Peter Kolesar

An Algorithm for the Dynamic Relocation of Fire Companies

When all the fire companies in a region are engaged in fighting fires, protection against a future fire is considerably reduced. It is standard practice in many urban fire departments to protect the exposed region by relocating outside fire companies temporarily to some of the vacant houses. In New York City, situations requiring such relocations arise ten times a day on the average. The Fire Department of the City of New York FDNY currently makes its relocations according to a system of preplanned moves. This system was designed at a time when alarm rates were low and is based on the assumption that only one fire is in progress at a time. Because of the high alarm rates currently being experienced in parts of New York City, this assumption is no longer valid, and the preplanned relocation system breaks down at the times when it is needed most. This paper describes a computer-based method for determining relocations that overcomes the deficiencies of the existing method by utilizing the computers ability to 1 store up-to-date information about the status of all fires in progress and the location and activity of all fire companies, 2 generate and compare many alternative relocation plans quickly. The method, which will become part of the FDNYs real-time Management Information and Control System MICS, is designed to be fast and to require little computer memory. After giving some background of the problem and the objectives of relocation, we give the problem a mathematical programming formulation and then describe the heuristic algorithm to be used for generating relocations in the MICS. The remainder of the paper is devoted to a discussion of an example illustrating how the algorithm works, a rigorous test of the algorithm using a computer simulation model of Fire-Department operations, and a description of the current use of the computer algorithm by dispatchers in an interactive time-shared environment. The results of the testing indicate that the proposed algorithm is a significant improvement over existing methods, particularly in crisis situations. Although designed to solve a problem for the New York City Fire Department, the algorithm should be applicable to other cities.

ANNIVERSARY ARTICLE: Improving Emergency Responsiveness with Management Science

While the goal of OR/MS is to aid decision makers, implementation of published models occurs less frequently than one might hope. However, one area that has been significantly impacted by management science is emergency response systems. Dozens of papers on emergency service management appeared in the OR/MS literature in the 1970s alone, many of which were published inManagement Science. Three of these papers won major prizes. More importantly, many of these papers led to the implementation of substantially new policies and practices, particularly in policing and firefighting. Much of this work originated in New York City, though many other cities subsequently adopted the resulting models and strategies. In this paper, we look at the context, content, and nature of the research and the factors that led to these early implementation successes. We then track the extent to which these original models are still affecting decision making in emergency response systems. We also examine the pace of development of new OR/MS models and applications in the area. Finally, we look at issues in emergency responsiveness that have emerged recently as a result of the national focus on terrorism and discuss the potential for future OR/MS modeling and application.

A Queuing-Linear Programming Approach to Scheduling Police Patrol Cars

In any city the arrival rate of calls for police patrol-car service varies considerably through the day. Using queuing theory and integer linear programming, we present a method for scheduling patrol cars so that specified service standards are met at each hour of the day. Two models are used. The first is an M/M/n queuing model with time-dependent parameters that is solved numerically. The second is an integer linear program in which the decision variables are the number of patrol cars working each tour and the times at which they go out of service for meals. The programs constraints are determined by the output of the queuing model. Use of the method with data from the New York City Police Department indicates that it can lead to substantial improvements in police service.

Some effects of nonstationarity on multiserver Markovian queueing systems

We examine the effects of nonstationarity on the performance of multiserver queueing systems with exponential service times and sinusoidal Poisson input streams. Our primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. We focus on a particular question: How nonstationary can an arrival process be before a simple stationary approximation fails? Our analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary. Other findings include confirmation and elaboration of S. M. Rosss conjecture that expected delays increase with nonstationarity, and the identification of easily computed and tight lower and upper bounds for expected delay and the probability of delay. These empirical results are based on a series of computer experiments in which the differential equations governing system behavior are solved numerically.

Using Simulation to Develop and Validate Analytic Models: Some Case Studies

Simulation models are generally costly tools to use in systems analyses. Whenever applicable, a simple analytic model is preferable. However, in many cases the conditions assumed by solvable analytic models do not hold in the real world; hence an analyst would hesitate to use them. A simulation can be used to suggest an appropriate approximate model and to determine how good an approximation a given analytic model is. We show how simulations of New York Citys fire and police operations have been used to develop and validate simple analytic models that are now being used to analyze the deployment of resources in these two services.

Optimal Dispatching of an Infinite-Capacity Shuttle: Control at a Single Terminal

We study the optimal control of a shuttle system consisting of a single infinite-capacity carrier transporting passengers between two terminals. Passengers arrive according to independent Poisson processes, and at only one of the terminals can the dispatcher hold the carrier for more passengers. Our objective: to determine dispatching rules that minimize the long-run average of a linear passenger-waiting-time cost and a charge per trip made by the carrier. When complete information about the system state is available, and travel times are not random, we prove that it is best to dispatch the carrier if, and only if, the total number of passengers waiting at both terminals is greater than a cutoff value. To compute this cutoff value, we propose an iterative method and find that we can approximate it quite well by a simple function of system costs and parameters similar to the economic-lot-size formula. We propose a dispatching rule which may not be optimal for the case when only the number of passengers waiting at one terminal is known, and we compare its efficiency to that of the optimal rule that uses complete information. We outline extensions to other optimality criteria and to the case of stochastic travel times.

A Model for Predicting Average Fire Engine Travel Times

We propose, motivate, and test a model for predicting ET, the expected fire engine travel time in a region, given the regions area, A; the number of fire engines stationed there, n; the alarm rate, λ; and the expected total service time per alarm, ES. The model is ET = α + β [A/n-λES]γ. Estimates of the values of parameters α, β, and γ are given for New York City, where the model has been validated, and used in analyzing fire engine deployment problems. Recent changes in the number and location of fire engines in New York City were based partially on this analysis.

OPERATING CHARACTERISTICS OF A SIMPLE SHUTTLE UNDER LOCAL DISPATCHING RULES

We treat a transportation system with Poisson passenger arrivals at each of two terminals and a carrier of capacity one that shuttles back and forth between the terminals. We study the consequences of the control decision: how long should the carrier wait empty at a terminal? This dispatch decision is made without knowledge of the queue at the other terminal. Exact and approximate expressions are obtained for the number of carrier trips per unit time and average queue size at each terminal. They are used to show that it is best never to hold the carrier at the slow terminal and not to randomize in the decision process. Further, we show that holding the carrier at the fast terminal sometimes reduces both trip rate and the sum of the average queue sizes.

The relevance of research on statistical process control to the total quality movement

Abstract We review the history of statistical process control research from its origins at Bell Laboratories with Shewhart in 1924 up to the present and integrate it with the history of the larger total quality management movement that emerged from these same statistical process control origins. The original research was very philosophical and very practical and is still implemented today. Our view is that the majority of the enormous research literature after Duncans 1956 seminal paper on optimal design of control charts has had little practical relevance. The research formulations became more mechanical, less philosophical and less practical. We explore the reasons for this and make suggestions for new research directions. We also propose changes in the supporting industry-university relationships to facilitate a program of more relevant research in statistical process control.

Mathematical optimization of glaucoma visual field screening protocols

There is potential for significantly shortening the time required for visual field screening protocols by a precise specification of the number, exact location, and sequence of points to be tested. Through statistical and mathematical methods, protocols have been developed for maximizing the probability of detecting at least one visual field defect in a subject who is a risk for early glaucomatous field loss. The mathematical formulation was derived in a generalized manner so that it could be applied to most kinetically or statically determined visual field screening methods.