The General Two-Server Queueing Loss System: Discrete-Time Analysis and Numerical Approximation of Continuous-Time Systems

1995 ◽  
Vol 46 (3) ◽  
pp. 386-397 ◽  
Author(s):  
J. Ben Atkinson
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Numerical Approximation ◽  
Time Analysis ◽  
Loss System ◽  
Continuous Time Systems ◽  
Time Systems

scholarly journals On the calculation of steady-state loss probabilities in the GI/G/2/0 queue

1994 ◽  
Vol 7 (3) ◽  
pp. 397-410 ◽  
Author(s):  
Igor N. Kovalenko ◽  
J. Ben Atkinson
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Continuous Time ◽  
Numerical Approximation ◽  
Approximation Scheme ◽  
Loss Probability ◽  
Loss Probabilities ◽  
Continuous Time Systems ◽  
Alternative Approach ◽  
Time Systems

This paper considers methods for calculating the steady-state loss probability in the GI/G/2/0 queue. A previous study analyzed this queue in discrete time and this led to an efficient, numerical approximation scheme for continuous-time systems. The primary aim of the present work is to provide an alternative approach by analyzing the GI/ME/2/0 queue; i.e., assuming that the service time can be represented by a matrix-exponential distribution. An efficient computational scheme based on this method is developed and some numerical examples are studied. Some comparisons are made with the discrete-time approach, and the two methods are seen to be complementary.

scholarly journals Analysis and comparison of the stability of discrete-time and continuous-time linear systems

2016 ◽  
Vol 26 (4) ◽  
pp. 551-563
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Continuous Time ◽  
Asymptotically Stable ◽  
Discrete Time Systems ◽  
Continuous Time Systems ◽  
The Matrix ◽  
Discretization Step ◽  
Time Systems ◽  
Time Linear

Abstract The asymptotic stability of discrete-time and continuous-time linear systems described by the equations xi+1 = Ākxi and x(t) = Akx(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix Āk and of the continuous-time systems depends only on phases of the eigenvalues of the matrix Ak, 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.

Sign in / Sign up

Export Citation Format

Share Document