER on the MSCOCO 5K Testing set is improved by 5% and 2.4% on caption retrieval and image retrieval without any external knowledge or pre-trained model while enjoying over 60 times faster inference speed. Our source code will be released at https://github.com/zhangy0822/USER.

A dynamic queuing model based distributed task offloading algorithm using deep reinforcement learning in mobile edge computing

A dynamic queuing model based distributed task offloading algorithm using deep reinforcement learning in mobile edge computing

Maximum Throughput Dispatch for Shared Autonomous Vehicles Including Vehicle Rebalancing

Shared autonomous vehicles (SAVs) provide on demand point-to-point transportation for passengers. This service has been extensively studied using dispatch heuristics and agent based simulations of large urban areas. However, these approaches make no mathematical guarantees of the passenger throughput for the SAV network. This study builds on the dynamic queuing model design of Kang and Levin which provides a maximum stability dispatch policy for SAVs. This model is extended to include rebalancing of empty vehicles to regions of high demand. The modified dispatch policy is proven to maximize throughput. Simulation results show that this dispatch policy reduces waiting times (between vehicle dispatch and passenger pickup) compared to the original formulation. However, vehicle time traveling empty increases in some scenarios. Simulation results also show that rebalancing often reduces passenger waiting times, but not when too many vehicles rebalance at once and are not available for dispatch.

Upstream-gating merge-control for maximising network capacity: With an application to urban traffic management

This paper considers a simple network with a merge and a downstream bottleneck, which corresponds to a very congested part of the City of York road network - Gillygate. We focus on “upstream-gating” control strategies which hold traffic back at traffic signals just ahead of the merge to prevent the formation of a queue at a downstream bottleneck; and we also consider different ways of further, additionally, controlling the two inflows to the merge. We show, by considering the simple network, that if the added upstream merge-control uses only flows to control the two approaches to the merge then equilibrium may not exist. For example, with the “zipper” rule (which equalises the two inflows at the merge) an equilibrium cannot exist for certain feasible demands on this network. On the other hand, we show that adding upstream merge-control which equalises the two delays felt at the merge allows an equilibrium for all feasible demands on this network, and so maximises the network capacity, notwithstanding the upstream gating. This suggests that, in general, delays should probably be used to control merges and downstream queues, rather than only flows, if network capacity is to be maximised. This observation may help the design of good control strategies, using both flows and delays, for upstream-gating designed to remove or reduce queues at specific downstream locations. The equilibrium analysis in our example is supported by (i) a dynamic analysis allowing for the dynamic growth of queues in the example network and (ii) real-life results of upstream-gating applied to Gillygate in York (UK) which provided motivation for this paper. The analysis here makes reasonable allowance for the spatial extent of queues but does not consider within-cycle or cycle-to-cycle queueing dynamics.

Self-supervised contrastive speaker verification with nearest neighbor positive instances

Self-supervised contrastive learning (SSCL) has achieved a great success in speaker verification (SV). All recent works treat within-utterance speaker embeddings (SE) to be positive instances, encouraging them to be as close as possible. However, positive instances from the same utterance have similar channel and related semantic information, which are difficult to distinguish from the speaker features. Moreover, these positive instances can only provide limited variances in a certain speaker. To tackle the above problems, we propose to use nearest neighbor (NN) positive instances for training, which are selected from a dynamic queue. The NN positive instances can provide different channel and semantic information, increasing the variances in a certain speaker. Our proposed method are validated through comprehensive experiments on VoxCeleb and CNCeleb1 datasets, demonstrating its effectiveness in improving both SSCL and fine-tuning results. Additionally, our SSCL model outperforms supervised training model in cross-dataset testing due to the use of massive unlabeled data.

