Workload Limits Research Articles

Heavy Traffic Analysis of a Controlled Multiclass Queueing Network via Weak Convergence Methods

The workload formulation due to Harrison and coworkers of multiclass queueing networks has been fundamental to its analysis. Until recently, there was no actual theory which started with the physical queue and showed that under heavy traffic conditions, the optimal costs could be approximated by those for an optimization problem using the ``limit'' workload equations. Recently, this was done via viscosity solution methods by Martins, Shreve, and Soner for one important class. For this same class of problems (and including the cases not treated there), we use weak convergence methods to show that the sequence of optimal costs for the original network converges to the optimal cost for the workload limit problem. The proof is simpler and allows weaker (and non-Markovian) conditions. It uses current techniques in weak convergence analysis. It seems to be the first analysis of such multiclass ``workload'' problems by weak convergence methods. The general structure of the development seems applicable to the analysis of more complex systems.

Factors affecting the radiation dose to the lens of the eye during cardiac catheterization procedures.

Concern has been expressed about the relatively high radiation doses to the lens of the eye received by the operator during cardiac catheterization studies. A study was undertaken to assess the occupational doses received by cardiologists and to examine the factors that affect the individual's eye dose. Eighteen cardiologists working in five catheterization laboratories at three centres were included in the study. Their eye doses, workload and individual study details were monitored at each centre. Operating dose rates and scattered radiation were also measured for each unit to compare equipment performance. The study demonstrated that the relationships between the cardiologist's eye dose and factors such as the dose efficiency of the X-ray equipment, scattered dose rates, examination protocols and workload are complex and vary from centre to centre. Because of these variations general workload limits may be inaccurate and should only be used for general guidance when no direct measurements are available. Such limits should be verified by local measurements as soon as is practical.

An enroute ATC simulation experiment for sector capacity estimation

A series of enroute ATC simulation experiments was conducted to estimate the airspace capacity of existing sectors in Japan and to evaluate a new route structure for accommodating the traffic increase in the future. A simulation method for capacity estimation and the results of the experiments focusing on the controller's workload limit are presented. From the results of regression analysis, the relationship between the airspace capacity and the controller's intervention in the traffic flow is discussed. About 40% increase of capacity is attained with an introduction of parallel routes and traffic flow management.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Maximal Covering Location Problem with Capacities on Total Workload

The Maximal Covering Location Problem (MCLP) has been the focus of considerable attention both in research and practice for some time, and numerous extensions have been proposed to broaden its appeal and enhance its applicability. In this paper, we are concerned with the addition of workload limits on the facilities. While not generally difficult to formulate, these capacity constraints make the model substantially more difficult to solve, as well as create certain pathological results, particularly in the assignment of uncovered demand to facilities. First we discuss these pathologies and extend the capacitated MCLP to address them. Then, we present an efficient solution procedure that is applicable to both simple and extended problem formulations. Finally, results of extensive tests on the solution procedure are presented and a “real-world” scale example is solved to explore the implications of the model.

A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types

The central result of this paper is a heavy traffic limit theorem for the vector of total station workloads in an open network of queues with multiple customer types, under first-come-first-served and priority disciplines. The limit process is a regulated Brownian motion on the nonnegative orthant, with parameters specified from the first two moments of the interarrival and service time distributions and a matrix of reduced routing information. Through the phenomenon of state space collapse, associated limit results for queue length, workload and sojourn time processes by customer type are obtained jointly as simple transformations of the total workload limit process. Diffusion approximations based on the theorem are discussed.

The Siting of Emergency Service Facilities with Workload Capacities and Backup Service

By the very nature of the demand that they serve, emergency service systems require that timely service be readily available to those who need it. Yet, the distinct possibility exists that the closest facility will be occupied with another call for service, and when this primary responding unit is busy, a secondary or backup facility must be assigned. The need for backup service is most prevalent in heavily used systems, which are also prone to facility workloads that can be excessive if uncontrolled. The effective design of these systems should address the siting of both the primary responding facility and a designated backup unit, as well as reasonable workload limits on these facilities. In this paper, a model formulation for emergency service systems is presented where facility workload is controlled and backup service for some or all demand points is provided. The model is sufficiently general to allow it to be adapted to several problem settings and decision criteria. An effective solution procedure was developed using a Lagrangean relaxation of the original model formulation. Results of extensive computational experiments testing this solution procedure are discussed. Finally, a large-scale example using real world data was solved and a summary of results is presented to demonstrate the applicability of the model and the solution procedure.