The asymptotic variance of departures in critically loaded queues

We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case that the system load rho equals 1, and prove that the asymptotic variance rate satisfies lim_t Var D(t)/t = lambda (1 - 2/pi) (c_a2 + c_s2) where lambda is the arrival rate and c_a2 and c_s2 are squared coefficients of variation of the inter-arrival and service times respectively. As a consequence, the departures variability has a remarkable singularity in case rho equals 1, in line with the BRAVO effect (Balancing Reduces Asymptotic Variance of Outputs) which was previously encountered in the finite-capacity birth-death queues. Under certain technical conditions, our result generalizes to multi-server queues, as well as to queues with more general arrival and service patterns. For the M/M/1 queue we present an explicit expression of the variance of D(t) for any t

Analyses of serial production line systems for interdeparture time variability and WIP inventory systems

This paper investigates the well-known and extensively studied unpaced production line problem for the interdeparture time variability and work-in-process (WIP) inventory. The primary objective is to examine the relationships between the interdeparture time variability and some system design factors such as the number of stations, buffer capacity, and location of a bottleneck station. The performance of the system is also evaluated for average and variance of WIP inventory. Simulation is used as a modeling and analysis tool with the results being tested by appropriate statistical procedures. The analysis of the results reveals several important findings on the interdeparture time variability and WIP inventory. We confirm and strengthen some of the previous findings on throughput. In this paper, we also discuss managerial implications and suggest further research areas

Analytical evaluation of the output variability in production systems with general Markovian structure

Performance evaluation models are used by companies to design, adapt, manage and control their production systems. In the literature, most of the effort has been dedicated to the development of efficient methodologies to estimate the first moment performance measures of production systems, such as the expected production rate, the buffer levels and the mean completion time. However, there is industrial evidence that the variability of the production output may drastically impact on the capability of managing the system operations, causing the observed system performance to be highly different from what expected. This paper presents a general methodology to analyze the variability of the output of unreliable single machines and small-scale multi-stage production systems modeled as General Markovian structure. The generality of the approach allows modeling and studying performance measures such as the variance of the cumulated output and the variance of the inter-departure time under many system configurations within a unique framework. The proposed method is based on the characterization of the autocorrelation structure of the system output. The impact of different system parameters on the output variability is investigated and characterized. Moreover, managerial actions that allow reducing the output variability are identified. The computational complexity of the method is studied on an extensive set of computer experiments. Finally, the limits of this approach while studying long multi-stage production lines are highlighted. © 2013 Springer-Verlag Berlin Heidelberg

Analyses of serial production lines and assembly systems for throughput and inyerdeparture time variability

Ankara : Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent Univ., 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 77-81In this thesis, we study three different but closely related production system design problems. First, we investigate the effects of various design factors such as number of stations, buffer capacity, allocation of bulfers and location of a bottleneck on the interdeparture time variability of serial production lines. In the second part, we study the effects of number of component stations, processing time distributions, buffers and buffer allocation schemes on throughput and interdeparture time variability of assembly systems. As an alternative to work transfer, we introduce variability transfer and assess its effectiveness. We analyze the anomaly displayed by optimal throughput for some processing time distributions and uncover the underlying details of this behavior. In the third part, we analyze serial production lines and assembly systems under constant workload condition. In addition to investigating the problem of determining the optimal system size, we examine the effects of other design factors such as buffers and material handling time on throughput, interdeparture time variability and cost related measures. Each part reveals several important findings. We also discuss the managerial implications of these findings to present guidelines for the practitioners.Kök, Abdullah GürhanM.S

On the distribution of throughput of transfer lines

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 86-107A transfer line corresponds to a manufacturing system consisting of a number of work stations in series integrated into one system by a common transfer mechanism and a control system. There is a vast literature on the transfer lines. However, little has been done on the transient analysis of these systems by making use of the higher order moments of their performance measures due to the difficulty in determining the evolution of the stochastic processes under consideration. This thesis examines the transient behavior of relatively short transfer lines and derives the distribution of the performance measures of interest. The proposed method based on the analytical derivation of the distribution of throughput is also applied to the systems with two-part types. An experiment is designed in order to compare the results of this study with the state-space representations and the simulation. They are also interpreted from the point of view of the line behavior and design issue. Furthermore, extensions are briefly discussed and directions for future research are suggested.Deler, BaharM.S