Sorting with Robots: where to drop off the parcel?

This paper presents a method for assigning destinations to drop off points in robotic sorting systems, taking into account robot congestion

An Analytical Approximation of the Joint Distribution of Aggregate Queue-Lengths in an Urban Network

Traditional queueing network models assume infinite queue capacities due to the complexity of capturing interactions between finite capacity queues. Accounting for this correlation can help explain how congestion propagates through a network. Joint queue-length distribution can be accurately estimated through simulation. Nonetheless, simulation is a computationally intensive technique, and its use for optimization purposes is challenging. By modeling the system analytically, we lose accuracy but gain efficiency and adaptability and can contribute novel information to a variety of congestion related problems, such as traffic signal optimization. We formulate an analytical technique that combines queueing theory with aggregation-disaggregation techniques in order to approximate the joint network distribution, considering an aggregate description of the network. We propose a stationary formulation. We consider a tandem network with three queues. The model is validated by comparing the aggregate joint distribution of the three queue system with the exact results determined by a simulation over several scenarios. It derives a good approximation of aggregate joint distributions

Capacity planning of prisons in the Netherlands

In this paper we describe a decision support system developed to help in assessing the need for various type of prison cells. In particular we predict the probability that a criminal has to be sent home because of a shortage of cells. The problem is modelled through a queueing network with blocking after service. We focus in particular on the new analytical method to solve this network

A tractable analytical model for large-scale congested protein synthesis networks

This paper presents an analytical model, based on finite capacity queueing network theory, to evaluate congestion in protein synthesis networks. These networks are modeled as a set of single server bufferless queues in a tandem topology. This model proposes a detailed state space formulation, which provides a fine description of congestion and contributes to a better understanding of how the protein synthesis rate is deteriorated. The model approximates the marginal stationary distributions of each queue. It consists of a system of linear and quadratic equations that can be decoupled. The numerical performance of this method is evaluated for networks with up to 100,000 queues, considering scenarios with various levels of congestion. It is a computationally efficient and scalable method that is suitable to evaluate congestion for large-scale networks. Additionally, this paper generalizes the concept of blocking: blocking events can be triggered by an arbitrary set of queues. This generalization allows for a variety of blocking phenomena to be modeled.Swiss National Science Foundation (Grant 205320-117581

A tractable analytical model for large-scale congested protein synthesis networks

This paper presents a finite capacity queueing network model to evaluate congestion in protein synthesis networks. These networks are modeled as single server bufferless queues in a tandem topology. The model approximates the marginal stationary distributions of each queue. It consists of a system of linear and quadratic equations that can be decoupled. It is therefore a tractable and scalable method that is suitable for large-scale networks. This model proposes a detailed state space formulation, which provides a fine description of congestion and contributes to a better understanding of how the protein synthesis rate is deteriorated. This paper also generalizes the concept of blocking: blocking events can be triggered by an arbitrary set of queues. The numerical performance of this method is evaluated for networks with up to 100,000 queues, considering scenarios with various levels of congestion. Since tandem topology networks are of interest for a variety of application fields, the numerical efficiency and scalability of this model is of wide interest

Throughput and Latency in Finite-Buffer Line Networks

This work investigates the effect of finite buffer sizes on the throughput capacity and packet delay of line networks with packet erasure links that have perfect feedback. These performance measures are shown to be linked to the stationary distribution of an underlying irreducible Markov chain that models the system exactly. Using simple strategies, bounds on the throughput capacity are derived. The work then presents two iterative schemes to approximate the steady-state distribution of node occupancies by decoupling the chain to smaller queueing blocks. These approximate solutions are used to understand the effect of buffer sizes on throughput capacity and the distribution of packet delay. Using the exact modeling for line networks, it is shown that the throughput capacity is unaltered in the absence of hop-by-hop feedback provided packet-level network coding is allowed. Finally, using simulations, it is confirmed that the proposed framework yields accurate estimates of the throughput capacity and delay distribution and captures the vital trends and tradeoffs in these networks.Comment: 19 pages, 14 figures, accepted in IEEE Transactions on Information Theor

Modeling Patient Flow in a Network of Intensive Care Units (ICUs)

Beginning in 2012, the Department of Health and Human Services (HHS) started adjusting payment for specific conditions by 30% for hospitals with 30-day patient readmission rates higher than the 75th percentile (HHS.gov, 2011). Furthermore, starting in 2013, HHS requires hospitals to publish their readmission rates (HHS.gov, 2011). It is also estimated that by 2013, healthcare expenditures in the United States will account for 18.7% of the Gross Domestic Product (GDP) (Centers of Medicare and Medicaid Services and US Bureau of Census, 2004). Yet the US healthcare system still suffers from congestion and rising costs as illustrated by hospital congestion. One way to reduce congestion and improve patient flow in the hospital is by modeling patient flow. Using queueing theory, we determined the steady state solution of an open queueing network, while accounting for instantaneous and delayed feedback. We also built a discrete event simulation model of patient flow in a network of Intensive Care Units (ICUs), while considering instantaneous and delayed readmissions, and validated the model using real patient flow data that was collected over four years. In addition, we compared several statistical and data mining techniques in terms of classifying patient status at discharge from the ICU (highly imbalanced data) and identify methods that perform the best. Our work has several contributions. Modeling patient flow while accounting for instantaneous and delayed feedback is considered a major contribution, as we are unaware of any patient flow study that has done so. Validating the discrete event simulation model allows for the implementation and application of the model in the real world by unit managers and administrators. The simulation model could be used to test different scenarios of patient flow, and to identify optimal resource allocation strategies in terms of number of beds and/or staff schedules in order to maximize patient throughput, reduce patient wait time and improve patients’ outcome. Moreover, identifying high risk patients who are more likely to die in the ICU ensures that those patients are receiving appropriate and timely care, so their risk of death is reduced

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277