scholarly journals A study on some infinite server queues in discrete-time

10.26524/cm78 ◽  
2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Syed Tahir Hussainy ◽  
Lokesh D
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Shot Noise ◽  
Busy Period ◽  
Transient State ◽  
System Size ◽  
Differentiation Formula ◽  
Work Analysis ◽  
Shot Noise Process ◽  
Infinite Server Queues

This work analysis some discrete-time queueing mechanisms with infinitely many servers.By using a shot noise process, general results on the system size in discrete-time are given both in transient state and in steady state. For this we use the classical differentiation formula of F´a di Bruno. First two moments of the system size and distribution of the busy period of the system are also computed.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (3) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (03) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

Design Method for Improvement of Transient-State Intersample Output of Multirate Systems Including Integrators

2016 ◽  
Vol 28 (5) ◽  
pp. 702-706 ◽  
Author(s):  
Tomonori Kamiya ◽  
◽  
Takao Sato ◽  
Nozomu Araki ◽  
Yasuo Konishi
Keyword(s):  
Steady State ◽  
Conventional Method ◽  
Discrete Time ◽  
Design Method ◽  
Transient State ◽  
Sampling Interval ◽  
Time Response ◽  
Control Input ◽  
Multirate System ◽  
Difference Operation

[abstFig src='/00280005/12.jpg' width='300' text='Comparison of output responses' ] This paper discusses a design method for a multirate system including integrators, where the update interval of the control input is shorter than the sampling interval of the plant output. In such a multirate control system, intersample output might oscillate between sampled outputs in the steady state even if the sampled output converges to the reference input. This is because the control input can be updated between the sampled outputs. In a conventional method, a predesigned control law is extended such that the steady-state ripples are eliminated independent of a discrete-time response. However, the conventional method is invalid when integrators are included in a controlled plant. In this study, a difference operation in discrete time is used to address this issue. Moreover, the transient-state intersample response is improved independent of a pre-designed discrete-time response.

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

2006 ◽  
Vol 23 (02) ◽  
pp. 247-271 ◽  
Author(s):  
IVAN ATENCIA ◽  
PILAR MORENO
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing System ◽  
Retrial Queue ◽  
System Size ◽  
Stochastic Decomposition ◽  
Recursive Procedure ◽  
Server Breakdown

This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

Analysis of state-dependent discrete-time queue with system disaster

2019 ◽  
Vol 53 (5) ◽  
pp. 1915-1927
Author(s):  
Ramupillai Sudhesh ◽  
Arumugam Vaithiyanathan
Keyword(s):  
Discrete Time ◽  
Busy Period ◽  
System Size ◽  
Time Dependent ◽  
System Effect ◽  
Period Distribution ◽  
State Dependent ◽  
Discrete Time Queue ◽  
Formal Power ◽  
Time Dependent System

An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the nth state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo/Geo/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.

scholarly journals On the Steady-State System Size Distribution for a Discrete-Time Geo/G/1 Repairable Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Renbin Liu ◽  
Zhaohui Deng
Keyword(s):  
Steady State ◽  
Size Distribution ◽  
Discrete Time ◽  
Queueing System ◽  
System Size ◽  
State System ◽  
System Capacity ◽  
Analysis Method ◽  
Network Access ◽  
Capacity Design

This paper studies a discrete-time N-policy Geo/G/1 queueing system with feedback and repairable server. With a probabilistic analysis method and renewal process theory, the steady-state system size distribution is derived. Further, the steady-state system size distribution derived in this work is extremely suitable for numerical calculations. Numerical example illustrates the important application of steady-state system size distribution in system capacity design for a network access proxy system.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

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