scholarly journals Tail asymptotics of signal-to-interference ratio dis­tribution in spatial cellular network models

2018 ◽  
Vol 37 (2) ◽  
pp. 431-453 ◽  
Author(s):  
Naoto Miyoshi ◽  
Tomoyuki Shirai
Keyword(s):  
Point Process ◽  
Upper Bound ◽  
Cellular Network ◽  
Path Loss ◽  
Network Models ◽  
Base Stations ◽  
Sufficient Condition ◽  
Tail Asymptotics ◽  
Tail Distribution ◽  
Stationary Point Process

TAIL ASYMPTOTICS OF SIGNAL-TO-INTERFERENCE RATI ODISTRIBUTION IN SPATIAL CELLULAR NETWORK MODELSWe consider a spatial stochastic model of wireless cellular networks, where the base stations BSs are deployed according to a simple and stationary point process on Rd, d > 2. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio SIR, which is a key quantity in wireless communications. In the case where the pathloss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an appropriate sufficient condition. While we show that widely-used models based on a Poisson point process and on a determinantal point process meet the sufficient condition, we also give a counterexample violating it. In the case of bounded path-loss functions, we derive a logarithmically asymptotic upper bound on the SIR tail distribution for the Poisson-based and -Ginibrebased models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.

DEVELOPMENT OF VALUATION METHOD OF THE STATUS OF BASE STATIONS FOR DETERMINING THE NEED OF THEIR UPGRADING

2017 ◽  
pp. 60-70
Author(s):  
Natalya Ivanovna Shaposhnikova ◽  
Alexander Aleksandrovich Sorokin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Cellular Network ◽  
New Technologies ◽  
Base Station ◽  
Base Stations ◽  
Valuation Method ◽  
The Status ◽  
Telecommunications Services ◽  
Theory Of Fuzzy Sets

The article consideres the problems of determining the need to modernize the base stations of the cellular network based on the mathematical apparatus of the theory of fuzzy sets. To improve the quality of telecommunications services the operators should send significant funding for upgrading the equipment of base stations. Modernization can improve and extend the functions of base stations to provide cellular communication, increase the reliability of the base station in operation and the functionality of its individual elements, and reduce the cost of maintenance and repair when working on a cellular network. The complexity in collecting information about the equipment condition is determined by a large number of factors that affect its operation, as well as the imperfection of obtaining and processing the information received. For a comprehensive assessment of the need for modernization, it is necessary to take into account a number of indicators. In the structure of indicators of the need for modernization, there were introduced the parameters reflecting both the degree of aging and obsolescence(the technical gap and the backlog in connection with the emergence of new technologies and standards). In the process of a problem solving, the basic stages of decision-making on modernization have been allocated. Decision-making on the need for modernization is based not only on measuring information that takes into account the decision-makers, but also on linguistic and verbal information. Therefore, to determine the need for upgrading the base stations, the theory of fuzzy sets is used, with the help of which experts can be attracted to this issue. They will be able to formulate additional fuzzy judgments that help to take into account not only measuring characteristics, but also poorly formalized fuzzy information. To do this, the main indicators of the modernization need have been defined, and fuzzy estimates of the need for modernization for all indicators and a set of indicators reflecting the need for upgrading the base stations have been formulated.

scholarly journals Tail Asymptotics for Monotone-Separable Networks

2007 ◽  
Vol 44 (02) ◽  
pp. 306-320
Author(s):  
Marc Lelarge
Keyword(s):  
Queueing Network ◽  
Network Models ◽  
Moment Generating Function ◽  
Stochastic Petri Nets ◽  
Arrival Process ◽  
Polling Systems ◽  
Tail Asymptotics ◽  
State Variables ◽  
Monotone Functions ◽  
Jackson Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

scholarly journals Energy Efficient Operation of Cellular Network Using On/Off Base Stations

2015 ◽  
Vol 11 (8) ◽  
pp. 108210 ◽  
Author(s):  
Yong-Hoon Choi ◽  
Jungerl Lee ◽  
Juhoon Back ◽  
Suwon Park ◽  
Young-uk Chung ◽  
...  
Keyword(s):  
Energy Efficient ◽  
Cellular Network ◽  
Base Stations ◽  
Efficient Operation

On projected thick sections of stationary point processes and Boolean models

1996 ◽  
Vol 28 (2) ◽  
pp. 335-335
Author(s):  
Markus Kiderlen
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Linear Subspace ◽  
Isotropic Case ◽  
Thick Section ◽  
Boolean Models ◽  
Dimensional Linear Subspace ◽  
Stationary Point Process ◽  
Stationary Point Processes

For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

The extension of the Miles-Howard theorem to compressible fluids

1970 ◽  
Vol 43 (4) ◽  
pp. 833-836 ◽  
Author(s):  
G. Chimonas
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Upper Bound ◽  
Unstable Mode ◽  
Vertical Gradient ◽  
Flow Speed ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Sufficient Condition ◽  
Parallel Shear Flow

A statically stable, gravitationally stratified compressible fluid containing a parallel shear flow is examined for stability against infinitesimal adiabatic perturbations. It is found that the Miles–Howard theorem of incompressible fluids may be generalized to this system, so that n2 ≥ ¼U′2 throughout the flow is a sufficient condition for stability. Here n2 is the Brunt–Väissälä frequency and U’ is the vertical gradient of the flow speed. Howard's upper bound on the growth rate of an unstable mode also generalizes to this compressible system.

On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

1977 ◽  
Vol 14 (01) ◽  
pp. 114-126 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Gaussian Process ◽  
Point Process ◽  
Stationary Point ◽  
Stationary Gaussian Process ◽  
Time Curve ◽  
Second Moment ◽  
Stationary Point Process ◽  
Class Of Estimators

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ (V*(tTα ) – V(tTα )), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα ) is replaced by a suitable estimator.

scholarly journals Stochastic comparison of point random fields

1997 ◽  
Vol 34 (04) ◽  
pp. 868-881 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Torsten Küneth
Keyword(s):  
Point Process ◽  
Random Fields ◽  
Alternative Proof ◽  
Probability Measures ◽  
Stochastic Comparison ◽  
Sufficient Condition ◽  
Stochastic Domination ◽  
Positive Correlations ◽  
Increasing Functions

We give an alternative proof of a point-process version of the FKG–Holley–Preston inequality which provides a sufficient condition for stochastic domination of probability measures, and for positive correlations of increasing functions.

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