Analysis of a Discrete-Time Queueing System with a Markov-Modulated input Process and constant service Rate

1996 ◽  
Vol 10 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Woo-Yong Choi ◽  
Chi-Hyuck Jun
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Service Rate ◽  
System State ◽  
Input Process ◽  
New Approach ◽  
One Dimensional ◽  
Markov Modulated ◽  
Modulated Process ◽  
Renewal Cycle

We propose a new approach to the analysis of a discrete-time queueing system whose input is generated by a Markov-modulated process and whose service rate is constant. Renewal cycles are identified and the system state on each renewal cycle is modeled as a one-dimensional Markov chain.

Optimal Thresholds of an Infinite Buffer Discrete-Time Two-Server System with Triadic Policy

2011 ◽  
Vol 2 (4) ◽  
pp. 75-88
Author(s):  
Veena Goswami ◽  
G. B. Mund
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Minimum Cost ◽  
Service Rate ◽  
Closed Form Solutions ◽  
Optimal Thresholds ◽  
Optimal Service ◽  
Number Of Customers ◽  
System Operating ◽  
Server System

This paper analyzes a discrete-time infinite-buffer Geo/Geo/2 queue, in which the number of servers can be adjusted depending on the number of customers in the system one at a time at arrival or at service completion epoch. Analytical closed-form solutions of the infinite-buffer Geo/Geo/2 queueing system operating under the triadic (0, Q N, M) policy are derived. The total expected cost function is developed to obtain the optimal operating (0, Q N, M) policy and the optimal service rate at minimum cost using direct search method. Some performance measures and sensitivity analysis have been presented.

scholarly journals Performance Measures of State Dependent MMPP/M/1 Queue

2018 ◽  
Vol 7 (4.10) ◽  
pp. 942 ◽  
Author(s):  
R. Sakthi ◽  
V. Vidhya ◽  
K. Mahaboob Hassain Sherieff ◽  
. .
Keyword(s):  
Performance Measures ◽  
Research Work ◽  
Arrival Process ◽  
Service Rate ◽  
Single Server ◽  
State Dependent ◽  
Markov Modulated ◽  
Service State ◽  
Modulated Process ◽  
Stationary Probability Vector

In this research work we are concerned with single unit server queue  queue with Markov Modulated process in Poisson fashion and the service time follow exponential distribution. The system is framed as a state dependent with the arrival process as Markov Modulated input and service is rendered by a single server with variation in service rate based on the intensity of service state of the system. The rate matrix that is essential to compute the stationary probability vector is obtained and various performance measures are computed using matrix method.

scholarly journals Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period

2017 ◽  
Vol 5 (2) ◽  
pp. 176-192
Author(s):  
Shaojun Lan ◽  
Yinghui Tang
Keyword(s):  
Performance Measures ◽  
Generating Function ◽  
Discrete Time ◽  
Queueing System ◽  
Operating Cost ◽  
Probability Generating Function ◽  
Repair Process ◽  
Function Technique ◽  
Service Rate ◽  
The Stability

Abstract This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service. We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution. Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.

scholarly journals A new approach to constrained state estimation for discrete-time linear systems with unknown inputs

2017 ◽  
Vol 28 (1) ◽  
pp. 326-341 ◽  
Author(s):  
Jose Fernando Garcia Tirado ◽  
Alejandro Marquez-Ruiz ◽  
Hector Botero Castro ◽  
Fabiola Angulo
Keyword(s):  
State Estimation ◽  
Linear Systems ◽  
Discrete Time ◽  
New Approach ◽  
Unknown Inputs ◽  
Time Linear

DEBUGGING PROCESS-ORIENTED DISCRETE SOFTWARE RELIABILITY MODELING

2009 ◽  
Vol 16 (04) ◽  
pp. 357-370 ◽  
Author(s):  
SHINJI INOUE ◽  
NAOKI IWAMOTO ◽  
SHIGERU YAMADA
Keyword(s):  
Discrete Time ◽  
Software Reliability ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Reliability Growth ◽  
Reliability Modeling ◽  
New Approach ◽  
Time Modeling ◽  
Software Reliability Growth ◽  
Discrete Time Modeling

This paper discusses an new approach for discrete-time software reliability growth modeling based on an discrete-time infinite server queueing model, which describes a debugging process in a testing phase. Our approach enables us to develop discrete-time software reliability growth models (SRGMs) which could not be developed under conventional discrete-time modeling approaches. This paper also discuss goodness-of-fit comparisons of our discrete-time SRGMs with conventional continuous-time SRGMs in terms of the criterion of the mean squared errors, and show numerical examples for software reliability analysis of our models by using actual data.

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