Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved

Many-Sources Large Deviations for Max-Weight Scheduling

In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and where the service discipline is the max-weight policy. Under the assumption that the arrival processes satisfy a many-sources LDP, this is accomplished by employing Garcia's extended contraction principle that is applicable to quasi-continuous mappings. For the simplex rate-region, an LDP for the stationary workload is also established under the additional requirements that the scheduling policy be work-conserving and that the arrival processes satisfy certain mixing conditions. The LDP results can be used to calculate asymptotic buffer overflow probabilities accounting for the multiplexing gain, when the arrival process is an average of \emph{i.i.d.} processes. The rate function for the stationary workload is expressed in term of the rate functions of the finite-horizon workloads when the arrival processes have \emph{i.i.d.} increments.Comment: 44 page

An Analytical Approach to Cycle Time Evaluation in an Unreliable Multi-Product Production Line with Finite Buffers

This thesis develops an analytical approximation method to measure the performance of a multi-product unreliable production line with finite buffers between workstations. The performance measure used in this thesis is Total Cycle Time. The proposed approximation method generalizes the processing times to relax the variation of product types in a multi-product system. A decomposition method is then employed to approximate the production rate of a multi-product production line. The decomposition method considers generally distributed processing times as well as random failure and repair. A GI/G/1/N queuing model is also applied to obtain parameters such as blocking and starving probabilities that are needed for the approximation procedure. Several numerical experiments under different scenarios are performed, and results are validated by simulation models in order to assess the accuracy and strength of the approximation method. Consequent analysis and discussion of the results is also presented

Fluid flow models in performance analysis

We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions

Queues with Congestion-dependent Feedback

This dissertation expands the theory of feedback queueing systems and applies a number of these models to a performance analysis of the Transmission Control Protocol, a flow control protocol commonly used in the Internet

Stability criteria for controlled queueing networks

We give criteria for the stability of a very general queueing model under different levels of control. A complete classification of stability (or positive recurrence), transience and null-recurrence is presented for the two queue model. The stability and instability results are extended for models with N > 3 queues. We look at a broad class of models which can have the following features: Customers arrive at one, several or all of the queues from the outside with exponential inter arrival times. We often have the case where a arrival stream can be routed so that under different routing schemes each queue can have external arrivals, i.e. we assume we have some control over the routing of the arrivals. We also consider models where the arrival streams are fixed. We view the service in a more abstract way, in that we allow a number к of different service configurations. Under every such service configuration service is provided to some or all of the queues, length of service time can change from one service configuration to another and we can change from one configuration to another according two some control policy. The service times are assumed to be exponentially distributed. The queueing models we consider are networks where, after completion at one queue, a customer might be fed back into another queue where it will be served another time often under with a different service time. These feedback probabilities change with the service configurations. Our interest is in different types of control policies which allow us to change the routing of arrivals and configurations of the service from time to time so that the controlled queue length process (which in most cases is Markov) is stable. The semi-martingale or Lyapunov function methods we use give necessary and sufficient conditions for the stability classification. We will look at some two queue models with different inter arrival and service times where the queueing process is still Markov

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