MAESTRO-X: Distributed Orchestration of Rotary-Wing UAV-Relay Swarms

This work details a scalable framework to orchestrate a swarm of rotary-wing UAVs serving as cellular relays to facilitate beyond line-of-sight connectivity and traffic offloading for ground users. First, a Multiscale Adaptive Energyconscious Scheduling and TRajectory Optimization (MAESTRO) framework is developed for a single UAV. Aiming to minimize the time-averaged latency to serve user requests, subject to an average UAV power constraint, it is shown that the optimization problem can be cast as a semi-Markov decision process, and exhibits a multiscale structure: outer actions on radial wait velocities and terminal service positions minimize the longterm delay-power trade-off, optimized via value iteration; given these outer actions, inner actions on angular wait velocities and service trajectories minimize a short-term delay-energy cost; finally, rate adaptation is embedded along the trajectory to leverage air-to-ground channel propagation conditions. A novel hierarchical competitive swarm optimization scheme is developed in the inner optimization, to devise high-resolution trajectories via iterative pair-wise updates. Next, MAESTRO is eXtended to UAV swarms (MAESTRO-X) via scalable policy replication, enabled by a decentralized command-and-control network augmented with: (1) spread maximization to proactively position UAVs to serve future requests; (2) consensus-driven conflict resolution to orchestrate scheduling decisions based on delay-energy costs including queuing dynamics; (3) adaptive frequency reuse to improve spectrum utilization across the network; and (4) a piggybacking mechanism allowing UAVs to serve multiple ground users simultaneously. Numerical evaluations show that, for user requests of 10 Mbits, generated according to a Poisson arrival process with rate 0.2 req/min/UAV, single-agent MAESTRO offers 3.8× faster service than a high-altitude platform and 29% faster than a static UAV deployment; moreover, for a swarm of 3 UAV-relays, MAESTRO-X delivers data payloads 4.7× faster than a successive convex approximation scheme; and remarkably, a single UAV optimized via MAESTRO outclasses 3 UAVs optimized via a deep-Q network by 38%.

FMS-dispatch: a fast maximum stability dispatch policy for shared autonomous vehicles including exiting passengers under stochastic travel demand

Shared autonomous vehicles (SAVs) are a fleet of autonomous taxis that provide point-to-point transportation services for travellers, and have the potential to reshape the nature of the transportation market in terms of operational costs, environmental outcomes, increased tolling efficiency, etc. However, the number of waiting passengers could become arbitrarily large when the fleet size is too small for travel demand, which could cause an unstable network. An unstable network will make passengers impatient and some people will choose some other alternative travel modes, such as metro or bus. To achieve stable and reliable SAV services, this study designs a dynamic queueing model for waiting passengers and provides a fast maximum stability dispatch policy for SAVs when the average number of waiting for passengers is bounded in expectation, which is analytically proven by the Lyapunov drift techniques. After that, we expand the stability proof to a more realistic scenario accounting for the existence of exiting passengers. Unlike previous work, this study considers exiting passengers in stability analyses for the first time. Moreover, the maximum stability of the network doesn't require a planning horizon based on the proposed dispatch policy. The simulation results show that the proposed dispatch policy can ensure the waiting queues and the number of exiting passengers remain bound in several experimental settings.

Latency-Aware Multi-Antenna SWIPT System With Battery-Constrained Receivers

Power splitting (PS) based simultaneous wireless information and power transfer (SWIPT) is considered in a multi-user multiple-input-single-output broadcast scenario. Specifically, we focus on jointly configuring the transmit beamforming vectors and receive PS ratios to minimize the total transmit energy of the base station under the user-specific latency and energy harvesting (EH) requirements. The battery depletion phenomenon is avoided by preemptively incorporating information regarding the receivers' battery state and EH fluctuations into the resource allocation design. The resulting time-average sum-power minimization problem is temporally correlated, non-convex (including mutually coupled latency-battery queue dynamics), and in general intractable. We use the Lyapunov optimization framework and derive a dynamic control algorithm to transform the original problem into a sequence of deterministic and independent subproblems, which are then solved via two alternative approaches: i) semidefinite relaxation combined with fractional programming, and ii) successive convex approximation. Furthermore, we design a low-complexity closed-form iterative algorithm exploiting the Karush-Kuhn-Tucker optimality conditions for a specific scenario with delay bounded batteryless receivers. Numerical results provide insights on the robustness of the proposed design to realize an energy-efficient SWIPT system while ensuring latency and EH requirements in a time dynamic mobile access network.

Traffic Breakdown Probability Estimation for Mixed Flow of Autonomous Vehicles and Human Driven Vehicles.

