A Bayesian Approach to Parameter Inference in Queueing Networks

The application of queueing network models to real-world applications often involves the task of estimating the service demand placed by requests at queueing nodes. In this article, we propose a methodology to estimate service demands in closed multiclass queueing networks based on Gibbs sampling. Our methodology requires measurements of the number of jobs at resources and can accept prior probabilities on the demands. Gibbs sampling is challenging to apply to estimation problems for queueing networks since it requires one to efficiently evaluate a likelihood function on the measured data. This likelihood function depends on the equilibrium solution of the network, which is difficult to compute in closed models due to the presence of the normalizing constant of the equilibrium state probabilities. To tackle this obstacle, we define a novel iterative approximation of the normalizing constant and show the improved accuracy of this approach, compared to existing methods, for use in conjunction with Gibbs sampling. We also demonstrate that, as a demand estimation tool, Gibbs sampling outperforms other popular Markov Chain Monte Carlo approximations. Experimental validation based on traces from a cloud application demonstrates the effectiveness of Gibbs sampling for service demand estimation in real-world studies

Memory-aware sizing for in-memory databases

In-memory database systems are among the technological drivers of big data processing. In this paper we apply analytical modeling to enable efficient sizing of in-memory databases. We present novel response time approximations under online analytical processing workloads to model thread-level forkjoin and per-class memory occupation.We combine these approximations with a non-linear optimization program to minimize memory swapping in in-memory database clusters. We compare our approach with state-of-the-art response time approximations and trace-driven simulation using real data from an SAP HANA in-memory system and show that our optimization model is significantly more accurate than existing approaches at similar computational costs

Information-theoretic and stochastic methods for managing the quality of service and satisfaction in healthcare systems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research investigates and develops a new approach to the management of service quality with the emphasis on patient and staff satisfaction in the healthcare sector. The challenge of measuring the quality of service in healthcare requires us to view the problem from multiple perspectives. At the philosophical level, the true nature of quality is still debated; at the psychological level, an accurate conceptual representation is problematic; whilst at the physical level, an accurate measurement of the concept still remains elusive to practitioners and academics. This research focuses on the problem of quality measurement in the healthcare sector. The contributions of this research are fourfold: Firstly, it argues that from the technological point of view the research to date into quality of service in healthcare has not considered methods of real-time measurement and monitoring. This research identifies the key elements that are necessary for developing a real-time quality monitoring system for the healthcare environment.Secondly, a unique index is proposed for the monitoring and improvement of healthcare performance using information-theoretic entropy formalism. The index is formulated based on five key performance indicators and was tested as a Healthcare Quality Index (HQI) based on three key quality indicators of dignity, confidence and communication in an Accident and Emergency department. Thirdly, using an M/G/1 queuing model and its underlying Little’s Law, the concept of Effective Satisfaction in healthcare has been proposed. The concept is based on a Staff-Patient Satisfaction Relation Model (S-PSRM) developed using a patient satisfaction model and an empirically tested model developed for measuring staff satisfaction with workload (service time). The argument is presented that a synergy between patient satisfaction and staff satisfaction is the key to sustainable improvement in healthcare quality. The final contribution is the proposal of a Discrete Event Simulation (DES) modelling platform as a descriptive model that captures the random and stochastic nature of healthcare service provision process to prove the applicability of the proposed quality measurement models

