J. MacGregor Smith

The generalized expansion method for open finite queueing networks

Blocking makes the exact analytical analysis of open queueing networks with finite capacities intractable except for very small networks, therefore, approximation approaches are needed to analyze these types of networks. For exponential open finite queueing networks, some methods have been proposed but little has been done so far on nonexponential open finite queueing networks. This paper introduces a new approximation technique for the analysis of general open finite queueing networks. Extensive numerical examples are performed for different network topologies and the results are compared with simulation.

TOPOLOGICAL NETWORK DESIGN OF PEDESTRIAN NETWORKS

The design and analysis of series, merge, and splitting topologies of pedestrian networks is presented and an analytical approximation methodology is developed to compute the network performance measures. State dependent queuing networks are appropriate tools for modelling congestion in vehicular and pedestrian traffic networks, and many others where congestion occurs due to a decay in the service rate with increased density of customer traffic. This paper focuses on models for pedestrian network design. Also, an optimization methodology is developed for determining the optimal capacity requirements of these networks and extensive experimental results are included.

Buffer Space Allocation in Automated Assembly Lines

Automated assembly lines are modeled as finite open queueing networks and a heuristic for buffer space allocation within these lines is presented. The Expansion Method, an analytical technique for modeling finite open queueing networks and Powells unconstrained optimization procedure are integrated in a design methodology, which evaluates alternative line topologies, system throughputs, and their optimal buffer sizes. The resulting design methodology is demonstrated for series, merging and splitting topologies of automated assembly lines with balanced and unbalanced service rates.

Path-distance heuristics for the Steiner problem in undirected networks

An integrative overview of the algorithmic characteristics of three well-known polynomialtime heuristics for the undirected Steiner minimum tree problem:shortest path heuristic (SPH),distance network heuristic (DNH), andaverage distance heuristic (ADH) is given. The performance of thesesingle-pass heuristics (and some variants) is compared and contrasted with several heuristics based onrepetitive applications of the SPH. It is shown that two of these repetitive SPH variants generate solutions that in general are better than solutions obtained by any single-pass heuristic. The worst-case time complexity of the two new variants isO(pn3) andO(p3n2), while the worst-case time complexity of the SPH, DNH, and ADH is respectivelyO(pn2),O(m + n logn), andO(n3) wherep is the number of vertices to be spanned,n is the total number of vertices, andm is the total number of edges. However, use of few simple tests is shown to provide large reductions of problem instances (both in terms of vertices and in term of edges). As a consequence, a substantial speed-up is obtained so that the repetitive variants are also competitive with respect to running times.

Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows

The generality and usefulness ofM/G/C/C state dependent queueing models for modelling pedestrian traffic flows is explored in this paper. We demonstrate that the departure process and the reversed process of these generalizedM/G/C/C queues is a Poisson process and that the limiting distribution of the number of customers in the queue depends onG only through its mean. Consequently, the models developed in this paper are useful not only for the analysis of pedestrian traffic flows, but also for the design of the physical systems accommodating these flows. We demonstrate how theM/G/C/C state dependent model is incorporated into the modelling of large scale facilities where the blocking probabilities in the links of the network can be controlled. Finally, extensions of this work to queueing network applications where blocking cannot be controlled are also presented, and we examine an approximation technique based on the expansion method for incorporating theseM/G/C/C queues in series, merge, and splitting topologies of these networks.

The buffer allocation problem for general finite buffer queueing networks

Abstract The Buffer Allocation Problem (BAP) is a difficult stochastic, integer, nonlinear programming problem. In general, the objective function and constraints of the problem are not available in a closed form. An approximation formula for predicting the optimal buffer allocation is developed based upon a two-moment approximation formula involving the expressions for M/ M/1/ K systems. The closed-form expressions of the M/ M/1/ K and M/ G/1/ K systems are utilized for the BAP in series, merge, and splitting topologies of finite buffer queueing networks. Extensive computational results demonstrate the efficacy of the approach.

An O(n log n) heuristic for steiner minimal tree problems on the euclidean metric

An O(n log n) heuristic for the Euclidean Steiner Minimal Tree (ESMT) problem is presented. The algorithm is based on a decomposition approach which first partitions the vertex set into triangles via the Delaunay triangulation, then “recomposes” the suboptimal Steiner Minimal Tree (SMT) according to the Voronoi diagram and Minimum Spanning Tree (MST) of the point set. The ESMT algorithm was implemented in FORTRAN-IV and tested on a number of randomly generated point sets in the plane drawn from a uniform distribution. Comparison of the O(n log n) algorithm with an O(n4) algorithm clearly indicates that the O(n log n) algorithm is as good as the previous O(n4) algorithm in achieving reductions in the ratio SMT/MST of the given vertex set. This is somewhat surprising since the O(n4) algorithm considers more potential Steiner points and alternative tree configurations.

Modeling circulation systems in buildings using state dependent queueing models

Circulation systems within buildings are analyzed using M/G/C/C queueing models. Congestion aspects of the traffic flow are represented by introducing state dependent service rates as a function of the number of occupants in each region of the circulation system. Analytical models for unidirectional and multi-source/single sink flows are presented. Finally, use of the queueing models to analytically determine the optimal size and capacity of the links of the circulation systems is incorporated into a series of software programs available from the authors.

Asymptotic behavior of the expansion method for open finite queueing networks

In previous papers, we have reported on the use of the expansion method for estimating sojourn times in finite network topologies. In this paper, we focus on comparing the expansion method with P. C. Bells consistency conditions where subject to unbalanced service rates at tandem queues, other decomposition approaches yield impossible throughput results. We compare numerical results of the expansion method with the other approaches in light of these conditions.

M/G/c/K blocking probability models and system performance

An exact solution for the M/G/c/K model is only possible for special cases, such as exponential service, a single server, or no waiting room at all. Instead of basing the approximation on an infinite capacity queue as is often the case, an approximation based on a closed-form expression derivable from the finite capacity exponential queue is presented. Properties of the closed-form expression along with its use in approximating the blocking probability of M/G/c/K systems are discussed. Extensive experiments are provided to test and verify the efficacy of our approximate results.