STAFFING TO STABILIZE BLOCKING IN LOSS MODELS WITH TIME-VARYING ARRIVAL RATES

2015 ◽  
Vol 30 (2) ◽  
pp. 185-211 ◽  
Author(s):  
Andrew Li ◽  
Ward Whitt ◽  
Jingtong Zhao
Keyword(s):  
Small Time ◽  
Time Interval ◽  
Time Varying ◽  
Blocking Probabilities ◽  
Small Time Interval ◽  
Delay Models ◽  
Customer Abandonment ◽  
Loss Models ◽  
The Times ◽  
Multi Server

The modified-offered-load approximation can be used to choose a staffing function (the time-varying number of servers) to stabilize delay probabilities at target levels in multi-server delay models with time-varying arrival rates, with or without customer abandonment. In contrast, as we confirm with simulations, it is not possible to stabilize blocking probabilities to the same extent in corresponding loss models, without extra waiting space, because these probabilities necessarily change dramatically after each staffing change. Nevertheless, blocking probabilities can be stabilized provided that we either randomize the times of staffing changes or average the blocking probabilities over a suitably small time interval. We develop systematic procedures and study how to choose the averaging parameters.

On diffracted wave fronts

1979 ◽  
Vol 84 (1-2) ◽  
pp. 35-54
Author(s):  
Peter Wolfe
Keyword(s):  
Wave Equation ◽  
Wave Front ◽  
Incident Wave ◽  
Spherical Wave ◽  
Small Time ◽  
Time Interval ◽  
Wave Fronts ◽  
Incident Plane ◽  
Small Time Interval ◽  
Propagation Of Singularities

SynopsisIn this paper we study the wave equation, in particular the propagation of discontinuities. Two problems are considered: diffraction of a normally incident plane pulse by a plane screen and diffraction of a spherical wave by the same screen. It is shown that when an incident wave front strikes the edge of the screen a diffracted wave front is produced. The discontinuities are precisely computed in a neighbourhood of the edge for a small time interval after the arrival of the incident wave front and a theorem of Hörmander on the propagation of singularities is used to obtain a globalresult.

GENERIC QUANTUM MARKOV SEMIGROUPS, CYCLE DECOMPOSITION AND DEVIATION FROM EQUILIBRIUM

2012 ◽  
Vol 15 (03) ◽  
pp. 1250016 ◽  
Author(s):  
FRANCO FAGNOLA ◽  
VERONICA UMANITÀ
Keyword(s):  
Small Time ◽  
Jump Processes ◽  
Time Interval ◽  
Markov Semigroup ◽  
Cycle Decomposition ◽  
Markov Jump ◽  
Partial Isometries ◽  
Small Time Interval ◽  
Positive Weights ◽  
The Difference

A generic quantum Markov semigroup [Formula: see text] of a d-level quantum open system with a faithful normal invariant state ρ admits a dual semigroup [Formula: see text] with respect to the scalar product induced by ρ. We show that the difference of the generators [Formula: see text] can be written as the sum of a derivation 2i[H, ⋅] and a weighted difference of automorphisms [Formula: see text] where [Formula: see text] is a family of cycles on the d levels of the system, wc are positive weights and [Formula: see text] are unitaries. This formula allows us to represent the deviation from equilibrium (in a "small" time interval) as the superposition of cycles of the system where the difference between the forward and backward evolution is written as the difference of a reversible evolution and its time reversal. Moreover, it generalises cycle decomposition of Markov jump processes. We also find a similar formula with partial isometries instead of unitaries.

scholarly journals INVERSE PROBLEM FOR THE TIME-FRACTIONAL EULER-BERNOULLI BEAM EQUATION

2021 ◽  
Vol 26 (3) ◽  
pp. 503-518
Author(s):  
Ibrahim Tekin ◽  
He Yang
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Small Time ◽  
Beam Equation ◽  
Time Interval ◽  
Existence And Uniqueness Theorem ◽  
Bernoulli Beam ◽  
Additional Measurement ◽  
Small Time Interval ◽  
Euler Bernoulli Beam

In this paper, the classical Euler-Bernoulli beam equation is considered by utilizing fractional calculus. Such an equation is called the time-fractional EulerBernoulli beam equation. The problem of determining the time-dependent coefficient for the fractional Euler-Bernoulli beam equation with homogeneous boundary conditions and an additional measurement is considered, and the existence and uniqueness theorem of the solution is proved by means of the contraction principle on a sufficiently small time interval. Numerical experiments are also provided to verify the theoretical findings.

