Control of a tandem queue with a startup cost for the second server

Various systems across a broad range of applications contain tandem queues. Strong dependence between the servers has proven to make such networks complicated and difficult to study. Exact analysis is rarely computationally tractable and sometimes not even possible. Nevertheless, as it is most often the case in reality, there are costs associated with running such systems, and therefore, optimizing the control of tandem queues is of main interest from both a theoretical and a practical point of view. Motivated by this, the present paper considers a tandem queueing network with linear holding costs and a startup cost for the second server. In our work, we present a rather intuitive, easy to understand, and at the same time very accurate technique to approximate the optimal decision policy. Extensive numerical experimentation shows that the approximation works extremely well for a wide range of parameter combinations

Dynamic control and Resource management for Mission Critical Multi-tier Applications in Cloud Data Center

The multi-tier architecture style has become an industry standard in modern data centers with each tier providing certain functionality. To avoid congestion and to adhere the SLA under fluctuating workload and unpredictable failures of Mission Critical Multi-tier applications hosted in the cloud, we need a Dynamic admission control policy, such that the requests must be processed from the first tier to the last without any delay. This paper presents the least strict admission control policy, which will induce the maximal throughput, for a two-tier system with parallel servers. We propose an optimization model to minimize the total number of virtual machines for computing resources in each tier by dynamically varying the mean service rate of the VMs. Some performance indicators and computational results showing the effect of model parameters are presented. This model is also applicable to priority as well as real-time based applications in Cloud based environment

Non-Preemptive Shunting in M/M/1 and Dynamic Service Queueing Systems

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in which a server with infinite capacity moves among indexed linear service nodes, receives customers at various nodes, and transports the customers to other indexed nodes in the hierarchy. We determine the expected waiting times at the nodes, expected service times, expected number of customers at a given node, expected number in the system, and expected number in service. The probabilities that an arrival finds n customers at a particular node, and in the entire system are obtained

Optimal admission control in tandem and parallel queueing systems with applications to computer networks

Modern computer networks require advanced, efficient algorithms to control several aspects of their operations, including routing data packets, access to secure systems and data, capacity and resource allocation, task scheduling, etc. A particular class of problems that arises frequently in computer networks is that of admission and routing control. Two areas where admission control problems are common are traffic control and authentication procedures. This thesis focuses on developing tools to solve problems in these areas. We begin the thesis with a brief introductory chapter describing the problems we will be addressing. Then, we follow this with a review of the relevant literature on the problems we study and the methodologies we use. Then, we have the main body of the dissertation, which is divided into three parts, described below. In the first part, we analyze a problem related to data routing in a network. Specifically, we study the problem of admission control to a system of two stations in tandem with finite buffers, Poisson arrivals to the first station, and exponentially distributed service times at both stations. We assume costs are incurred either when a customer is rejected at the time of arrival to the first station or when the second station is full at the time of service completion at the first station. We propose a Markov decision process formulation for this problem. Then, we use this model to show that, when one of the buffers has size one, the structure of the optimal policy is threshold and that only two particular policies can be optimal. We provide the exact optimality thresholds for small systems. For larger systems, we formulate heuristic policies and use numerical experiments to show that these policies achieve near-optimal performance. For the second part of this thesis, we investigate the system described above in a more general case, where the capacity of the buffers at both station is equal, finite and arbitrary. We focus on two specific, extremal policies, which we call the Prudent and Greedy policies. We derive a closed-form expression for the long-run average reward under the Prudent policy and provide a necessary and sufficient threshold condition for it to be optimal. For the Greedy policy, we give a matrix-analytic solution for the long-run average reward and provide a sufficient condition for it to be optimal. We also prove that it is always optimal to admit customers in the states where the Prudent policy admits customers. Next, we use an example to illustrate that the optimal policy can have a complicated form. Finally, we propose two heuristic policies and use numerical experiments to show that they perform much better than the Prudent and Greedy policies, and in fact, achieve near-optimal performance. In the third and final part of this dissertation, we shift our attention to a different admission and routing control problem. We study a centralized system where requests for authentication arrive from different users. The system has multiple authentication methods available and a controller must decide how to assign a method to each request. We consider three different performance measures: usability, operating cost, and security. First, we model the problem using a cost-based approach, which assigns a cost to each measure of performance. Under this approach, we find that if each authentication method has infinitely many servers the optimal policy is static and deterministic. On the other hand, if there is one method that has finite capacity and the rest have infinitely many servers, we show that the optimal policy is of trunk reservation form. Then, we model the problem using a constraint-based approach, which assumes hard constraints on some of the measures of performance. We show that if each method has infinitely many servers, the optimal policy is static and randomized. While, if one method has finite capacity and the rest have infinitely many servers, we show that the optimal policy has a 2-randomized trunk reservation form. Finally, we illustrate how to use our results to construct an efficient frontier of non-dominated solutions. We end this dissertation with a short recapitulation of our main contributions and a discussion on potential avenues for future research.Ph.D

