Larry J. LeBlanc

An efficient approach to solving the road network equilibrium traffic assignment problem

This paper presents a solution technique that requires only the solution of a sequence of shortest route problems, such as computing time for the one dimensional searches being insignificant. The computing time for finding an approximate solution to the equilibrium problem was less than that required by the simplex method by orders of magnitude even on a fairly small network. For larger problems the savings would be even greater, since for multi-commodity network problems the number of constraints grows as the square of the conservation of flow and non-negativity constraints used explicitly in this technique. Preliminary computational results indicate that the number of shortest route subproblems for a network equilibrium problem with several hundred nodes will not be excessive; thus the solution approach presented appears very promising for large network equilibrium problems.

Continuous equilibrium network design models

It is known that the network design problem with the assumption of user optimal flows can be modeled as a 0-1 mixed integer programming problem. Instead, we formulate the network design problem with continuous investment variables subject to equilibrium assignment as a nonlinear optimization problem. We show that this optimization problem is equivalent to an unconstrained problem which we solve by direct search techniques. For convex investment cost functions, the performance of both Powells method and the method of Hooke and Jeeves is approximately the same with respect to computational requirements for a 24 node, 76 arc network. For the case of concave investment functions, Hooke and Jeeves was superior. The solution to the concave continuous model was very similar to that of the 0-1 model. Furthermore, the required solution time was far less than that required by the corresponding discrete model of the same network. The advantages and disadvantages of the continuous approach as well as the computational requirements are discussed.

A new class of instantaneous dynamic user-optimal traffic assignment models

The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints, they have unique solutions. A numerical example is presented indicating that this class of models yields realistic results.

Forecasting Emergency Department Crowding: A Discrete Event Simulation

STUDY OBJECTIVE To develop a discrete event simulation of emergency department (ED) patient flow for the purpose of forecasting near-future operating conditions and to validate the forecasts with several measures of ED crowding. METHODS We developed a discrete event simulation of patient flow with evidence from the literature. Development was purely theoretical, whereas validation involved patient data from an academic ED. The model inputs and outputs, respectively, are 6-variable descriptions of every present and future patient in the ED. We validated the model by using a sliding-window design, ensuring separation of fitting and validation data in time series. We sampled consecutive 10-minute observations during 2006 (n=52,560). The outcome measures--all forecast 2, 4, 6, and 8 hours into the future from each observation--were the waiting count, waiting time, occupancy level, length of stay, boarding count, boarding time, and ambulance diversion. Forecasting performance was assessed with Pearsons correlation, residual summary statistics, and area under the receiver operating characteristic curve. RESULTS The correlations between crowding forecasts and actual outcomes started high and decreased gradually up to 8 hours into the future (lowest Pearsons r for waiting count=0.56; waiting time=0.49; occupancy level=0.78; length of stay=0.86; boarding count=0.79; boarding time=0.80). The residual means were unbiased for all outcomes except the boarding time. The discriminatory power for ambulance diversion remained consistently high up to 8 hours into the future (lowest area under the receiver operating characteristic curve=0.86). CONCLUSION By modeling patient flow, rather than operational summary variables, our simulation forecasts several measures of near-future ED crowding, with various degrees of good performance.

Modeling emergency department operations using advanced computer simulation systems

We developed a computer simulation model of emergency department operations using simulation software. This model uses multiple levels of preemptive patient priority; assigns each patient to an individual nurse and physician; incorporates all standard tests, procedures, and consultations; and allows patient service processes to proceed simultaneously, sequentially, repetitively, or a combination of these. Selected input data, including the number of physicians, nurses, and treatment beds, and the blood test turnaround time, then were varied systematically to determine their simulated effect on patient throughput time, selected queue sizes, and rates of resource utilization. Patient throughput time varied directly with laboratory service times and inversely with the number of physician or nurse servers. Resource utilization rates varied inversely with resource availability, and patient waiting time and patient throughput time varied indirectly with the level of patient acuity. The simulation can be animated on a computer monitor, showing simulated patients, specimens, and staff members moving throughout the ED. Computer simulation is a potentially useful tool that can help predict the results of changes in the ED system without actually altering it and may have implications for planning, optimizing resources, and improving the efficiency and quality of care.

Implementation and Computational Issues for Combined Models of Location, Destination, Mode, and Route Choice

A unified approach to deriving models of urban location, destination, mode, and route choice is illustrated, and an algorithm based on Evanss approach and the Lagrange multiplier procedure is proposed. By examining derivatives of the Lagrangian function, we show that the Newton—Raphson technique can be implemented for finding the optimal Lagrange multipliers for these models. Procedures for identifying values of generalized cost-function coefficients are studied.

Improved efficiency of the Frank-Wolfe algorithm for convex network programs

We discuss methods for speeding up convergence of the Frank-Wolfe algorithm for solving nonlinear convex programs. Models involving hydraulic networks, road networks and factory-warehouse networks are described. The PARTAN technique and heuristic variations of the Frank-Wolfe algorithm are described which serve to significantly improve the convergence rate with no significant increase in memory requirements. Computational results for large-scale models are reported.

Selection of a trip table which reproduces observed link flows

In urban traffic management and planning, an important problem is estimating the number of drivers traveling between each origin-destination zone. We review a model due to Nguyen for estimating these numbers of drivers, based on counts of the traffic flows on each street, and develop an effective algorithm for solving it. The multiplicity of solutions of this model poses the additional question of which solution to use; we introduce a secondary optimization problem to overcome this difficulty. Efficient solution techniques are described for these problems and computational results are reported. It is noted that the most efficient solution methods involve user interaction to specify values of parameters which improve the convergence rates.

Transit system network design

This article formulates a transit network design model for determining frequencies of each transit line in a network. This transit network design model requires a mode-split assignment model with distinct transit lines, each with its own specified frequency, to capture the mode split effects of increases or decreases in individual transit line frequencies. It is shown how to refine conventional mode-split assignment models to include this feature. The resulting model includes more precise measures of transit access and transfer delays, so that it more accurately predicts mode choices and link flows. This variation of the mode-split assignment model uses Dials transit loader to solve Frank-Wolfe subproblems, using frequencies of individual transit lines to find fastest transit paths, considering access time, ride time, and any transfer delays. Computational shortcuts using the standard Hooke-Jeeves algorithm are demonstrated.

Scheduling projects to maximize net present value -- the case of time-dependent, contingent cash flows

Abstract The problem of scheduling activities in a project to maximize its Net Present Value (NPV) has been solved for the case where net cash flow magnitudes are independent of the time of realization. This paper models a more realistic version of this problem — because of incentive payments and penalties for early and late event occurrences, respectively, and because of changing costs of resources over time, net cash flow magnitudes are dependent on the time of realization. We formulate an optimization program for this more general problem and present a simulated annealing solution approach. We test different implementation strategies for this algorithm and suggest a method for choosing neighborhood moves. We compare the NPVs of the solutions obtained from our formulation with the NPVs of early start schedules and with late start schedules for 168 different problems. These computational results show that the simulated annealing approach consistently produces substantially better solutions than the early start or late start schedules. Even poor simulated annealing neighborhood moves give improved solutions for most problems studied.