AD–AS model

The AD–AS or aggregate demand–aggregate supply model is a macroeconomic model that explains price level and output through the relationship of aggregate demand (AD) and aggregate supply (AS). It is based on the theory of John Maynard Keynes presented in his work The General Theory of Employment, Interest and Money. It is one of the primary simplified representations in the modern field of macroeconomics, and is used by a broad array of economists, from libertarian, monetarist supporters of laissez-faire, such as Milton Friedman, to post-Keynesian supporters of economic interventionism, such as Joan Robinson. Modeling The AD/AS model is used to illustrate the Keynesian model of the business cycle. Movements of the two curves can be used to predict the effects that various exogenous events will have on two variables: real GDP and the price level. Furthermore, the model can be incorporated as a component in any of a variety of dynamic models (models of how variables like t

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Accounting for congestion and spillbacks in fixed-time traffic signal optimization: an analytical queueing model approach

Michel Bierlaire, Carolina Osorio Pizano

We present and analyze a new aggregate model of urban traffic. The objective is to analytically capture the correlation between the different components of the network while maintaining a tractable model that can be used in an optimization framework. Existing analytical queueing models for urban networks are formulated for a single intersection, and thus do no take into account the interactions among upstream and downstream roads. We formulate a model that considers a set of intersections and captures the correlation structure between consecutive roads based on finite capacity queueing theory. It therefore provides a detailed description of congestion. It identifies the sources of congestion (e.g. bottlenecks), describes how congestion propagates and dissipates; and quantifies the impact on the network performance. We use the model in the context of fixed-time traffic signal optimization. Although there is a great variety of signal control methodologies in the literature, there is still a need for solutions that are appropriate and efficient under saturated conditions, where the performance of signal control strategies and the formation and propagation of queues are strongly related. To the best of our knowledge, the existing signal control strategies based on analytical network models have not taken spillbacks into account. We formulate a fixed-time signal control problem where the network model is included as a set of constraints. We apply this methodology to a subnetwork of the Lausanne city center and use a microscopic traffic simulator to analyze its performance. We compare its performance to that of several other methods. The results show the importance of taking the correlation between consecutive roads into account.

2008

An Analytic Finite Capacity Queueing Network Model Capturing Congestion and Spillbacks

Michel Bierlaire, Carolina Osorio Pizano

Analytic queueing network models constitute a flexible tool for the study of network flow. These aggregate models are simple to manipulate and their analytic aspect renders them suitable for use within an optimization framework. Analytic queueing network models often assume infinite capacity for all queues. For real systems this infinite capacity assumption does not hold, but is often maintained due to the difficulty of grasping the between-queue correlation structure present in finite capacity networks. This correlation structure helps explain bottleneck effects and spillbacks, the latter being of special interest in networks containing loops because they are a source of potential deadlock (i.e. gridlock). We present an analytic queueing network model which acknowledges the finite capacity of the different queues. The model is adapted for multiple server finite capacity queueing networks with an arbitrary topology and blocking-after-service. By explicitly modelling the blocking phase the model yields a description of the congestion effects. A decomposition method allowing the evaluation of the model is also described. The methods validation, by comparison to both pre-existing methods and simulation results, is presented, as well as its application to the study of patient flow in a network of operative and post-operative units of the Geneva University Hospital.

2007

An analytic finite capacity queueing network model capturing congestion and spillbacks

Michel Bierlaire, Carolina Osorio Pizano

2007

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In macroeconomics, aggregate demand (AD) or domestic final demand (DFD) is the total demand for final goods and services in an economy at a given time. It is often called effective demand, though at

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A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine the comparative static