Operational Analysis Revisited: Error Measure Limits of Assumptions

The assumptions used to develop operational analysiscomputer performance measures, such as number of jobs at adevice or response times, are stated in terms of the data itself,rather than the underlying system which produces the data. Inspite of claims of validity and as an aid in introducing queueingtheory in teaching, little has been written about operationalanalysis in the past ten years. Accuracy of operational analysisperformance measures depend on data behavior assumptionswhich can be validated with data based error measures.Increased soundness of the operational analysis approach may beobtained by determining the limits of assumption errors as thetime period of observation increases. Part I of this paper is areview of operational analysis and addresses some of the previousconcerns with its approach. Part II develops furtherunderstanding of operational analysis assumption errors byexamining their limits. Limits are found for the assumptionerrors of job flow balance, homogeneous arrivals andhomogenous services. While the job flow balance assumptionerror measure is shown to approach zero over time, thehomogeneity assumption error measures, in general, do not

A Fixed-Point Algorithm for Closed Queueing Networks

In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)

Stochastic analyses arising from a new approach for closed queueing networks

Analyses are addressed for a number of problems in queueing systems and stochastic modeling that arose due to an investigation into techniques that could be used to approximate general closed networks. In Chapter II, a method is presented to calculate the system size distribution at an arbitrary point in time and at departures for a (n)/G/1/N queue. The analysis is carried out using an embedded Markov chain approach. An algorithm is also developed that combines our analysis with the recursive method of Gupta and Rao. This algorithm compares favorably with that of Gupta and Rao and will solve some situations when Gupta and Rao's method fails or becomes intractable. In Chapter III, an approach is developed for generating exact solutions of the time-dependent conditional joint probability distributions for a phase-type renewal process. Closed-form expressions are derived when a class of Coxian distributions are used for the inter-renewal distribution. The class of Coxian distributions was chosen so that solutions could be obtained for any mean and variance desired in the inter-renewal times. In Chapter IV, an algorithm is developed to generate numerical solutions for the steady-state system size probabilities and waiting time distribution functions of the SM/PH/1/N queue by using the matrix-analytic method. Closed form results are also obtained for particular situations of the preceding queue. In addition, it is demonstrated that the SM/PH/1/N model can be implemented to the analysis of a sequential two-queue system. This is an extension to the work by Neuts and Chakravarthy. In Chapter V, principal results developed in the preceding chapters are employed for approximate analysis of the closed network of queues with arbitrary service times. Specifically, the (n)/G/1/N queue is applied to closed networks of a general topology, and a sequential two-queue model consisting of the (n)/G/1/N and SM/PH/1/N queues is proposed for tandem queueing networks

Throughput Analysis of Manual Order Picking Systems with Congestion Consideration

Throughput in manual order picking systems with narrow aisles suffers from congestion as pickers cannot pass each other. Only few models incorporate congestion but they have very strict assumptions. In this work, queueing theory is used to analyze systems with traversal routing as well as different storage policies. The models are able to estimate throughput for many alternative designs in a relatively short amount of time. New guidelines for narrow-­aisle order picking systems are introduced