Delay QoS Provisioning and Optimal Resource Allocation for Wireless Networks

Recent years have witnessed a significant growth in wireless communication and networking due to the exponential growth in mobile applications and smart devices, fueling unprecedented increase in both mobile data traffic and energy demand. Among such data traffic, real-time data transmissions in wireless systems require certain quality of service (QoS) constraints e.g., in terms of delay, buffer overflow or packet drop/loss probabilities, so that acceptable performance levels can be guaranteed for the end-users, especially in delay sensitive scenarios, such as live video transmission, interactive video (e.g., teleconferencing), and mobile online gaming. With this motivation, statistical queuing constraints are considered in this thesis, imposed as limitations on the decay rate of buffer overflow probabilities. In particular, the throughput and energy efficiency of different types of wireless network models are analyzed under QoS constraints, and optimal resource allocation algorithms are proposed to maximize the throughput or minimize the delay. In the first part of the thesis, the throughput and energy efficiency analysis for hybrid automatic repeat request (HARQ) protocols are conducted under QoS constraints. Approximations are employed for small QoS exponent values in order to obtain closed-form expressions for the throughput and energy efficiency metrics. Also, the impact of random arrivals, deadline constraints, outage probability and QoS constraints are studied. For the same system setting, the throughput of HARQ system is also analyzed using a recurrence approach, which provides more accurate results for any value of the QoS exponent. Similarly, random arrival models and deadline constraints are considered, and these results are further extended to the finite-blocklength coding regime. Next, cooperative relay networks are considered under QoS constraints. Specifically, the throughput performance in the two-hop relay channel, two-way relay channel, and multi-source multi-destination relay networks is analyzed. Finite-blocklength codes are considered for the two-hop relay channel, and optimization over the error probabilities is investigated. For the multi-source multi-destination relay network model, the throughput for both cases of with and without CSI at the transmitter sides is studied. When there is perfect CSI at the transmitter, transmission rates can be varied according to instantaneous channel conditions. When CSI is not available at the transmitter side, transmissions are performed at fixed rates, and decoding failures lead to retransmission requests via an ARQ protocol. Following the analysis of cooperative networks, the performance of both half-duplex and full-duplex operations is studied for the two-way multiple input multiple output (MIMO) system under QoS constraints. In full-duplex mode, the self-interference inflicted on the reception of a user due to simultaneous transmissions from the same user is taken into account. In this setting, the system throughput is formulated by considering the sum of the effective capacities of the users in both half-duplex and full-duplex modes. The low signal to noise ratio (SNR) regime is considered and the optimal transmission/power-allocation strategies are characterized by identifying the optimal input covariance matrices. Next, mode selection and resource allocation for device-to-device (D2D) cellular networks are studied. As the starting point, ransmission mode selection and resource allocation are analyzed for a time-division multiplexed (TDM) cellular network with one cellular user, one base station, and a pair of D2D users under rate and QoS constraints. For a more complicated setting with multiple cellular and D2D users, two joint mode selection and resource allocation algorithms are proposed. In the first algorithm, the channel allocation problem is formulated as a maximum-weight matching problem, which can be solved by employing the Hungarian algorithm. In the second algorithm, the problem is divided into three subproblems, namely user partition, power allocation and channel assignment, and a novel three-step method is proposed by combining the algorithms designed for the three subproblems. In the final part of the thesis, resource allocation algorithms are investigated for content delivery over wireless networks. Three different systems are considered. Initially, a caching algorithm is designed, which minimizes the average delay of a single-cell network. The proposed algorithm is applicable in settings with very general popularity models, with no assumptions on how file popularity varies among different users, and this algorithm is further extended to a more general setting, in which the system parameters and the distributions of channel fading change over time. Next, for D2D cellular networks operating under deadline constraints, a scheduling algorithm is designed, which manages mode selection, channel allocation and power maximization with acceptable complexity. This proposed scheduling algorithm is designed based on the convex delay cost method for a D2D cellular network with deadline constraints in an OFDMA setting. Power optimization algorithms are proposed for all possible modes, based on our utility definition. Finally, a two-step intercell interference (ICI)-aware scheduling algorithm is proposed for cloud radio access networks (C-RANs), which performs user grouping and resource allocation with the goal of minimizing delay violation probability. A novel user grouping algorithm is developed for the user grouping step, which controls the interference among the users in the same group, and the channel assignment problem is formulated as a maximum-weight matching problem in the second step, which can be solved using standard algorithms in graph theory

Alternate Samplingmethods for Estimating Multivariate Normal Probabilities

We study the performance of alternative sampling methods for estimating multivariate normal probabilities through the GHK simulator. The sampling methods are randomized versions of some quasi-Monte Carlo samples (Halton, Niederreiter, Niederreiter-Xing sequences and lattice points) and some samples based on orthogonal arrays (Latin hypercube, orthogonal array and orthogonal array based Latin hypercube samples). In general, these samples turn out to have a better performance than Monte Carlo and antithetic Monte Carlo samples. Improvements over these are large for low-dimensional (4 and 10) cases and still significant for dimensions as large as 50

