A Simple Multifractal Model for Self-Similar Traffic Flows in High-Speed Computer Networks

This paper presents a simple and fast technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov Modulated Poisson Process models has been performed.

Development of multifractal models for self-similar traffic flows

This paper presents a simple technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov Modulated Poisson Process models has been performed.

A simple multifractal model for self-similar traffic flows in high-speed computer networks

This paper presents a simple and fast technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov Modulated Poisson Process models has been performed.

An Exact Analytical Model for an IoT Network with MMPP Arrivals

Analytical modeling of the Internet of Things (IoT) networks is challenging. This is due to the presence of a large number of devices in these networks and the complexity of the priorities between different types of traffic. Taking these aspects into account, the objective of this paper is to analyze the performance of an IoT network where the IoT devices work independently of one another. To this end, we developed a novel multi-dimensional Continuous-Time Markov Chain (CTMC) model with threshold-based preemption. In this model, each IoT device is modeled as a Markov Modulated Poisson Process (MMPP) that can transmit regular and alarm packets. Alarm packets have higher priority over regular packets. To measure access to the channel between alarm and regular packets, we introduced a threshold parameter where the threshold is the number of packets in the alarm queue that indicates when preemption starts. The performance measures include blocking probability, the average delay of regular packets and alarm packets, discard rate , and success probability of regular packets. Comprehensive numerical analysis was conducted. Our results indicate that impact of the threshold on performance measures is higher on the boundary values of the threshold. The model was proven to be efficient in analyzing the performance of IoT networks on a wide range of parameter values. These results may be used in the future to develop and assess a protocol that utilizes a scheduling algorithm with a dynamic preemption threshold to optimize the performance of the IoT network.

Analysis of Queueing System MMPP/M/K/K with Delayed Feedback

The model of multi-channel queuing system with Markov modulated Poisson process (MMPP) flow and delayed feedback is considered. After the customer is served completely, they will decide either to join the retrial group again for another service (feedback) with some state-dependent probability or to leave the system forever with complimentary probability. Feedback calls organize an orbit of repeated calls (r-calls). If upon arrival of an r-call all the channels of the system are busy, then it either leaves the system with some state-dependent probability or with a complementary probability returns to orbit. Methods to calculate the steady-state probabilities of the appropriate three-dimensional Markov chain as well as performance measures of investigated system are developed. Results of numerical experiments are demonstrated.

Analytically Explicit Results for the Distribution of the Number of Customers Served during a Busy Period for Special Cases of the M/G/1 Queue

This paper presents analytically explicit results for the distribution of the number of customers served during a busy period for special cases of the M/G/1 queues when initiated with m customers. The functional equation for the Laplace transform of the number of customers served during a busy period is widely known, but several researchers state that, in general, it is not easy to invert it except for some simple cases such as M/M/1 and M/D/1 queues. Using the Lagrange inversion theorem, we give an elegant solution to this equation. We obtain the distribution of the number of customers served during a busy period for various service-time distributions such as exponential, deterministic, Erlang-k, gamma, chi-square, inverse Gaussian, generalized Erlang, matrix exponential, hyperexponential, uniform, Coxian, phase-type, Markov-modulated Poisson process, and interrupted Poisson process. Further, we also provide computational results using our method. The derivations are very fast and robust due to the lucidity of the expressions.

Parsimonious modelling of winter season rainfall incorporating reanalysis climatological data

Several Markov modulated Poisson process (MMPP) models are developed to describe winter season rainfall with parsimonious parameter use. We propose a methodology for determining the best form of seasonal model for fine-scale rainfall within a MMPP framework. Of those proposed here, a model with a fixed transition rate is shown to be superior over the other MMPP models considered. The model is expanded to include covariate data for sea-level air pressure, relative humidity, and temperature using reanalysis data over 14 years from the coordinates covering the Bracknell rainfall collection site in England. Results are compared using the likelihood ratio test and the second-order properties of aggregated rainfall.