scholarly journals MODELLING SELF-SIMILAR TRAFFIC OF MULTISERVICE NETWORKS

2019 ◽  
Vol 1 ◽  
pp. 46-54
Author(s):  
Zakir Maharramov ◽  
Vugar Abdullayev ◽  
Tamilla Mammadova
Keyword(s):  
Computer Simulation ◽  
Simulation Modelling ◽  
Similar Process ◽  
Load Factor ◽  
Queuing Systems ◽  
Weibull Distributions ◽  
Time Intervals ◽  
Multiservice Networks ◽  
Self Similar ◽  
Service Duration

Simulation modelling is carried out, which allows adequate describing the traffic of multiservice networks with the commutation of packets with the characteristic of burstiness. One of the most effective methods for studying the traffic of telecommunications systems is computer simulation modelling. By using the theory of queuing systems (QS), computer simulation modelling of packet flows (traffic) in modern multi-service networks is performed as a random self-similar process. Distribution laws such as exponential, Poisson and normal-logarithmic distributions, Pareto and Weibull distributions have been considered. The distribution of time intervals between arrivals of packages and the service duration of service of packages at different system loads has been studied. The research results show that the distribution function of time intervals between packet arrivals and the service duration of packages is in good agreement with the Pareto and Weibull distributions, but in most cases the Pareto distribution prevails. The queuing systems with the queues M/Pa/1 and Pa/M/1 has been studied, and the fractality of the intervals of requests arriving have been compared by the properties of the estimates of the system load and the service duration. It has been found out that in the system Pa/M/1, with the parameter of the form a> 2, the fractality of the intervals of requests arriving does not affect the average waiting time and load factor. However, when 𝑎≤2, as in the M/Pa/1 system, both considered statistical estimates differ. The application of adequate mathematical models of traffic allows to correctly assess the characteristics of the quality of service (QoS) of the network.

Earthquake “Quanta” as an explanation for observed magnitudes and stress drops

1995 ◽  
Vol 85 (3) ◽  
pp. 808-813
Author(s):  
I. Selwyn Sacks ◽  
Paul A. Rydelek
Keyword(s):  
Computer Simulation ◽  
Linear Relation ◽  
Stress Drop ◽  
Constant Stress ◽  
Similar Process ◽  
Self Similar ◽  
Stress Drops

Abstract The familiar linear relation (Gutenberg-Richter) between the logarithm of the number of earthquakes and their magnitude is commonly ascribed to the distribution (fractal) of fault sizes in a self-similar process. We show that a concept of earthquake quanta whose failure is governed by simple physics and suggested by observations explains not only the Gutenberg-Richter relation but also the relatively constant stress drop for larger magnitude events. Results from computer simulation are consistent with observations from detailed seismicity studies.

scholarly journals DELAYS IN QUEUES OF QUEUING SYSTEMS WITH STATIONARY REQUESTS FLOWS

T-Comm ◽  
2021 ◽  
Vol 15 (2) ◽  
pp. 54-58
Author(s):  
Boris Ya. Likhttsinder ◽  
◽  
Yulia O. Bakai ◽  
Keyword(s):  
Flow Model ◽  
Resource Constraints ◽  
Interval Methods ◽  
Queuing Systems ◽  
Channel Switching ◽  
Time Intervals ◽  
Flow Models ◽  
Average Value ◽  
Multiservice Networks ◽  
Stationary Flows

During all periods of the study of telecommunications systems traffic, the analysis was based on mass service theory. The subjects of the study here are request flows to be processed by some limited performance resources. Resource constraints and the random nature of requests’ receipt lead to refusals in processing or queues. The first works devoted to the analysis of teletraffic belong to A. K. Erlang. Request flows represented flows of requests for connections in networks with channel switching. Since requests were received from a large number of independent users, the flows of such requests could be defined as stationary, ordinary with no effect, or as recurring requests, with an exponential distribution of time intervals between neighboring requests. Connection request flows to a telephone exchange node are a superposition of a large number of low-intensity flows from independent users. Therefore, the fixed Poisson flow model describes the real flows in telephone exchanges with channel switching quite well. Therefore, the stationary Poisson flow model describes real flows in telephone exchanges with channel switching rather well. The emergence of telecommunications networks with packet switching, especially multiservice networks, showed the impossibility of using Poisson flow models for their analysis. The article is devoted to the analysis of delays in queues of queuing systems with correlated stationary flows of general type requests. The traffic of packets in multiservice networks is typically characterized by a high degree of correlation. On the basis of interval methods of analysis, the relations generalizing the Khinchin-Pollaczek formula for the average value of waiting time in queuing systems with flows of the general kind of requests are obtained. The main parameters to be analyzed when outputting the above formulas are time intervals between neighboring requests. It is shown that the values of time delays in queues depend on the dispersion and dispersion index of a random value characterizing the degree of additional maintenance of processed requests.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

scholarly journals POWER FOR PROCESSING APPLICATION FLOWS AND QUEUE SIZES IN MASS SERVICE SYSTEMS

T-Comm ◽  
2020 ◽  
Vol 14 (9) ◽  
pp. 10-16
Author(s):  
Boris Ya. Lichtzinder ◽  
◽  
Igor A. Blatov ◽  
Keyword(s):  
Queuing Theory ◽  
Load Factor ◽  
Cyclic Process ◽  
Variable Component ◽  
Strongly Correlated ◽  
Processing Application ◽  
Conditional Average ◽  
Multiservice Networks ◽  
Processing Power ◽  
Average Size

The classical queuing theory studies time series processing under the assumption of sampling independence. However, the traffic of modern multiservice networks is usually strongly correlated and the methods of classical theory do not work. In this paper, we consider the cyclic process of queuing, conditional and unconditional mutual correlations. Conditional average values of queues are considered. The concept of processing power of the flow of applications in queuing systems (QS) is introduced. It is shown that the variable component of the indicated power is determined by the change in the load factor and corresponds to the conditional average size of the queue of applications in the QS.

A kinematic self-similar rupture process for earthquakes

1994 ◽  
Vol 84 (4) ◽  
pp. 1216-1228 ◽  
Author(s):  
A. Herrero ◽  
P. Bernard
Keyword(s):  
Stress Drop ◽  
Numerical Models ◽  
Kinematic Model ◽  
Body Waves ◽  
Partial Slip ◽  
Wave Radiation ◽  
Similar Process ◽  
Dislocation Model ◽  
Radiation Spectra ◽  
Self Similar

Abstract The basic assumption that the self-similarity and the spectral law of the seismic body-wave radiation (e.g., ω-square model) must find their origin in some simple self-similar process during the seismic rupture led us to construct a kinematic, self-similar model of earthquakes. It is first assumed that the amplitude of the slip distribution high-pass filtered at high wavenumber does not depend on the size of the ruptured fault. This leads to the following “k-square” model for the slip spectrum, for k > 1/L: Δ~uL(k)=CΔσμLk2, where L is the ruptured fault dimension, k the radial wavenumber, Δσ the mean stress drop, μ the rigidity, and C an adimensional constant of the order of 1. The associated stress-drop spectrum, for k > 1/L, is approximated by Δ~σL(k)=ΔσLk. The rupture front is assumed to propagate on the fault plane with a constant velocity v, and the rise time function is assumed to be scale dependent. The partial slip associated to a given wavelength 1/k is assumed to be completed in a time 1/kv, based on simple dynamical considerations. We therefore considered a simple dislocation model (instantaneous slip at the final value), which indeed correctly reproduces this self-similar characteristic of the slip duration at any scale. For a simple rectangular fault with isochrones propagating in the x direction, the resulting far-field displacement spectrum is related to the slip spectrum as u˜(ω)=FΔ~u(kx=1Cdωv,ky=0), where the factor F includes radiation pattern and distance effect, and Cd is the classical directivity coefficient 1/[1 − v/c cos (θ)]. The k-square model for the slip thus leads to the ω-square model, with the assumptions above. Independently of the adequacy of these assumptions, which should be tested with dynamic numerical models, such a kinematic model has several important applications. It may indeed be used for generating realistic synthetics at any frequency, including body waves, surface waves, and near-field terms, even for sites close to the fault, which is often of particular importance; it also provides some clues for estimating the weighting factors for the empirical Green's function methods. Finally, the slip spectrum may easily be modified in order to model other power-law decay of the radiation spectra, as well as composite earthquakes.

scholarly journals Capacity and patient flow planning in post-term pregnancy outpatient clinics: a computer simulation modelling study

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Joe Viana ◽  
Tone Breines Simonsen ◽  
Hildegunn E. Faraas ◽  
Nina Schmidt ◽  
Fredrik A. Dahl ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Patient Flow ◽  
Simulation Modelling ◽  
Outpatient Clinics ◽  
Term Pregnancy ◽  
Post Term Pregnancy ◽  
Modelling Study
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