Adaptive Matching for Expert Systems with Uncertain Task Types

A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the expert resources are often scarce. The efficient utilization of experts in these platforms is made challenging by the fact that the information available about the parties involved is usually limited. To address this challenge, we develop a model of a task-expert matching system where a task is matched to an expert using not only the prior information about the task but also the feedback obtained from the past matches. In our model the tasks arrive online while the experts are fixed and constrained by a finite service capacity. For this model, we characterize the maximum task resolution throughput a platform can achieve. We show that the natural greedy approaches where each expert is assigned a task most suitable to her skill is suboptimal, as it does not internalize the above externality. We develop a throughput optimal backpressure algorithm which does so by accounting for the `congestion' among different task types. Finally, we validate our model and confirm our theoretical findings with data-driven simulations via logs of Math.StackExchange, a StackOverflow forum dedicated to mathematics.Comment: A part of it presented at Allerton Conference 2017, 18 page

Information-theoretic and stochastic methods for managing the quality of service and satisfaction in healthcare systems

This research investigates and develops a new approach to the management of service quality with the emphasis on patient and staff satisfaction in the healthcare sector. The challenge of measuring the quality of service in healthcare requires us to view the problem from multiple perspectives. At the philosophical level, the true nature of quality is still debated; at the psychological level, an accurate conceptual representation is problematic; whilst at the physical level, an accurate measurement of the concept still remains elusive to practitioners and academics. This research focuses on the problem of quality measurement in the healthcare sector. The contributions of this research are fourfold: Firstly, it argues that from the technological point of view the research to date into quality of service in healthcare has not considered methods of real-time measurement and monitoring. This research identifies the key elements that are necessary for developing a real-time quality monitoring system for the healthcare environment.Secondly, a unique index is proposed for the monitoring and improvement of healthcare performance using information-theoretic entropy formalism. The index is formulated based on five key performance indicators and was tested as a Healthcare Quality Index (HQI) based on three key quality indicators of dignity, confidence and communication in an Accident and Emergency department. Thirdly, using an M/G/1 queuing model and its underlying Little’s Law, the concept of Effective Satisfaction in healthcare has been proposed. The concept is based on a Staff-Patient Satisfaction Relation Model (S-PSRM) developed using a patient satisfaction model and an empirically tested model developed for measuring staff satisfaction with workload (service time). The argument is presented that a synergy between patient satisfaction and staff satisfaction is the key to sustainable improvement in healthcare quality. The final contribution is the proposal of a Discrete Event Simulation (DES) modelling platform as a descriptive model that captures the random and stochastic nature of healthcare service provision process to prove the applicability of the proposed quality measurement models.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

MINA - a tool for MSC-based performance analysis and simulation of distributed systems

Performance analysis can help to address quantitative system analysis from the early stages of the system development life cycle, e.g., to compare design alternatives or to identify system bottlenecks. This thesis addresses the problem of performance evaluation of distributed systems by employing a viewpoint where analytical and simulative evaluation techniques are unified in the MINA tool to make use of both techniques. We suggest a modelling tool chain to evaluate the performance of distributed systems like computer and communication systems based on an MSC description of the system. MSC-based performance evaluation of distributed systems is an approach that uses performance models, which are based on an MSC description of a system to evaluate system performance measures. To determine the system performance, these descriptions can be extended by notions for time consumption and resource usage and afterwards be included in a system performance model. Based on this unique model specification, analytical as well as simulative techniques can be applied to achieve either quick mean value results by queueing networks analysis or confidence intervals or transient measures by simulation. The applicability to real world systems and the advantages of the tool has been demonstrated by a large application example in the field of mobile communication systems, and its effectiveness has been evaluated by comparing it with other approaches. The experimental results show that the tool is scalable, the way it can model simple as well as complex systems. Moreover, it is straightforward and has the ability to find reasonable solutions in an efficient manner

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia