The Efficacy of Spreadsheet Modelling As an Alternative Means of Teaching Process Simulation

Spreadsheet based simulation has many advantages over the pre-programmed simulation applications more commonly used in teaching simulation in undergraduate courses. They are almost universally ubiquitous in business settings around the world. There is near certainty that students will have access to them after graduation since spreadsheets are a standard business tool used by nearly all engineers [1]. In addition, spreadsheets are already present within most standard operating systems. This means that there will be no need to buy or get approvals from Information Technology software committees or other managerial roadblocks. As an alternative to this, there are now free OpenOffice and LibreOffice spreadsheets available on most platforms which make their access effectively universal. Aside from their excellent availability, spreadsheets are an extremely capable learning tool for best practices in process simulation. Most engineering students are arriving at college with a good set of spreadsheet skills from their primary education and then the rest tend to pick it up early as underclassmen [2]. Spreadsheet simulation is easy to explain and generally very simple to debug. Although the now mainly antiquated code-based simulation packages used to offer these same advantages, they have now been largely replaced by more graphically oriented packages which depend in part on subtle mouse clicks and sometimes complex sub-menu structures. In addition, spreadsheets offer easily accessible native analysis and excellent graphing capabilities. Several advantages and potential disadvantages of spreadsheet simulation are presented in comparison to contemporary process simulation. Several simulation projects are then discussed related to Markovian processes including stochastic scatter patterns, sequential random object movement, multi-server queueing processes, dynamic intercept models, complex traffic and evacuation models, and Susceptible-Infected-Removed infections design simulations were taught using spreadsheet simulation.

BOUNDARY CROSSING PROBABILITIES FOR THE CUMULATIVE SAMPLE MEAN

We develop a new measure of reliability for the mean behavior of a process by calculating the probability the cumulative sample mean will stay within a given distance from the true mean over a period of time. This probability is derived using boundary-crossing properties of Brownian bridges. We derive finite sample results for independent and identically distributed normal data, limiting results for data meeting a functional central limit theorem, and draw parallels to standard normal confidence intervals. We deliver numerical results for i.i.d., dependent, and queueing processes.

Exclusive queueing processes and their application to traffic systems

Pedestrian queues like those observed at ticket counters or supermarket checkouts are usually described by classical queueing theory. However, models like the M/M/1 queue neglect the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered on a microscopic level. It is equivalent to a Totally Asymmetric Exclusion Process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability α and the service probability β. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used. In this paper, we review the main properties of the EQP and its applications to pedestrian dynamics, vehicular traffic and biological systems. We also mention extensions of the EQP and some related models.

TAIL PROBABILITIES IN QUEUEING PROCESSES

In the study of large scale stochastic networks with resource management, differential equations and mean-field limits are two key techniques. Recent research shows that the expected fraction vector (that is, the tail probability vector) plays a key role in setting up mean-field differential equations. To further apply the technique of tail probability vector to deal with resource management of large scale stochastic networks, this paper discusses tail probabilities in some basic queueing processes including QBD processes, Markov chains of GI/M/1 type and of M/G/1 type, and also provides some effective and efficient algorithms for computing the tail probabilities by means of the matrix-geometric solution, the matrix-iterative solution, the matrix-product solution and the two types of RG-factorizations. Furthermore, we consider four queueing examples: The M/M/1 retrial queue, the M(n)/M(n)/1 queue, the M/M/1 queue with server multiple vacations and the M/M/1 queue with repairable server, where the M/M/1 retrial queue is given a detailed discussion, while the other three examples are analyzed in less detail. Note that the results given in this paper will be very useful in the study of large scale stochastic networks with resource management, including the supermarket models and the work stealing models.

Fluid Limits of Optimally Controlled Queueing Networks

We consider a class of queueing processes represented by a Skorokhod problem coupled with a controlled point process. Posing a discounted control problem for such processes, we show that the optimal value functions converge, in the fluid limit, to the value of an analogous deterministic control problem for fluid processes.