Frederico R. B. Cruz

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 M/G/C/C state-dependent network simulation model

A discrete-event digital simulation model is developed to study traffic flows in M/G/C/C state-dependent queueing networks. Several performance measures are evaluated, namely (i) the blocking probability, (ii) throughput, (iii) the expected number of the customers in the system, and (iv) expected travel (service) time. Series, merge, and split topologies are examined with special application to pedestrian planning evacuation problems in buildings. Extensive computational experiments are presented showing that the simulation model is an effective and insightful tool to validate analytical expressions and also to analyze general accessibility in network evacuation problems especially in high-rise buildings.

Approximate analysis of M/G/c/c state-dependent queueing networks

Congestion is ever present in most practical situations. We describe a methodology for approximate analysis of open state-dependent M/G/c/c queueing networks in which the service rate is subject to congestion, that is, it is a function of the number of customers in the system. Important performance measurements are easily computed with high accuracy, such as the blocking probability, throughput, expected number of customers in the system (known also as work-in-process), and expected waiting time. The methodology forms a basic building block useful in many practical applications and contexts. Computational results demonstrate that the methodology provides accurate results in many topological configurations as well as in the analysis of network evacuation problems in high-rise buildings.

Extension to the product partition model: computing the probability of a change

The well-known product partition model (PPM) is considered for the identification of multiple change points in the means and variances of normal data sequences. In a natural fashion, the PPM may provide product estimates of these parameters at each instant of time, as well as the posterior distributions of the partitions and the number of change points. Prior distributions are assumed for the means, variances, and for the probability p that each individual time is a change point. The PPM is extended to generate the posterior distribution of p and the posterior probability that each instant of time is a change point. A Gibbs sampling scheme is used to compute all estimates of interest. The methodology is applied to an important time series from the Brazilian stock market. A sensitivity analysis is performed assuming different prior specifications of p.

Service and capacity allocation in M/G/c/c state-dependent queueing networks

The problem of service and capacity allocation in state-dependent M/G/c/c queueing networks is analyzed and algorithms are developed to compute the optimal allocation c. The model is applied to the modeling of pedestrian circulation systems and basic series, merge, and split topologies are examined. Also of interest are applications to problems of evacuation planning in buildings. Computational experiments assert the algorithms speed, robustness, and effectiveness. The results obtained indicate that the pattern of the optimal capacity surprisingly repeats over different topologies and it is also heavily dependent upon the arrival rate. Additional computational simulation results are provided to show the accuracy of the approach in all configurations tested.

Solving to optimality the uncapacitated fixed-charge network flow problem

We present the uncapacitated fixed-charge network flow problem and two mathematical programming formulations. We use an exact approach to solve the problem, the well-known branch-and-bound algorithm. We derive bounds for the algorithm using Lagrangean Relaxation and also propose an efficient branching strategy which is based on an important property of the optimal solution. We also use a Lagrangean Relaxation of the problem to develop a new reduction test. The practical efficiency of all the procedures is demonstrated through a comprehensive set of computational experiments.

A Gibbs sampling scheme to the product partition model: an application to change-point problems

This paper extends previous results for the classical product partition model applied to the identification of multiple change points in the means and variances of time series. Prior distributions for these two parameters and for the probability p that a change takes place at a particular period of time are considered and a new scheme based on Gibbs sampling to estimate the posterior relevances of the model is proposed. The resulting algorithm is applied to the analysis of two Brazilian stock market data. The computational experiments seem to indicate that the algorithm runs fast in common PC-like machines and it may be a useful tool for analyzing change-point problems.

Throughput maximization of queueing networks with simultaneous minimization of service rates and buffers.

The throughput of an acyclic, general-service time queueing network was optimized, and the total number of buffers and the overall service rate was reduced. To satisfy these conflicting objectives, a multiobjective genetic algorithm was developed and employed. Thus, our method produced a set of efficient solutions for more than one objective in the objective function. A comprehensive set of computational experiments was conducted to determine the efficacy and efficiency of the proposed approach. Interesting insights obtained from the analysis of a complex network may assist practitioners in planning general-service queueing networks.

Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models

In this paper we investigate bootstrap techniques applied to the estimation of the fractional differential parameter in ARFIMA models, d. The novelty is the focus on the local bootstrap of the periodogram function. The approach is then applied to three different semiparametric estimators of d, known from the literature, based upon the periodogram function. By means of an extensive set of simulation experiments, the bias and mean square errors are quantified for each estimator and the efficacy of the local bootstrap is stated in terms of low bias, short confidence intervals, and low CPU times. Finally, a real data set is analyzed to demonstrate that the methodology may be quite effective in solving real problems.

An analysis of the influence of some prior specifications in the identification of change points via product partition model

In this paper, we consider the product partition model for the estimation of normal means and variances of a sequence of observations that experiences changes in these parameters at unknown times. The estimates of the parameters by using product partition model are the weighted average of the estimates based in blocks (groups) of observations by the posterior relevance of these blocks which depends on the prior cohesions. We implement the Barry and Hartigans method to this change point problem and propose an easy-to-implement modification to their method. We use Yaos prior cohesions and investigate the influence of different prior distributions to the parameter that indexes these cohesions in the product estimates. A comparison between the estimates obtained by using both these methods and those provided by using Yaos method is done considering different settings for its application. We apply the three methods presented in this paper to stock market data. The results seem to indicate that the method proposed is competitive and also that the prior specifications influence in the product estimates.