Automated vehicles are expected to greatly boost traffic efficiency. However, how to estimate traffic breakdown probability for the mixed flow of autonomous vehicles and human driven vehicles around ramping areas remains to be answered. In this paper, we propose a stochastic temporal queueing model to reliably depict the queue dynamics of mixed traffic flow at ramping bottlenecks. The new model is a specified Newell's car-following model that allows two kinds of vehicle velocities and first-in-first-out (FIFO) queueing behaviors. The jam queue join time is supposed to be a random variable for human driven vehicles but a constant for automated vehicles. Different from many known models, we check the occurrence of significant velocity drop along the road instead of examining the duration of the simulated jam queue so as to avoid drawing the wrong conclusions of traffic breakdown. Monte Carlo simulation results show that the generated breakdown probability curves for pure human driven vehicles agree well with empirical observations. Having noticed that various driving strategy of automated vehicles exist, we carry out further analysis to show that the chosen car-following strategy of automated vehicles characterizes the breakdown probabilities. Further tests indicate that when the penetration rate of automated vehicles is larger than 20%, the traffic breakdown probability curve of the mixed traffic will be noticeably shifted rightward, if an appropriate car-following strategy is applied. This indicates the potential benefit of automated vehicles in improving traffic efficiency.

MoCo4SRec: A momentum contrastive learning framework for sequential recommendation

Sequential recommendation (SR) is an essential component of modern recommender systems. It models the dynamic interest of users based on their sequential interactions. Recently, several studies have utilized sequential deep learning models such as Recurrent Neural Networks and Transformers to facilitate sequential recommendation, which shows promising results. Inspired by the rise of contrastive learning techniques, some methods are devoted to enhance sequential deep learning models by designing contrastive learning loss on self-supervised signals. However, there are still a number of obstacles that make it challenging to efficiently learn user representations by contrastive learning. These issues include, but are not limited to, data sparsity, noisy data, and sampling bias (e.g., false negative), particularly in complex, parameter-intensive models.In light of these challenges, we examine how to deal with data sparsity and noisy data by implementing contrastive Self-Supervised Learning (SSL) and Momentum Contrast (MoCo) to the sequential recommendation. Except typical in-batch negatives, our basic idea is to maintain a dynamic queue to expand negative samples with a moving-averaged encoder. After being augmented by sequence-level and embedding-level methods, the representations from all historical encoder output are pushed into the dynamic queue, which usually leads to sampling bias when potential positives in the queue are used as expanded negative samples in contrastive learning. To tackle this issue, we integrate momentum updating mechanism with a novel instance weighting mechanism to penalize false negatives and guarantee the model’s efficacy. To this end, we introduce a fresh framework called Momentum Contrastive Learning Framework for Sequential Recommendation (MoCo4SRec). Experiments on eight real-world datasets demonstrate how the suggested strategy might boost model performance over current benchmarks by adopting improved user representations.

Modelling and assessment of the arrival and departure process at the terminal area: A case study of Chennai international airport

Airport and terminal area traffic congestion is a growing concern of the air traffic management (ATM) system. A major step towards mitigating the impacts of congestion is understanding the fluctuating arrival and departure process at airports. Exploring the intrinsic time-varying nature of the arrival and departure process enhances this understanding, hence, is instrumental in formulating operational policies for managing airport capacity and delays. This paper presents a data-driven statistical framework to investigate, understand, and model the time-varying fluctuations in the aircraft arrival and departure process. We have considered one-month data obtained from Chennai international airport operations for this study. The dynamic evolution and fluctuation characteristics of arrivals and departures are conducted using Seasonality and Multifractal Detrended Fluctuation Analysis. Six theoretical probability distributions were used to fit the observed aircraft arrivals and departures at different temporal scales using the maximum likelihood estimation method. This study also develops a G1(t)/G2(t)/KFirst Come First Serve dynamic queuing model for a day’s arrival and departure process. The results suggest that arrival and departure processes exhibit weak but visible multifractal characteristics. Fluctuations are higher at a smaller temporal scale compared to a larger scale, and the probability distributions of arrival and departure are also time-varying. The framework has universal applicability, and the insights have important implications for operational policies on the air transportation workforce and infrastructure management.

