Ajay K. Rathi

A Mean-Variance Model for Route Guidance in Advanced Traveler Information Systems

Traditional models of route generation are based on choosing routes that minimize expected travel-time between origin and destination. Such approaches do not account for the fact that travelers often incorporate travel-time variability within their decision making. Thus, a route with lower travel-time variability is preferred by some travelers, even if such a route is not one with the lowest mean travel-time. Such traveler behavior is best captured by a multiobjective model in which the choice of a route is based on the mean as well as the variance of the path travel-time. Our route-planning model is intended to help travelers make choices that reflect their decision-making process better. We formulate a network flow multiobjective model in which one of the objectives (expectation) is linear, whereas, the other (variance) is quadratic. In order to present the user with a series of options, we solve a series of parametric 0-1 quadratic integer programs. By utilizing the network structure of the problem, we devise an effective algorithm in which the 0-1 quadratic program is solved by using a continuous relaxation together with an enumeration of some selected paths. Finally, we note that the data requirements for the model can be easily satisfied in practice.

A restricted branch-and-bound approach for generating maximum bandwidth signal timing plans for traffic networks

The synchronization of traffic signals located along the urban/suburban arterials in metropolitan areas is perhaps one of the most cost-effective methods for improving traffic flow along these streets. The main objective of synchronized signal timing is to keep traffic moving in platoons throughout the signal controlled system, by setting the signals along the arterials/networks to provide maximum bandwidth progression. A popular technique for generating signal timing plans formulates the problem as a mixed-integer linear program and uses the Land and Powell branch-and-bound search technique to arrive at the optimal solution. Due to numerical instability of the solution technique and the exhaustive nature of the search procedure, the current implementation tends to be computationally inefficient and infeasable for realistic network problems. Furthermore, numerical instability results in suboptimal or no solutions for network problems with a range of variable cycle times. This paper presents the development of a fast and numerically stable heuristic for the maximum bandwidth signal setting problem. The heuristic is computationally efficient, can generate optimal/near-optimal solutions, and is implemented on a PC. It is based on restricted search of the integer variables in the solution space. The efficiency of this heuristic is supported by computational results for a number of test problems. 1998 Elsevier Science Ltd. All rights reserved

Comparison of NETSIM, NETFLO I, and NETFLO II Traffic Simulation Models for Fixed-Time Signal Control

This paper documents a comparative analysis of the NETSIM, NETFLO I, and NETFLO II traffic simulation models when simulating traffic networks with fixed-time signal control. The objective was to find out whether the results of simulating the same traffic network with the three models were compatible. The three models employ different approaches to simulate traffic flow on urban street networks. Four different scenarios with varying network configurations and intersection geometries were simulated for three volume levels. The average speed and delay measures of effectiveness generated by the three models were compared for each scenario. Analysis of variance techniques were used for statistical analyses of the simulation output data. The execution speeds of the models were also compared. The quickness of simulation will be very important in the ITS applications, real-time traffic adaptive systems, and so forth. The results of this study indicated that the estimated measures of effectiveness from the three m...

The use of common random numbers to reduce the variance in network simulation of traffic

Computer simulation is now used routinely as a decision support tool in many facets of transportation engineering. Simulation models are often used to compare system alternatives, i.e. alternative system designs and/or operating policies. The presence of high variance of the simulation output variables is a critical problem in such comparative analyses because the models must either be run longer or executed several times to achieve reasonably accurate point and interval estimates of the parameters of interest. The high variability in output measures can also lead to concern about the validity of the model when they are used by the practitioners who are not intimately familiar with the stochastic nature of the model processes. This paper describes and illustrates the effectiveness of variance reduction based on the concept of common random numbers (CRN) for the TRAF-NETSIM simulation model.

An improved response surface methodology algorithm with an application to traffic signal optimization for urban networks

Illustrates the use of the simulation-optimization technique of response surface methodology (RSM) in traffic signal optimization of urban networks. It also quantifies the gains of using the common random number (CRN) variance reduction strategy in such an optimization procedure. An enhanced RSM algorithm which employs conjugate gradient search techniques and successive second-order models is presented instead of the conventional approach. An illustrative example using an urban traffic network exhibits the superiority of using the CRN strategy over direct simulation in performing traffic signal optimization. The relative performance of the two strategies is quantified with computational results using the total network-wide delay as the measure of effectiveness.

An application of variance reduction techniques in freeway simulation

Computer simulation models are used in a variety of applications in transportation engineering and have become a prime aid in decision making. The applications range from evaluating traffic control strategies for single intersections to such complex decision processes as evaluating the impact of removing toll facilities at the George Washington Bridge in New York City. While it is widely accepted that simulation offers an unmatchable capability of evaluating alternate control policies, the high variance of the output variable presents a critical problem in such comparative analyses. The simulation models with high output variance must be run longer or replicated many times to achieve a desired precision level, and that corresponds to increased cost of computer resources. This paper describes and illustrates the application of variance reduction concepts that can improve the reliability and efficiency of the simulation experimental process by taking advantage of the simulation model structure. The two variance reduction concepts (common random numbers and antithetic variates) reduce the variance of the output variable by replacing the original sampling procedure with a new procedure that yields the same expected value but with a smaller variance. The application of the variance reduction concept was illustrated using results from experiments with a freeway simulation model. The results indicate that both common random numbers and antithetic variates sampling procedures appreciably reduce the variance of the simulation output measure.

A simulation model of freeway lane closures

A model to simulate traffic operations at freeway lane closures is described. The model logic is based on a rational description of the behavior of the drivers in a freeway lane closure situa tion, and the program is written in SIMSCRIPT 11.5. An applica tion of the model is illustrated with evaluation of potential safety impacts of reduced speed zones in freeway lane closures at differ ent levels of assumed driver compliance.

A macro level analysis of the airlift deployment problem

Abstract This paper presents mathematical models for a macro level analysis of the airlift deployment problem which involves the allocation of a limited number of aircraft towards the shipment of cargo and personnel between many origins and destinations within prescribed time windows. The problem has been modeled by three linear programming formulations in a manner such that it can be solved in a personal computer environment in a timely manner. The first and second formulations represent an explicit statement of the problem. These formulations attempt to optimally allocate strategic airlift resources towards the shipment of demand (cargo and personnel) such that the maximum amount of demand is delivered on time using preferred aircraft types. A much smaller statement of the problem is achieved in the third formulation by assuming that lateness is distributed evenly over all routes. Thus, the formulations offer a tradeoff between the degree of control to be exercised by the planner and the speed of computation. The paper presents the basic structure of these formulations along with some test results.