Analysis of networks buffer using discrete-time queueing models

Many important factors affect the spread of childhood infectious disease. To better understand the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients in discrete-time models. In this paper, we build upon this previous work and also develop a framework for efficient estimation using continuous differential equation models. We introduce nonlinear programming formulations to efficiently estimate model parameters and seasonal transmission profiles from existing case count data for the childhood disease, measles. We compare results from discrete time and continuous time models and address several shortcomings of the discrete-time method, including removing the need for the data reporting interval to match the time between successive cases in the chain of transmission or serial interval of the disease. Using a simultaneous approach for optimization of differential equation systems, we demonstrate that seasonal transmission parameters can be effectively estimated using continuous time models instead of discrete-time models.

A discrete-time multi-server queueing model for opportunistic spectrum access systems

American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison

Granger Causality and the Sampling of Economic Processes

We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space — discrete time version of this model and, under suitable scaling, we show its functional convergence to a continuous space — discrete time model. Then, we show a thermodynamic limit of the empirical distribution to the solution of a kinetic equation of Boltzmann type. We solve this equation and we show that the solutions coincide with the appropriate limits of the invariant measure for the Markov chain. In this way we complete Boltzmann’s program of deriving kinetic equations from random dynamics for this simple model. Three families of invariant measures for the mean field limit are discovered and we show that only two of those families can be obtained as limits of the discrete system while the third is extraneous.

This paper addresses the problem of idle speed control of hydrogen fueled internal combustion engine (H2ICE) using model predictive control (MPC) and sampled data control (SDC) theories. In the first step, results from SDC theory and a version of MPC are collectively employed to obtain a rigorously developed new generic control strategy. Here, a controller, based on a family of approximate discrete time models, is designed within a previously proposed framework to have guaranteed practical asymptotic stability of the exact (unknown) discrete time model. Controller design, accomplished using MPC theory, is facilitated by successive online linearizations of the nonlinear discrete time model at each sampling instant. In the second step, the technique is implemented in the idle speed control of hydrogen internal combustion engine (H2ICE). Various conditions under which this theory can be implemented are presented and their validity for idle speed control problem are discussed. Simulations are presented to illustrate the effectiveness of the control scheme.

