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The Mexico City Metrobus is one of the most popular forms of public transportation inside the city, and since its opening in 2005, it has become a vital piece of infrastructure for the city; this is why the optimal functioning of the system is of key importance to Mexico City, as it plays a crucial role in moving millions of passengers every day. This paper presents a model to simulate Line 1 of the Mexico City Metrobus, which can be adapted to simulate other bus rapid transit (BRT) systems. We give a detailed description of the model development so that the reader can replicate our model. We developed various response variables in order to evaluate the system's performance, which focused on passenger satisfaction and measured the maximum occupancy that a passenger experiences inside the buses, as well as the time that he spends in the queues at the stations. The results of the experiments show that it is possible to increase passenger satisfaction by considering different combinations of routes while maintaining the same fuel consumption. It was shown that, by considering an appropriate combination of routes, the average passenger satisfaction could surpass the satisfaction levels obtained by a 10% increase in total fuel consumption. [ABSTRACT FROM AUTHOR]

When there is uncertainty in the value of parameters of the input random components of a stochastic simulation model, two-level nested simulation algorithms are used to estimate the expectation of performance variables of interest. In the outer level of the algorithm n observations are generated for the parameters, and in the inner level m observations of the simulation model are generated with the values of parameters fixed at the values generated in the outer level. In this article, we consider the case in which the observations at both levels of the algorithm are independent and show how the variance of the observations can be decomposed into the sum of a parametric variance and a stochastic variance. Next, we derive central limit theorems that allow us to compute asymptotic confidence intervals to assess the accuracy of the simulation-based estimators for the point forecast and the variance components. Under this framework, we derive analytical expressions for the point forecast and the variance components of a Bayesian model to forecast sporadic demand, and we use these expressions to illustrate the validity of our theoretical results by performing simulation experiments with this forecast model. We found that, given a fixed number of total observations n m , the choice of only one replication in the inner level ( m = 1 ) is recommended to obtain a more accurate estimator for the expectation of a performance variable. [ABSTRACT FROM AUTHOR]

The formulation and solution to the newsvendor problem using a Bayesian approach is presented. This approach allows us to incorporate the uncertainty in the parameters of demand distribution (introduced in the process of parameter estimation). An example that allows obtaining an analytical solution is presented and experiments are performed with the model in order to compare the results using the proposed Bayesian approach versus the classical method. In addition, the optimal order size is determined using stochastic simulation, methodology that is suggested when model complexity does not allow obtaining an analytical solution. [ABSTRACT FROM AUTHOR]

In this article, a review of the main techniques proposed for the analysis of random components in stochastic simulations is presented. Two main topics are discussed: classical modeling using univariate distributions and advanced modeling techniques. The use of a library is introduced in the first topic; this library is named Simple Analyzer and can be downloaded for free from the web. In the second topic, techniques for input analysis that are currently not included in available commercial software of simulation experiments are discussed. Also the fitting of data of multimodal, correlated and time-dependent input components, and the incorporation of parameter uncertainty in the input model are analyzed. [ABSTRACT FROM AUTHOR]

In this article three methods (multiple replications, non-overlapping batches and spaced batches) to estimate the expectation, the variance and the 90%-quantile of the steady-state waiting time in an M/M/1 queue are compared. Our comparison is based on the empirical coverage, bias and relative error of 90% asymptotic confidence intervals from 1000 independent replications of a simulation-based estimation. Experimental results show that all three methods provide similar (and valid) empirical coverage for the estimation of the expectation, variance and quantile; and the method of non-overlapping batches provided smaller bias and relative errors than the other two methods. In addition to this, an example of a continuous state-space Markov chain that is ergodic but non-geometric, is presented. For this case asymptotically valid confidence intervals by using the methods considered in this paper are also obtained. [ABSTRACT FROM AUTHOR]