Time-dependent performance approximation of truck handling operations at an air cargo terminal

This paper provides an analytical solution for the time-dependent performance evaluation of truck handling operations at an air cargo terminal. The demand for loading and unloading operations is highly time-dependent and stochastic for two classes of trucks. Two heterogeneous handling facilities with multiple servers are available to handle trucks assuming exponentially distributed processing times. Trucks are routed to a handling facility depending on the current state of the system upon arrival. To approximate the time-dependent behavior of such heterogeneous queueing systems, we develop a stationary backlog-carryover (SBC) approach. A numerical study compares this approach with simulations and demonstrates its applicability to real-world input data

Nonlinear Markov Processes in Big Networks

Big networks express various large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to set up a broad class of nonlinear continuous-time block-structured Markov processes, which can be applied to deal with many practical stochastic systems. Firstly, a nonlinear Markov process is derived from a large number of interacting big networks with symmetric interactions, each of which is described as a continuous-time block-structured Markov process. Secondly, some effective algorithms are given for computing the fixed points of the nonlinear Markov process by means of the UL-type RG-factorization. Finally, the Birkhoff center, the Lyapunov functions and the relative entropy are used to analyze stability or metastability of the big network, and several interesting open problems are proposed with detailed interpretation. We believe that the results given in this paper can be useful and effective in the study of big networks.Comment: 28 pages in Special Matrices; 201

Transient laws of non-stationary queueing systems and their applications

Cover title.Includes bibliographical references (p. 37-39).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118D. Bertsimas and G. Mourtizinou

Transient laws of non-stationary queueing systems and their applications

Cover title.Includes bibliographical references (p. 37-39).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118D. Bertsimas and G. Mourtizinou

The pseudo-self-similar traffic model: application and validation

Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems

Performance analysis of time-dependent queueing systems: survey and classification

Many queueing systems are subject to time-dependent changes in system parameters, such as the arrival rate or number of servers. Examples include time-dependent call volumes and agents at inbound call centers, time-varying air traffic at airports, time-dependent truck arrival rates at seaports, and cyclic message volumes in computer systems.There are several approaches for the performance analysis of queueing systems with deterministic parameter changes over time. In this survey, we develop a classification scheme that groups these approaches according to their underlying key ideas into (i) numerical and analytical solutions,(ii)approaches based on models with piecewise constant parameters, and (iii) approaches based on mod-ified system characteristics. Additionally, we identify links between the different approaches and provide a survey of applications that are categorized into service, road and air traffic, and IT systems

Transient error approximation in a Lévy queue

Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of Lévy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can be significant