Block-Structured Supermarket Models

Supermarket models are a class of parallel queueing networks with an adaptive control scheme that play a key role in the study of resource management of, such as, computer networks, manufacturing systems and transportation networks. When the arrival processes are non-Poisson and the service times are non-exponential, analysis of such a supermarket model is always limited, interesting, and challenging. This paper describes a supermarket model with non-Poisson inputs: Markovian Arrival Processes (MAPs) and with non-exponential service times: Phase-type (PH) distributions, and provides a generalized matrix-analytic method which is first combined with the operator semigroup and the mean-field limit. When discussing such a more general supermarket model, this paper makes some new results and advances as follows: (1) Providing a detailed probability analysis for setting up an infinite-dimensional system of differential vector equations satisfied by the expected fraction vector, where "the invariance of environment factors" is given as an important result. (2) Introducing the phase-type structure to the operator semigroup and to the mean-field limit, and a Lipschitz condition can be obtained by means of a unified matrix-differential algorithm. (3) The matrix-analytic method is used to compute the fixed point which leads to performance computation of this system. Finally, we use some numerical examples to illustrate how the performance measures of this supermarket model depend on the non-Poisson inputs and on the non-exponential service times. Thus the results of this paper give new highlight on understanding influence of non-Poisson inputs and of non-exponential service times on performance measures of more general supermarket models.Comment: 65 pages; 7 figure

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times

In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations. Then we analyze the exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-exponential service requirements.Comment: 24 page

Super-Exponential Solution in Markovian Supermarket Models: Framework and Challenge

Marcel F. Neuts opened a key door in numerical computation of stochastic models by means of phase-type (PH) distributions and Markovian arrival processes (MAPs). To celebrate his 75th birthday, this paper reports a more general framework of Markovian supermarket models, including a system of differential equations for the fraction measure and a system of nonlinear equations for the fixed point. To understand this framework heuristically, this paper gives a detailed analysis for three important supermarket examples: M/G/1 type, GI/M/1 type and multiple choices, explains how to derive the system of differential equations by means of density-dependent jump Markov processes, and shows that the fixed point may be simply super-exponential through solving the system of nonlinear equations. Note that supermarket models are a class of complicated queueing systems and their analysis can not apply popular queueing theory, it is necessary in the study of supermarket models to summarize such a more general framework which enables us to focus on important research issues. On this line, this paper develops matrix-analytical methods of Markovian supermarket models. We hope this will be able to open a new avenue in performance evaluation of supermarket models by means of matrix-analytical methods.Comment: Randomized load balancing, supermarket model, matrix-analytic method, super-exponential solution, density-dependent jump Markov process, Batch Markovian Arrival Process (BMAP), phase-type (PH) distribution, fixed poin

The Links Between the Neighborhood Food Environment and Childhood Nutrition

Identifies key studies on the availability of, and residents' access to, healthy foods and how they influence the choices of low-income children and their families. Discusses efforts to bring about improvements and new research and policy priorities

Modeling the Influence of Land Use Developments on Transportation System Performance

The growth in the urban population has influenced urban sprawl, congestion, and subsequently, delays on the existing road infrastructure. New land use developments occur in every part of the city due to rapid economic development and to meet the demand for better living standards. The induced traffic volume generated from such land use developments often results in increased congestion and vehicular delay on the existing roads. With recent advancements in the technology, it is possible to capture continuous, and comprehensive travel time data for every major corridor in a city. Therefore, the goal of this research is to model the influence of land use developments on travel time variations to improve the mobility of people and goods. Data for 259 road links were selected within the city of Charlotte, North Carolina (NC). Three years of travel time data, from the year 2013 to the year 2015, were collected from the private agency. Thirty-five different types of land use developments were considered in this research. The spatial dependency was incorporated by considering the land use developments within 0.5 miles, 1 mile, 2 miles, and 3 miles of the selected road link. Forty-eight statistical models were developed. The results obtained indicate that land use developments have a significant influence on travel times. Different land use categories contribute to the average travel time based on the buffer width, area type, and the link speed limit. Developing the models by classifying the links based on the speed limit (\u3c 45 mph, 45 to 50 mph, and \u3e 50 mph) was observed to be the best approach to examine the relationship between land use developments and the average travel time. Also, typically travel time on a selected road link is higher during the evening peak period compared to the morning peak and the afternoon off-peak period. Further, the results obtained indicate that the number of lanes and the posted speed limit are negatively associated with the travel time of the selected link

Cognitively-inspired Agent-based Service Composition for Mobile & Pervasive Computing

Automatic service composition in mobile and pervasive computing faces many challenges due to the complex and highly dynamic nature of the environment. Common approaches consider service composition as a decision problem whose solution is usually addressed from optimization perspectives which are not feasible in practice due to the intractability of the problem, limited computational resources of smart devices, service host's mobility, and time constraints to tailor composition plans. Thus, our main contribution is the development of a cognitively-inspired agent-based service composition model focused on bounded rationality rather than optimality, which allows the system to compensate for limited resources by selectively filtering out continuous streams of data. Our approach exhibits features such as distributedness, modularity, emergent global functionality, and robustness, which endow it with capabilities to perform decentralized service composition by orchestrating manifold service providers and conflicting goals from multiple users. The evaluation of our approach shows promising results when compared against state-of-the-art service composition models.Comment: This paper will appear on AIMS'19 (International Conference on Artificial Intelligence and Mobile Services) on June 2