Gaussian approximation of some closed stochastic epidemic models

1977 ◽  
Vol 14 (02) ◽  
pp. 221-231
Author(s):  
Frank J. S. Wang
Keyword(s):  
Epidemic Model ◽  
Limit Theorems ◽  
Gaussian Approximation ◽  
Infected Individual ◽  
Small Time ◽  
Entire Population ◽  
Time Interval ◽  
Stochastic Epidemic Models ◽  
Small Time Interval ◽  
Stochastic Epidemic

A generalization of Bailey's general epidemic model is considered. In this generalized model, it is assumed that the probability of any particular susceptible becoming infected during the small time interval (t, t + Δt) is α(X(t))Δt + o(Δt), for some function a, where X(t) is the proportion of infected individuals in the entire population, the probability that an infected individual is infected for at least a length of time t is F(t), and recovered individuals are permanently immune from further attack. In this paper, central limit theorems are obtained for the proportion of infected individuals and the proportion of susceptibles in the entire population.

A nonlinear pseudoparabolic equation

1990 ◽  
Vol 114 (1-2) ◽  
pp. 119-133 ◽  
Author(s):  
Dang Dinh Ang ◽  
Tran Thanh
Keyword(s):  
Salient Feature ◽  
Small Time ◽  
Time Interval ◽  
Pseudoparabolic Equation ◽  
Nonhomogeneous Boundary ◽  
Small Time Interval ◽  
Nonhomogeneous Boundary Conditions ◽  
Image Position ◽  
Special Case ◽  
Nonlinear Pseudoparabolic Equation

SynopsisThe authors prove results on uniqueness and global existence of initial and boundary value problems for the nonlinear pseudoparabolic equationwith nonhomogeneous boundary conditions. A salient feature of the paper is that F and its partial derivatives are allowed to be unbounded. In the special case b(x, t)= α2 (a positive constant), it is proved that the corresponding solution uα, under appropriate conditions on the data (which are satisfied, for example, by the Benjamin–Bona–Mahony equation), uα→ u0 the solution corresponding to β = 0, on sufficiently small time interval. A result on the asymptotic behaviour of the solution is given for t → ∞.

scholarly journals Hardware Passwords Manager Based on Biometric Authentication

2021 ◽  
Vol 6 (1) ◽  
pp. 31
Author(s):  
Camelia Avram ◽  
Jose Machado ◽  
Adina Aştilean
Keyword(s):  
Small Time ◽  
Time Interval ◽  
Biometric Authentication ◽  
Secret Key ◽  
Security Systems ◽  
Web Browser ◽  
Cigarette Pack ◽  
Small Time Interval ◽  
Evolution Of Technology ◽  
Static Images

This paper presents a portable passwords manager which has a two-stage biometric-based access procedure. Data security using biometric methods was chosen as a variant of reduced complexity but was very effective in preventing cyber theft. The implementation of biometrics for the purpose of identification in high-security systems has become essential with the evolution of technology and the spike in identity theft. Unlike passwords or IDs, a biometric feature is an identifier that cannot be lost, stolen, or replicated, which provides biometric authentication systems with an increased level of security. During the first accessing step, the 3DPassManager portable device measures the heartbeat and uses fingerprint and iris features to realize a unique biometric-based authentication. While the specific characteristics of fingerprint and iris features are integrated to ensure that the person using the device is the rightful owner, the pulse is utilized to verify if previously acquired static images are not used. During the second accessing step, a password is generated based on fingerprint details, valid only for a small-time interval. The fingerprint is stored in a secret key with a 1024-bit length. Once access is allowed, the passwords are made available through an extension installed on the web browser. The device is the size of a cigarette pack and communicates with the PC by scanning a QR code. It is safe and was previously tested for dictionary and brute force attacks.

Impact With Finite Acceleration Time of Elastic and Elastic-Plastic Beams

1956 ◽  
Vol 23 (3) ◽  
pp. 411-415
Author(s):  
R. C. Alverson
Keyword(s):  
Plastic Deformation ◽  
Cross Section ◽  
Plastic Hinge ◽  
Small Time ◽  
Steel Beams ◽  
Time Interval ◽  
Transverse Impact ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Small Time Interval

Abstract The purpose of the work described in this paper was to provide information on the elastic and plastic deformation of steel beams subjected to transverse impact. The particular impact problem treated was chosen to correspond to conditions in tests in which a beam initially at rest is struck by a massive hammer, so that a specified change of velocity is imposed at a certain cross section in a small time interval. In the present analysis the initial elastic and subsequent elastic-plastic motions were obtained by methods similar to those used by Bleich and Salvadori (3). As in (3), it is assumed that plastic deformation occurs only at a single stationary plastic hinge (in this case at the struck cross section). Results obtained are compared with those of a “rigid-plastic” solution of the same problem, in which plasticity conditions are correctly taken into account but elastic vibrations are not included.

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