Modeling and analysis to improve the quality of healthcare services

For many healthcare services or medical procedures, patients have extensive risk of complication or face death when treatment is delayed. When a queue is formed in such a situation, it is very important to assess the suffering and risk faced by patients in queue and plan sufficient medical capabilities in advance to address the concerns. As the diversity of care settings increases, congestion in facilities causes many patients to unnecessarily spend extra days in intensive care facilities. Performance evaluation of current healthcare service systems using queueing theory gains more and more importance because of patient flows and systems complexity. Queueing models have been used in handsome number of healthcare studies, but the incorporation of blocking is still limited. In this research work, we study an efficient two-stage multi-class queueing network system with blocking and phase-type service time distribution to analyze such congestion processes. We also consider parallel servers at each station and first-come-first-serve non-preemptive service discipline are used to improve the performance of healthcare service systems

Maximizing throughput in zero-buffer tandem lines with dedicated and flexible servers

Abstract For tandem queues with no buffer spaces and both dedicated and flexible servers, we study how flexible servers should be assigned to maximize the throughput. When there is one flexible server and two stations each with a dedicated server, we completely characterize the optimal policy. We use the insights gained from applying the Policy Iteration algorithm on systems with three, four, and five stations to devise heuristics for systems of arbitrary size. These heuristics are verified by numerical analysis. We also discuss the throughput improvement, when for a given server assignment, dedicated servers are changed to flexible servers

Performance Modelling and Optimisation of Multi-hop Networks

A major challenge in the design of large-scale networks is to predict and optimise the total time and energy consumption required to deliver a packet from a source node to a destination node. Examples of such complex networks include wireless ad hoc and sensor networks which need to deal with the effects of node mobility, routing inaccuracies, higher packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the computational limitations of the nodes. They also include more reliable communication environments, such as wired networks, that are susceptible to random failures, security threats and malicious behaviours which compromise their quality of service (QoS) guarantees. In such networks, packets traverse a number of hops that cannot be determined in advance and encounter non-homogeneous network conditions that have been largely ignored in the literature. This thesis examines analytical properties of packet travel in large networks and investigates the implications of some packet coding techniques on both QoS and resource utilisation. Specifically, we use a mixed jump and diffusion model to represent packet traversal through large networks. The model accounts for network non-homogeneity regarding routing and the loss rate that a packet experiences as it passes successive segments of a source to destination route. A mixed analytical-numerical method is developed to compute the average packet travel time and the energy it consumes. The model is able to capture the effects of increased loss rate in areas remote from the source and destination, variable rate of advancement towards destination over the route, as well as of defending against malicious packets within a certain distance from the destination. We then consider sending multiple coded packets that follow independent paths to the destination node so as to mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium and obtain the time-dependent properties of the packet’s travel process, allowing us to compare the merits and limitations of coding, both in terms of delivery times and energy efficiency. Finally, we propose models that can assist in the analysis and optimisation of the performance of inter-flow network coding (NC). We analyse two queueing models for a router that carries out NC, in addition to its standard packet routing function. The approach is extended to the study of multiple hops, which leads to an optimisation problem that characterises the optimal time that packets should be held back in a router, waiting for coding opportunities to arise, so that the total packet end-to-end delay is minimised

Optimization of Multiclass Queueing Networks: Polyhedral and Nonlinear Characterizations of Achievable Performance

We consider open and closed multiclass queueing networks with Poisson arrivals (in open networks), exponentially distributed class dependent service times, and with class dependent deterministic or probabilistic routing. For open networks, the performance objective is to minimize, over all sequencing and routing policies, a weighted sum of the expected response times of different classes. Using a powerful technique involving quadratic or higher order potential functions, we propose variants of a method to derive polyhedral and nonlinear spaces which contain the entire set of achievable response times under stable and preemptive scheduling policies. By optimizing over these spaces, we obtain lower bounds on achievable performance. In particular, we obtain a sequence of progressively more complicated nonlinear approximations (relaxations) which are progressively closer to the exact achievable space. In the special case of single station networks (multiclass queues and Klimov's model) and homogenous multiclass networks, our characterization gives exactly the achievable region. Consequently, the proposed method can be viewed as the natural extension of conservation laws to multiclass queueing networks. For closed networks, the performance objective is to maximize throughput. We similarly find polyhedral and nonlinear spaces that include the performance space and by maximizing over these spaces we obtain an upper bound on the optimal throughput. We check the tightness of our bounds by simulating heuristic scheduling policies for simple open networks and we find that the first order approximation of our method is at least as good as simulation-based existing methods. In terms of computational complexity and in contrast to simulation-based existing methods, the calculation of our first order bounds consists of solving a linear programming problem with both the number of variables and constraints being polynomial (quadratic) in the number of classes in the network. The i-th order approximation involves solving a convex programming problem in dimension O(Ri+l), where R is the number of classes in the network, which can be solved efficiently using techniques from semi-definite programming