Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots

2016 ◽  
Vol 53 (4) ◽  
pp. 1078-1097 ◽  
Author(s):  
Gagandeep Singh ◽  
U. C. Gupta ◽  
M. L. Chaudhry
Keyword(s):  
Closed Form ◽  
Computational Analysis ◽  
Computation Time ◽  
Analytic Method ◽  
Actual System ◽  
Form Analysis ◽  
The Matrix ◽  
Queueing Time ◽  
System Time ◽  
Stieltjes Transforms

Abstract In this paper we present closed-form expressions for the distribution of the virtual (actual) queueing time for the BMAP/R/1 and BMAP/D/1 queues, where `R' represents a class of distributions having rational Laplace‒Stieltjes transforms. The closed-form analysis is based on the roots of the underlying characteristic equation. Numerical aspects have been tested for a variety of arrival and service-time distributions and results are matched with those obtained using the matrix-analytic method (MAM). Further, a comparative study of computation time of the proposed method with the MAM has been carried out. Finally, we also present closed-form expressions for the distribution of the virtual (actual) system time. The proposed method is analytically quite simple and easy to implement.

Analysis and Computation of Two Body Impact in Three Dimensions

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Yan-Bin Jia ◽  
Feifei Wang
Keyword(s):  
Closed Form ◽  
Contact Point ◽  
Positive Definiteness ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Sliding Velocity ◽  
Form Analysis ◽  
Coulomb’S Friction ◽  
The Matrix ◽  
Single Contact Point

A formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb's friction in three dimensions (3D). The tangential impulse at the contact is known to be linear in the sliding velocity whose trajectory, parametrized with the normal impulse and referred to as the hodograph, is governed by a generally nonintegrable ordinary differential equation (ODE). Evolution of the hodograph is bounded by rays in several invariant directions of sliding in the contact plane. Exact lower and upper bounds are derived for the number of such invariant directions, utilizing the established positive definiteness of the matrix defining the governing ODE. If the hodograph reaches the origin, it either terminates (i.e., the contact sticks) or continues in a new direction (i.e., the contact resumes sliding) whose existence and uniqueness, only assumed in the literature, are proven. Closed-form integration of the ODE becomes possible as soon as the sliding velocity turns zero or takes on an invariant direction. Assuming Stronge's energy-based restitution, a complete algorithm is described to combine fast numerical integration (NI) with a case-by-case closed-form analysis. A number of solved collision instances are presented. It remains open whether the modeled impact process will always terminate under Coulomb's friction and Stronge's (or Poisson's) restitution hypothesis.

COMPUTATIONAL ANALYSIS OF STATIONARY WAITING-TIME DISTRIBUTIONS OF GIX/R/1 AND GIX/D/1 QUEUES

2005 ◽  
Vol 19 (1) ◽  
pp. 121-140 ◽  
Author(s):  
Mohan L. Chaudhry ◽  
Dae W. Choi ◽  
Kyung C. Chae
Keyword(s):  
Closed Form ◽  
Waiting Time ◽  
Time Distribution ◽  
Computational Analysis ◽  
Rational Functions ◽  
Waiting Time Distribution ◽  
Generalized Distributions ◽  
Analytic Expression ◽  
Stationary Waiting Time ◽  
Stieltjes Transforms

In this article, we obtain, in a unified way, a closed-form analytic expression, in terms of roots of the so-called characteristic equation of the stationary waiting-time distribution for the GIX/R/1 queue, where R denotes the class of distributions whose Laplace–Stieltjes transforms are rational functions (ratios of a polynomial of degree at most n to a polynomial of degree n). The analysis is not restricted to generalized distributions with phases such as Coxian-n (Cn) but also covers nonphase-type distributions such as deterministic (D). In the latter case, we get approximate results. Numerical results are presented only for (1) the first two moments of waiting time and (2) the probability that waiting time is zero. It is expected that the results obtained from the present study should prove to be useful not only for practitioners but also for queuing theorists who would like to test the accuracies of inequalities, bounds, or approximations.

Closed-form Analysis of Age of Information in Energy Harvesting Network

2020 ◽  
Author(s):  
Siyu Wang ◽  
Xin Wang ◽  
Tianyi Peng ◽  
Jiaxi Zhou ◽  
Qi Qin ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Closed Form ◽  
Form Analysis ◽  
Age Of Information

scholarly journals Complex-analytic and matrix-analytic solutions for a queueing system with group service controlled by arrivals

2000 ◽  
Vol 13 (4) ◽  
pp. 415-427
Author(s):  
Lev Abolnikov ◽  
Alexander Dukhovny
Keyword(s):  
Block Size ◽  
Iteration Process ◽  
Analytic Solutions ◽  
Analytic Method ◽  
Service Time Distribution ◽  
Matrix Analytic Method ◽  
Queueing Process ◽  
The Matrix ◽  
Matrix Iteration ◽  
Necessary And Sufficient

A bulk M/G/1 system is considered that responds to large increases (decreases) of the queue during the service act by alternating between two service modes. The switching rule is based on two “up” and “down” thresholds for total arrivals over the service act. A necessary and sufficient condition for the ergodicity of a Markov chain embedded into the main queueing process is found. Both complex-analytic and matrix-analytic solutions are obtained for the steady-state distribution. Under the assumption of the same service time distribution in both modes, a combined complex-matrix-analytic method is introduced. The technique of “matrix unfolding” is used, which reduces the problem to a matrix iteration process with the block size much smaller than in the direct application of the matrix-analytic method.

A closed-form analysis for space dependent nuclear reactor transients

1972 ◽  
Vol 26 (9) ◽  
pp. 461-468
Author(s):  
W.J. Garland ◽  
A.A. Harms
Keyword(s):  
Closed Form ◽  
Nuclear Reactor ◽  
Form Analysis

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

Closed-Form Analysis of Reflection Losses in Microstrip Reflectarray Antennas

2012 ◽  
Vol 60 (10) ◽  
pp. 4650-4660 ◽  
Author(s):  
Filippo Costa ◽  
Agostino Monorchio
Keyword(s):  
Closed Form ◽  
Form Analysis

Peak AoI vs. Delay: Closed-Form Analysis in the Finite Block Length Regime

2021 ◽  
Author(s):  
Jie Cao ◽  
Xu Zhu ◽  
Yufei Jiang ◽  
Zhongxiang Wei ◽  
Sumei Sun ◽  
...  
Keyword(s):  
Closed Form ◽  
Block Length ◽  
Form Analysis
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