Variables aggregation in a time discrete linear model

This thesis is motivated by the limitations of the existing discrete time competing risks models vis-a-vis the treatment of data that comes with missing failure causes or a sizableproportions of cured subjects. The discrete time models that have been suggested to date (Davis and Lawrance, 1989; Tutz and Schmid, 2016; Ambrogi et al., 2009; Lee et al., 2018) are cause-specific-hazard denominated. Clearly, this fact summarily disqualifies these models from consideration if data comes with missing failure causes. It is also a well documented fact that naive application of the cause-specific-hazards to data that has a sizable proportion of cured subjects may produce downward biased estimates for these quantities. The existing models can be considered within the multiple imputation framework (Rubin, 1987) for handling missing failure causes, but the prospects of scaling them up for handling cured subjects are minimal, if not nil. In this thesis we address these issues concerning the treatment of missing failure causes and cured subjects in discrete time settings. Towards that end, we focus on the mixture model (Larson and Dinse, 1985) and the vertical model (Nicolaie et al., 2010) because these models possess certain properties which dovetail with the objectives of this thesis. The mixture model has been upgraded into a model that can handle cured subjects. Nicolaie et al. (2015) have demonstrated that the vertical model can also handle missing failure causes as is. Nicolaie et al. (2018) have also extended the vertical model to deal with cured subjects. Our strategy in this thesis is to exploit both the mixture model and the vertical model as a launching pad to advance discrete time models for handling data that comes with missing failure causes or cured subjects. Iqoqa. Isisusa salo mqingo wocwaningo silethwe ukugqoza kwezindlela ezibheka ubungozi bento kanye nendlela okubhekwa ngayo imininingo ekhuluma ngokwehluleka ukuhlonza imbangela yenkinga noma ukuqhamuka nekhambi lokwelapha lokho osekuyisisulu. Izindlela ezibheka isikhathi yizona ezisaphakanyiswayo kuze kube yimanje (Davis & Lawrance, 1989; Tutz & Schmid, 2016; Ambrogi et al., 2009; Lee et al., 2018) uma kubhekwa imbangela eqondene ngqo nengozi leyo. Kuyacaca ukuthi lezi zindlela ngeke zithathwe njengezisebenza kahle uma imininingo yocwaningo iveza ukuthi ziyahluleka ukuhlonza izimbangela zokungasebenzi kahle kokucwaningwayo. Kunobufakazi obusekwa wucwaningo futhi ukuthi ukusetshenziswa ngokungacopheleli izindlela ezibheka ngqo imbangela yenkinga ngemininingo yocwaningo eveza isibalo esikhulu sezisulu ezingalashwayo kuwukuhlehlela emuva kwezokwelapha ngoba kungaletha imiphumela echemile. Izindlela ezisebenzayo okwamanje zingahlolisiswa kusetshenziswa indlela exubile yokuhlola, imultiple imputation framework (Rubin, 1987) ukuhlonza izimbangela zokungasebenzi kahle kokucwaningwayo, kodwa amathuba okukhuphula ukusebenza kwazo ukulawula isibalo sokulashwa kwezisulu ezicwaningwayo mancane kakhulu, noma nje awekho. Kulo mqingo wocwaningo, sibheka lezi zinto nokuhluleka ukuhlonza izimbangela zokungasebenzi kahle kokucwaningwayo kanye nokwelashwa kwezisulu ngesikhathi esithize esibekiwe. Ekugcineni, sigxile ekusetshenzisweni kwendlela exubile (Nicolaie et al., 2010) ngoba le ndlela iyahambelana nezinhlosongqangi zalolu cwaningo. Indlela exubile ikwazile ukwenziwa kangcono ibe yindlela ekwaziyo ukulawula izisulu esezilaphekile. UNicolaie et al. (2015) bavezile ukuthi indlela ebheka phezulu iyakwazi ukulawula ukuhlonza izimbangela zokungasebenzi kahle kokucwaningwayo. UNicolaie et al. (2018) baphinde basebenzisa indlela eya phezulu ukubheka ukwelashwa kwezisulu. Isu lethu kulo mqingo wocwaningo ukusebenzisa kokubili, indlela yocwaningo exubile kanye nendlela eya phezulu njengezindlela ezikwazi ukubheka ukubaluleka kwesikhathi kanye nokucubungula imininingo mayelana nezimbangela zokungasebenzi kahle kokucwaningwayo.

We study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale h ℕ 0 h $h\mathbb{N}_0^h$ , where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

Continuous order identification of PHWR models under step-back for the design of hyper-damped power tracking controller with enhanced reactor safety

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.

A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GIX/Geo/c/N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a simple derivation for the model GIX/Geo/c/N that leads to a complete solution in an explicit form. The same method can also be used to solve the GIX/Geo/c/N queues with heavy-tailed inter-batch-arrival time distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue lengths at different time epochs. All queue-length distributions are in the form of sums of geometric terms.

In solving discrete time queueing models by numerical techniques, the computational requirements (computer memory and time) are a practical limitation and are particularly dependent on the number of discrete time intervals required in the discrete distribution chosen to match the general service distribution. This paper shows that the minimum number of points required for matching to the first two moments depends on the size of the discrete interval relative to the mean and also on the coefficient of variation. Equations and graphs are provided that will enable the OR practitioner to select the discrete distribution to be used as an approximation. Additionally, it is concluded that discrete time modelling, using these approximations to model service time, now provides a practical means to model both steady-state measures and transient behaviour of M/G/c, M(t)/G/c and M(t)/G/c(t) queueing systems on a personal computer.

In this paper, we deal with congestion control of one bottleneck type for TCP/AQM network systems and investigate the H 2 control performance limitation. To this end, we first represent the dynamics of the congestion window size at source nodes and the queue length at the bottleneck link by a discrete time model. We then prove the stability of the plant and provide the Youla parametrization of all stabilizing controllers. With this parametrization, we consider an H 2 optimization problem of the queue length at the bottleneck link. We derive an explicit form of the best achievable H 2 norm and discuss the control performance limitation with respect to the ratio of the transmission time of the packets from source nodes to the link and the round trip time.

New distribution theory for the estimation of structural break point in mean