Richard C. Larson

A hypercube queuing model for facility location and redistricting in urban emergency services

Abstract This paper develops computationally efficient algorithms for studying the analytical behavior of a multi-server queuing system with distinguishable servers. The model is intended for analyzing problems of vehicle location and response district design in urban emergency services, includes interdistrict as well as intradistrict responses, and allows computation of several pointspecific as well as area-specific performance measures.

Approximating the Performance of Urban Emergency Service Systems

This paper presents an approximate procedure for computing selected performance characteristics of an urban emergency service system. Based on a recently developed hypercube queuing model, the procedure requires for N servers solution of only N simultaneous equations, rather than 2N as in the exact model. The procedure relies on the theory of M/M/N queues in which servers are selected randomly and without replacement until the first available free server is found. The underlying model is intended for analyzing problems of vehicle location and response district design in urban emergency services, includes interdistrict as well as intradistrict responses, and allows computation of several point-specific as well as area-specific performance measures.

OR Forum—Perspectives on Queues: Social Justice and the Psychology of Queueing

Queues involve waiting, to be sure, but ones attitudes toward queues may be influenced more strongly by other factors. For instance, customers may become infuriated if they experience social injustice, defined as violation of first in, first out. Queueing environment and feedback regarding the likely magnitude of the delay can also influence customer attitudes and ultimately, in many instances, a firms market share. Even if we focus on the wait itself, the “outcome” of the queueing experience may vary nonlinearly with the delay, thus reducing the importance of average time in queue, the traditional measure of queueing performance. This speculative paper uses personal experiences, published and unpublished cases, and occasionally “the literature” to begin to organize our thoughts on the important attributes of queueing. To flesh out more of these issues, the author asks for your cards and letters.

Optimal Location of Discretionary Service Facilities

Automatic teller machines and gasoline service stations are two examples of a growing number of “discretionary service facilities.” In consuming service from these facilities, a significant fraction of customers do so on an otherwise preplanned trip (e.g., on the daily commute to and from work). A system planner, in determining the best locations of such facilities, is more concerned with placing the facilities along paths of customer flow rather than, say, near the center of a cluster of residences or work places. We formally model this problem and present a method for determining the optimal locations of m discretionary service facilities so as to intercept the maximum possible potential customer flow. We also show how to determine the minimal number of facilities required to intercept a prespecified fraction of total customer flow. Computational results are included.

Optimal Server Location on a Network Operating as an M/G/1 Queue

This paper extends Hakimis one-median problem by embedding it in a general queueing context. Demands for service arise solely on the nodes of a network G and occur in time as a Poisson process. A single mobile server resides at a facility located on G. The server, when available, is dispatched immediately to any demand that occurs. When a demand finds the server busy with a previous demand, it is either rejected Model 1 or entered into a queue that is depleted in a first-come, first-served manner Model 2. Service time for each demand comprises travel time to the scene, on-scene time, travel time back to the facility and possibly additional off-scene time. One desires to locate the facility on G so as to minimize average cost of response, which is either a weighted sum of mean travel time and cost of rejection Model 1, or the sum of mean queueing delay and mean travel time. For Model 1, one finds that the optimal location reduces to Hakimis familiar nodal result. For Model 2, nonlinearities in the objective function can yield an optimal solution that is either at a node or on a link. Properties of the objective function for Model 2 are utilized to develop efficient finite-step procedures for finding the optimal location. Certain interesting properties of the optimal location as a function of demand rate are also developed.

Finding minimum rectilinear distance paths in the presence of barriers

Given a set of origin-destination points in the plane and a set of polygonal barriers to travel, this paper develops an efficient algorithm for finding minimal distance feasible paths between the points, assuming that all travel occurs according to the rectilinear distance metric. By geometrical arguments the problem is reduced to a finite network problem. The nodes are the origin-destination points and the barrier vertices. The links designate those node pairs that ”communicate” in a simple way, where communication implies the existence of a node-to-node rectilinear path that is not made longer by the barriers. The weight of each link is the rectilinear distance between its two corresponding nodes. Solution of the minimal distance path problem on the network procedes in two steps. First, for a given origin or root node, a tree is generated containing a minimal distance path to each node that communicates with the root node. Second, a modified Diikstra-type iteration is utilized, starting with the nodes of the tree, sequentially adding nodes according to minimum “penalty distance,” where the penalty is the extra travel distance caused by the barriers. The paper concludes with a discussion of the computational complexity of the procedure, followed by a numerical example.

Facility Locations with the Manhattan Metric in the Presence of Barriers to Travel

This paper considers the optimal location of p facilities in the plane, under the assumption that all travel occurs according to the Manhattan or rectilinear or I1 metric in the presence of impenetrable barriers to travel. Facility users are distributed over a finite set of demand points, with the weight of each point proportional to its demand intensity. Each demand point is assigned to the closest facility. The objective is to locate facilities so as to minimize average Manhattan travel distance to a random demand. We show that an optimal set of facility locations can be drawn from a finite set of candidate points, all of which are easy to determine.

TRANSPORTING SLUDGE TO THE 106-MILE SITE: AN INVENTORY/ROUTING MODEL FOR FLEET SIZING AND LOGISTICS SYSTEM DESIGN

This paper develops a model that is being used by the City of New York to design a new logistics system to transport municipal sewage sludge from city-operated wastewater treatment plants to a new ocean dumping site 106 miles offshore. The model provides an integrative framework for considering such strategic planning issues as fleet sizing, choice of vessel size, sizing local inventory holding capacities, and analyzing system behavior with and without transshipment. A unique feature of the model is that plant visitation frequencies are determined naturally by the characteristics of the problem (vessel size, inventory holding capacities, statistics of sludge production, proximity of other plants), rather than stated as exogeneous constraints. The formulation should be useful in a more general class of depot-to-customer distribution systems, including the distribution of industrial gases. The paper concludes with a description of additional research that is required in refining both the assumptions and the mechanisms of execution of the model.

Models of a Total Criminal Justice System

The need to examine the total criminal justice system—police, prosecution, courts, and correction agencies—in an integrated way constitutes a central problem in improving law enforcement. Too, any such analysis must reflect the feedback into society of offenders released at various stages in the system. This paper formulates a model for the criminal justice system in one state; it depicts the flow of arrested persons through the system as a function of type of crime, and provides a basis for apportioning costs to system components and to types of crime. The models feedback feature includes the probability of rearrest as a decreasing function of age and a crime-switch matrix reflecting the successive-crime distribution. The results from the model include a cost distribution by crime type, criminal-career costs, an examination of the courses of criminal careers, and estimates of the sensitivities of costs and offender flows within the system to changes in its controllable variables.

Disasters: lessons from the past 105 years

Purpose – The purpose of this paper is to study and review some major impacts of the disasters during the past 105 years and develop a new theoretical classification of disasters.Design/methodology/approach – A detailed study of disasters in the world during the period (1900‐2005) has been obtained from the recent published sources. In that period more than 40 lessons have been reported based on statistical data analysis of disasters. Furthermore, a two‐dimensional probability density function is developed to categorize the different types of disasters. This paper studies and reviews some major impacts of disasters during the past 105 years and summarizes some major lessons for the future. Furthermore, a new scaling system is presented to determine the actual damage of disasters to human life.Findings – There is no doubt that the impacts of future disasters will not be the same as previous ones but lessons from the past can be very helpful for improving ones knowledge about disasters and providing better...