Quality of Service (QoS) Performance Analysis in a Traffic Engineering Model for Next-Generation Wireless Sensor Networks

Quality of Service (QoS) refers to techniques that function on a network to dependably execute high-priority applications and traffic reliably run high-priority applications and traffic even when the network’s capacity is limited. It is expected that data transmission over next-generation WSNs (Wireless Sensor Networks) 5G (5th generation) and beyond will increase significantly, especially for multimedia content such as video. Installing multiple IoT (Internet of Things refers to the network of devices that are all connected to each other) nodes on top of 5G networks makes the design more challenging. Maintaining a minimal level of service quality becomes more challenging as data volume and network density rise. QoS is critical in modern networks because it ensures critical performance metrics and improves end-user experience. Every client attempts to fulfill QoS access needs by selecting the optimal access device(s). Controllers will then identify optimum routes to meet clients’ core QoS needs in their core network. QoS-aware delivery is one of the most important aspects of wireless communications. Various models are proposed in the literature; however, an adaptive buffer size according to service type, priority, and incoming communication requests is required to ensure QoS-aware wireless communication. This article offers a hybrid end-to-end QoS delivery method involving customers and controllers and proposes a QoS-aware service delivery model for various types of communication with an adaptive buffer size according to the priority of the incoming service requests. For this purpose, this paper evaluates various QoS delivery models devised for service delivery in real time over IP networks. Multiple vulnerabilities are outlined that weaken QoS delivery in different models. Performance optimization is needed to ensure QoS delivery in next-generation WSN networks. This paper addresses the shortcomings of the existing service delivery models for real-time communication. An efficient queuing mechanism is adopted that assigns priorities based on input data type and queue length. This queuing mechanism ensures QoS efficiency in limited bandwidth networks and real-time traffic. The model reduces the over-provisioning of resources, delay, and packet loss ratio. The paper contributes a symmetrically-designed traffic engineering model for QoS-ensured service delivery for next-generation WSNs. A dynamic queuing mechanism that assigns priorities based on input data type and queue length is proposed to ensure QoS for wireless next-generation networks. The proposed queuing mechanism discusses topological symmetry to ensure QoS efficiency in limited bandwidth networks with real-time communication. The experimental results describe that the proposed model reduces the over-provisioning of resources, delay, and packet loss ratio.

An Intelligent Deterministic Scheduling Method for Ultralow Latency Communication in Edge Enabled Industrial Internet of Things

Edge enabled Industrial Internet of Things (IIoT) platform is of great significance to accelerate the development of smart industry. However, with the dramatic increase in real-time IIoT applications, it is a great challenge to support fast response time, low latency, and efficient bandwidth utilization. To address this issue, time sensitive network (TSN) is recently researched to realize low latency communication via deterministic scheduling. To the best of our knowledge, the combinability of multiple flows, which can significantly affect the scheduling performance, has never been systematically analyzed before. In this article, we first analyze the combinability problem. Then, a noncollision theory based deterministic scheduling (NDS) method is proposed to achieve ultralow latency communication for the time-sensitive flows. Moreover, to improve bandwidth utilization, a dynamic queue scheduling (DQS) method is presented for the best-effort flows. Experiment results demonstrate that NDS/DQS can well support deterministic ultralow latency services and guarantee efficient bandwidth utilization.

The False Economy of Seeking to Eliminate Delayed Transfers of Care: Some Lessons from Queueing Theory.

It is a stated ambition of many healthcare systems to eliminate delayed transfers of care (DTOCs) between acute and step-down community services. This study aims to demonstrate how, counter to intuition, pursual of such a policy is likely to be uneconomical, as it would require large amounts of community capacity to accommodate even the rarest of demand peaks, leaving much capacity unused for much of the time. Some standard results from queueing theory-a mathematical discipline for considering the dynamics of queues and queueing systems-are used to provide a model of patient flow from the acute to community setting. While queueing models have a track record of application in healthcare, they have not before been used to address this question. Results show that 'eliminating' DTOCs is a false economy: the additional community costs required are greater than the possible acute cost saving. While a substantial proportion of DTOCs can be attributed to inefficient use of resources, the remainder can be considered economically essential to ensuring cost-efficient service operation. For England's National Health Service (NHS), our modelling estimates annual cost savings of £117m if DTOCs are reduced to the 12% of current levels that can be regarded as economically essential. This study discourages the use of 'zero DTOC' targets and instead supports an assessment based on the specific characteristics of the healthcare system considered.