Robust Queueing Theory

We propose an alternative approach for studying queues based on robust optimization. We model the uncertainty in the arrivals and services via polyhedral uncertainty sets, which are inspired from the limit laws of probability. Using the generalized central limit theorem, this framework allows us to model heavy-tailed behavior characterized by bursts of rapidly occurring arrivals and long service times. We take a worst-case approach and obtain closed-form upper bounds on the system time in a multi-server queue. These expressions provide qualitative insights that mirror the conclusions obtained in the probabilistic setting for light-tailed arrivals and services and generalize them to the case of heavy-tailed behavior. We also develop a calculus for analyzing a network of queues based on the following key principles: (a) the departure from a queue, (b) the superposition, and (c) the thinning of arrival processes have the same uncertainty set representation as the original arrival processes. The proposed approach (a) yields results with error percentages in single digits relative to simulation, and (b) is to a large extent insensitive to the number of servers per queue, network size, degree of feedback, and traffic intensity; it is somewhat sensitive to the degree of diversity of external arrival distributions in the network

FAST TCP: Motivation, Architecture, Algorithms, Performance

We describe FAST TCP, a new TCP congestion control algorithm for high-speed long-latency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties which the current TCP implementation has at large windows. We describe the architecture and summarize some of the algorithms implemented in our prototype. We characterize its equilibrium and stability properties. We evaluate it experimentally in terms of throughput, fairness, stability, and responsiveness

Performance analysis of queueing networks via robust optimization

Performance analysis of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as product-form type queueing networks, there exist very few results that provide provable nonasymptotic upper and lower bounds on key performance measures. In this paper we propose a new performance analysis method, which is based on the robust optimization. The basic premise of our approach is as follows: rather than assuming that the stochastic primitives of a queueing model satisfy certain probability laws—such as i.i.d. interarrival and service times distributions—we assume that the underlying primitives are deterministic and satisfy the implications of such probability laws. These implications take the form of simple linear constraints, namely, those motivated by the law of the iterated logarithm (LIL). Using this approach we are able to obtain performance bounds on some key performance measures. Furthermore, these performance bounds imply similar bounds in the underlying stochastic queueing models. We demonstrate our approach on two types of queueing networks: (a) tandem single-class queueing network and (b) multiclass single-server queueing network. In both cases, using the proposed robust optimization approach, we are able to obtain explicit upper bounds on some steady-state performance measures. For example, for the case of TSC system we obtain a bound of the form C(1 – {rho})–1 ln ln((1 – {rho})–1) [C(1-p) superscript -1 ln ln ((1 - p) superscript -1)]on the expected steady-state sojourn time, where C is an explicit constant and {rho} is the bottleneck traffic intensity. This qualitatively agrees with the correct heavy traffic scaling of this performance measure up to the ln ln((1 – {rho})–1) [ln ln((1 - p) superscript -1)] correction factor.National Science Foundation (U.S.) (Grant DMI-0556106)National Science Foundation (U.S.) (Grant CMMI-0726733

Efficiency evaluation for pooling resources in health care

Hospitals traditionally segregate resources into centralized functional departments such as diagnostic departments, ambulatory care centers, and nursing wards. In recent years this organizational model has been challenged by the idea that higher quality of care and efficiency in service delivery can be achieved when services are organized around patient groups. Examples include specialized clinics for breast cancer patients and clinical pathways for diabetes patients. Hospitals are struggling with the question of whether to become more centralized to achieve economies of scale or more decentralized to achieve economies of focus. In this paper we examine service and patient group characteristics to study the conditions where a centralized model is more efficient, and conversely, where a decentralized model is more efficient. This relationship is examined analytically with a queuing model to determine themost influential factors and then with simulation to fine-tune the results. The tradeoffs between economies of scale and economies of focus measured by these models are used to derive general management guidelines

Some aspects of queueing and storage processes : a thesis in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University

In this study the nature of systems consisting of a single queue are first considered. Attention is then drawn to an analogy between such systems and storage systems. A development of the single queue viz queues with feedback is considered after first considering feedback processes in general. The behaviour of queues, some with feedback loops, combined into networks is then considered. Finally, the application of such networks to the analysis of interconnected reservoir systems is considered and the conclusion drawn that such analytic methods complement the more recently developed mathematical programming methods by providing analytic solutions for sub systems behaviour and thus guiding the development of a system model