James P. Jarvis

Modeling co-located servers and dispatch ties in the hypercube model

Abstract Several spatially distributed queuing models, notably the hypercube models, have been developed for emergency vehicle service systems. None of these models specifically address the issue of dispatch preference ties that is commonly encountered in systems with co-located units; e.g. ambulance systems. A variation of the hypercube model that accommodates preference ties is developed and applied to the emergency medical system of Greenville County, S.C.

Technical Note-Estimating the Probability Distribution of Travel Times for Urban Emergency Service Systems

We describe an extension of Larsons hypercube queuing model to enable it to calculate the probability distributions of travel times. In addition, we discuss the general need for this capability in emergency service models as a prerequisite for developing second-generation models that may relate direct outcome measures such as damage, loss of life, and arrests to the managerial decisions.

Optimal assignments in a markovian queueing system

Abstract A generalization of the Hypercube queueing model for exponential queueing systems is presented which allows for distinguishable servers and multiple types of customers. Given costs associated with each server-customer pair, the determination of the assignment policy which minimizes time-averaged costs is formulated as a Markov decision problem. A characterization of optimal policies is obtained and used in an efficient algorithm for determining the optimum. The algorithm combines the method of successive approximations and “Howards method” in a manner which is particularly applicable to Markov decision problems having large, sparse transition matrices.

An Improved Algorithm for Approximating the Performance of Stochastic Flow Networks

A problem encountered in the analysis of communication and other distribution systems is evaluating the performance of the system in meeting user demands with available resources. We consider the case in which user demands and available resources are only known stochastically and connecting links can operate at various levels. This situation can be modeled as a two-terminal stochastic network flow problem, in which each edge of the network assumes a finite number of values (corresponding to different capacity levels) with known probabilities. For each state of the network, we are interested in the maximum demand that can be met using the best allocation of resources. The approach used here to estimate the average unmet demand involves generating only “high leverage” states of the system—states having high probability and/or high values of unmet demand. A new algorithm is proposed for generating such states in monotone order, either by probability or by unmet demand. Bounds on the performance of the networ...

Forecasting recreation demand in the upper Savannah River Basin

Abstract Saunders, Paul R., Herman F. Senter, and James P. Jarvis, Forecasting Recreation Demand in the Upper Savannah River Basin. Annals of Tourism Research 1981, VIII(2):236–256. The Upper Savannah River Basin in Georgia and South Carolina, USA, offers opportunities for a variety of recreation activities. Four major reservoirs, and a fifth one under construction, are available for recreation use. Most users live within 80 to 160 kilometers of the two principal reservoirs, Hartwell Lake and Clark Hill Lake. A recreation demand model was developed for these two reservoirs and the soon to be completed Russell Lake, basing total demand on projected population and participation rates for fourteen selected activities. Total demand, consisting of met and unmet demand, was predicted for 1976, 1980, 1990, 2000 and 2010. The model is a relatively simple tool which can be used by state, local, and regional planners to predict both demand for facilities, and the supply of facilities needed to meet future demand.

Reliability Computations for Planar Networks

The two-terminal reliability problem for an undirected network involves calculating the probability that two distinguished sites are connected by a path of working edges. This problem is known to be NP-hard, even for the special case of planar systems. We present efficient data structures and algorithms for manipulating planar networks and for generating both paths an cutsets in such networks. A pseudopolynomial algorithm is then implemented, based on these generation procedures, to calculate two-terminal reliability for planar networks; that is, the algorithms time complexity is polynomially bounded in the number of paths (or the number of cutsets). Computational experience with this implementation is also presented, showing that it provides a substantial improvement over previous implementations of the pseudopolynomial algorithm. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

A location model with queueing constraints

Abstract Many models used for locating service facilities assume that customer demand is deterministic and that service facilities are always available. Stochastic demands for service may cause queueing if the server is not available. We consider a model which combines the spatial aspects of locating service faculties with the service delays caused by stochastic customer demands. The resulting 0–1 integer linear program may be solved by existing algorithms. An example is presented to illustrate the effect of the queueing considerations.

Algorithm 613: Minimum Spanning Tree for Moderate Integer Weights

The problem of determining a minimum spanning tree arises in a number of application areas, including network reliability, pattern recognition, clustering, and design of distribution systems. The present algorithm implements Prims procedure [7] for calculating a minimum spanning tree in an undirected network when the edge costs can be scaled to integers in a moderate range. While other codes for implementing Prims procedure have been published [4, 6, 8, 9], all have used a two-dimensional array for storing the edge costs. As a result, such implementations have been limited to fairly small networks (e.g., 100 or fewer vertices). Moreover, these previous codes do not take advantage of network sparsity to reduce the computational effort. In contrast, the present code does exploit network sparsity and has been used to calculate minimum spanning trees for networks with up to 500 vertices and 24,000 edges. Even such large problems required less than 0.7 seconds of CPU time on an IBM 370/3033 computer (IBM Extended H FORTRAN compiler). For the algorithm given here, the edge costs are assumed to be positive integers with maximum edge cost CMAX. The network, assumed to be connected with NV vertices, is represented in forward star form [2, 3]. That is, for each vertex i E {1 . . . . . NV}, EPT( i ) is a pointer to the first position in a list E L I S T where the vertices j adjacent to i are stored consecutively. A list ECOST, of the same size as ELIST, stores the corresponding edge costs c(i, j) for the edges (i, j). It

An Efficient Enumeration Algorithm for the Two-Sample Randomization Distribution

In many experimental situations, subjects are randomly allocated to treatment and control groups. Measurements are then made on the two groups to ascertain if there is in fact a statistically significant treatment effect. Exact calculation of the associated randomization distribution theoretically involves looking at all possible partitions of the original measurements into two appropriately-sized groups. Computing every possible partition is computationally wasteful, so our objective is to systematically enumerate partitions starting from the tail of the randomization distribution. A new enumeration scheme that only examines potentially worthwhile partitions is described, based on an underlying partial order. Numerical results show that the proposed method runs quickly compared to complete enumeration, and its effectiveness can be enhanced by use of certain pruning rules.