Analysis of a discrete-time single-server queue with an occasional extra server

We consider a discrete-time queueing system having two distinct servers: one server, the "regular" server, is permanently available, while the second server, referred to as the "extra" server, is only allocated to the system intermittently. Apart from their availability, the two servers are identical, in the sense that the customers have deterministic service times equal to 1 fixed-length time slot each, regardless of the server that processes them. In this paper, we assume that the extra server is available during random "up-periods", whereas it is unavailable during random "down-periods". Up-periods and down-periods occur alternately on the time axis. The up-periods have geometrically distributed lengths (expressed in time slots), whereas the distribution of the lengths of the down-periods is general, at least in the first instance. Customers enter the system according to a general independent arrival process, i.e., the numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. For this queueing model, we are able to derive closed-form expressions for the steady-state probability generating functions (pgfs) and the expected values of the numbers of customers in the system at various observation epochs, such as the start of an up-period, the start of a down-period and the beginning of an arbitrary time slot. At first sight, these formulas, however, appear to contain an infinite number of unknown constants. One major issue of the mathematical analysis turns out to be the determination of these constants. In the paper, we show that restricting the pgf of the down-periods to be a rational function of its argument, brings about the crucial simplification that the original infinite number of unknown constants appearing in the formulas can be expressed in terms of a finite number of independent unknowns. The latter can then be adequately determined based on the bounded nature of pgfs inside the complex unit disk, and an extensive use of properties of polynomials. Various special cases, both from the perspective of the arrival distribution and the down-period distribution, are discussed. The results are also illustrated by means of relevant numerical examples. Possible applications of this type of queueing model are numerous: the extra server could be the regular server of another similar queue, helping whenever an idle period occurs in its own queue; a geometric distribution for these idle times is then a very natural modeling assumption. A typical example would be the situation at the check-in counter at a gate in an airport: the regular server serves customers with a low-fare ticket, while the extra server gives priority to the business-class and first-class customers, but helps checking regular customers, whenever the priority line is empty. (C) 2017 Elsevier B.V. All rights reserved

Creation and Simulation of a Model for a Discrete Time Buffer System with Interrupted Poisson Arrivals and Uncorrelated Server Interruptions

A mathematical model for a discrete-time buffer system with both arrival and server interruptions is developed. In this model fixed-size packets arrive at the buffer according to a Poisson distribution and are stored there until they can be transmitted over the output channel. Service times are constant and the buffer is assumed to be of infinite size. Both arrival stream as well as the service of the packets are subjected to random interruptions described by Bernoulli processes, where the interruption process of the Poisson input stream is uncorrelated to the interruptions of the output line. Expressions are derived for the mean waiting time, the mean queue length, the average lengths of idle and busy periods of the server, and for the server utilization. The behavior of the system is demonstrated with a computer simulation; the simulation results are used to indicate optimal buffer sizes

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

Variance of the output in a deterministic two-machine line

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1995.Includes bibliographical references (p. 133-134).by Maria Carrascosa.M.S

Capacity dynamics of feed-forward, flow-matching networks exposed to random disruptions

While lean manufacturing has greatly improved the efficiency of production operations, it has left US enterprises in an increasingly risky environment. Causes of manufacturing disruptions continue to multiply, and today, seemingly minor disruptions can cause cascading sequences of capacity losses. Historically, enterprises have lacked viable tools for addressing operational volatility. As a result, each year US companies forfeit billions of dollars to unpredictable capacity disruptions and insurance premiums. In this dissertation we develop a number of stochastic models that capture the dynamics of capacity disruptions in complex multi-tier flow-matching feed-forward networks (FFN). In particular, we relax basic structural assumptions of FFN, introduce random propagation times, study the impact of inventory buffers on propagation times, and make initial efforts to model random network topology. These stochastic models are central to future methodologies supporting strategic risk management and enterprise network design

Analysis of buffer allocations in time-dependent and stochastic flow lines

This thesis reviews and classifies the literature on the Buffer Allocation Problem under steady-state conditions and on performance evaluation approaches for queueing systems with time-dependent parameters. Subsequently, new performance evaluation approaches are developed. Finally, a local search algorithm for the derivation of time-dependent buffer allocations is proposed. The algorithm is based on numerically observed monotonicity properties of the system performance in the time-dependent buffer allocations. Numerical examples illustrate that time-dependent buffer allocations represent an adequate way of minimizing the average WIP in the flow line while achieving a desired service level

Development and analysis of the Software Implemented Fault-Tolerance (SIFT) computer

SIFT (Software Implemented Fault Tolerance) is an experimental, fault-tolerant computer system designed to meet the extreme reliability requirements for safety-critical functions in advanced aircraft. Errors are masked by performing a majority voting operation over the results of identical computations, and faulty processors are removed from service by reassigning computations to the nonfaulty processors. This scheme has been implemented in a special architecture using a set of standard Bendix BDX930 processors, augmented by a special asynchronous-broadcast communication interface that provides direct, processor to processor communication among all processors. Fault isolation is accomplished in hardware; all other fault-tolerance functions, together with scheduling and synchronization are implemented exclusively by executive system software. The system reliability is predicted by a Markov model. Mathematical consistency of the system software with respect to the reliability model has been partially verified, using recently developed tools for machine-aided proof of program correctness