Recent Advances in Accumulating Priority Queues

This thesis extends the theory underlying the Accumulating Priority Queue (APQ) in three directions. In the first, we present a multi-class multi-server accumulating priority queue with Poisson arrivals and heterogeneous services. The waiting time distributions for different classes have been derived. A conservation law for systems with heterogeneous servers has been studied. We also investigate an optimization problem to find the optimal level of heterogeneity in the multi-server system. Numerical investigations through simulation are carried out to validate the model. We next focus on a queueing system with Poisson arrivals, generally distributed service times and nonlinear priority accumulation functions. We start with an extension of the power-law APQ in Kleinrock and Finkelstein (1967), and use a general argument to show that there is a linear system of the form discussed in Stanford, Taylor, and Ziedins (2014) which has the same priority ordering of all customers present at any given instant in time, for any sample path. Beyond the power-law case, we subsequently characterize the class of nonlinear accumulating priority queues for which an equivalent linear APQ can be found, in the sense that the waiting time distributions for each of the classes are identical in both the linear and nonlinear systems. Many operational queuing systems must adhere to waiting time targets known as Key Performance Indicators (KPIs), particularly in health care applications. In the last aspect, we address an optimization problem to minimize the weighted average of the expected excess waiting time (WAE), so as to achieve the optimal performance of a system operating under KPIs. We then find that the Accumulating Priority queuing discipline is well suited to systems with KPIs, in that each class of customers progresses fairly towards timely access by its own waiting time limit. Due to the difficulties in minimizing the WAE, we introduce a surrogate objective function, the integrated weighted average excess (IWAE), which provides a useful proxy for WAE. Finally, we propose a rule of thumb in which patients in the various classes accumulate priority credit at a rate that is inversely proportional to their time limits

Statistical Applications in Healthcare Systems

This thesis consists of three contributing manuscripts related to waiting times with possible applications in health care. The first manuscript is inspired by a practical problem related to decision making in an emergency department (ED). As short-run predictions of ED censuses are particularly important for efficient allocation and management of ED resources we model ED changes and present estimations for short term (hourly) ED censuses at each time point. We present a Markov-chain based algorithm to make census predictions in near future. Considering the variation in arrival pattern and service requirements, we apply and compare three models which best describe our data. We provide hourly predictions up to 24 hours in a day which will provide suggestions to ED managers on how to prevent over-crowding in their system. We illustrate our approach using 22 months data obtained from the ED of a hospital in south western Ontario. The next two manuscripts extend the theory underlying the Accumulating Priority queues (APQs). We focus on the queues with two classes of customers and Poisson arrivals. The first work in this topic derives the stationary waiting time distributions for the class of lowest priority customers in an Affine Accumulating Priority queues (Affine APQs). APQs were first studied by Kleinrock (1964) and later revisited by Stanford et al (2014) where they obtained explicit solution for the Laplace Stieltjes Transform (LST) of the stationary waiting times for all classes of customers. All subsequent publications on APQs, have assumed that all arriving customers accumulate priority credits over time starting from the same initial value (assumed, without loss of generality, to be 0). Whereas, our model studies Affine APQs which assume different initial priorities (without loss of generality in a two-class setting we assume the lowest class starts with 0 credit and the higher class customers with positive credit a. In this work we determine the waiting time distributions for the lower class of customers with Poisson arrivals and general service and present some numerical results for special cases of M/M/1, M/M/c and M/D/1. Inspired by health care applications, we have also considered a particular optimization problem related to the Affine APQ model, in order to select the optimum accumulation rate which allows for the lowest class customers to meet their associated KPIs. We next focus on the Analysis of the Maximum priority processes in the context of Affine APQ. Maximum Priority Processes were first introduced in the context of APQs in Stanford et al (2014). We derive the LST of the stationary steady state distributions of the Maximum Priority Processes as recursive functions and derive the explicit solutions for the LSTs in classical APQ (i.e. a = 0). We employ this argument to present a new approach to determine the LST of waiting time distribution for an APQ with two-classes of customers under the M=M=1 discipline. Since the Analysis of the Maximum Priority Processes in this work is done for the general class of Affine APQs, it has provided the grounds for future researches to obtain the LST of the waiting time distributions in the Affine APQs

Telecommunications Networks

This book guides readers through the basics of rapidly emerging networks to more advanced concepts and future expectations of Telecommunications Networks. It identifies and examines the most pressing research issues in Telecommunications and it contains chapters written by leading researchers, academics and industry professionals. Telecommunications Networks - Current Status and Future Trends covers surveys of recent publications that investigate key areas of interest such as: IMS, eTOM, 3G/4G, optimization problems, modeling, simulation, quality of service, etc. This book, that is suitable for both PhD and master students, is organized into six sections: New Generation Networks, Quality of Services, Sensor Networks, Telecommunications, Traffic Engineering and Routing

How to Make the Most Productive Intervention in a Complex Economic System

Information about supply and demand propagates through supply chains in a queueing network with people and computers as batch information processors. As each batch processor delays propagation of information whilst pursuing optimal local decisions, the effect is delay and distortion of the information that is used to commit resources to actions in the supply chain. This thesis investigates the effect of delay and imperfect information as a source of error, to establish the case for change in research focus from optimal exploitation of physical constraints to optimal exploitation of information. In the context of real world supply chains, the thesis asks "How does one make the most productive intervention in a complex economic system?" and pursues a meta-intervention which perpetually minimises the discovered error-term. Evidence from literature indicates that agent-based modelling permits real-time peer-to-peer communication and distributed optimisation. Based on the literature the research project designs and develops an agent-based model which operates in real-time without batch-processes and can perform incremental multi-objective optimisation under realistic (chronologically progressive) conditions for decision making. The agent based model is then used to investigate two real-world supply chains, as case studies, which reveals a significant improvement of profitability and order-fulfilment. The thesis concludes that agent-based modelling is a very promising direction for "making the most productive intervention" as it reduces delay to a minimum. Finally it recommends that continuous improvement of decision making methods is a role better suited for humans, rather than operational decision making where computers cope much better with the high amount of detailed information

Advances in Computational Intelligence Applications in the Mining Industry

This book captures advancements in the applications of computational intelligence (artificial intelligence, machine learning, etc.) to problems in the mineral and mining industries. The papers present the state of the art in four broad categories: mine operations, mine planning, mine safety, and advances in the sciences, primarily in image processing applications. Authors in the book include both researchers and industry practitioners

Dynamic Analysis of Healthcare Service Delivery: Application of Lean and Agile Concepts

Hospitals are looking to industry for proven tools to manage increasingly complex operations and reduce costs simultaneously with improving quality of care. Currently, €˜lean€™ is the preferred system redesign paradigm, which focuses on removing process waste and variation. However, the high level of complexity and uncertainty inherent to healthcare make it incredibly challenging to remove variability and achieve the stable process rates necessary for lean redesign efforts to be effective. This research explores the use of an alternative redesign paradigm €“ €˜agile€™ €“ which was developed in manufacturing to optimize product delivery in volatile demand environments with highly variable customer requirements. €˜Agile€™ redesign focuses on increasing system responsiveness to customers through improved resource coordination and flexibility. System dynamics simulation and empirical case study are used to explore the impact of following an agile redesign approach in healthcare on service access, care quality, and cost; determine the comparative effectiveness of individual agile redesign strategies; and identify opportunities where lean methods can contribute to the creation of responsive, agile enterprises by analyzing hybrid lean-agile approaches. This dissertation contributes to the emerging literature on applying supply chain management concepts in healthcare, and opens a new path for designing healthcare systems that provide the right care, at the right time, to the right patient, at the lowest price