Analysis of the M/G/1 and GI/M/1 queueing systems by the supplementary variable approach

1983 ◽  
Vol 66 (3) ◽  
pp. 14-23 ◽  
Author(s):  
Shinya Nogami ◽  
Yasuo Komota ◽  
Yukio Hoshiko
Keyword(s):  
Queueing Systems ◽  
Supplementary Variable ◽  
Variable Approach

SUPPLEMENTARY VARIABLE TECHNIQUE IN STOCHASTIC MODELS

2000 ◽  
Vol 14 (2) ◽  
pp. 203-218 ◽  
Author(s):  
Attahiru Sule Alfa ◽  
T. S. S. Srinivasa Rao
Keyword(s):  
Stochastic Models ◽  
Queueing Systems ◽  
Supplementary Variable ◽  
Kolmogorov Equations ◽  
Variable Technique ◽  
Supplementary Variable Technique ◽  
Supplementary Variables ◽  
Remaining Time

In this article, we formalize the framework for the supplementary variable technique in stochastic models. Specifically, we show that the use of remaining or elapsed times (or any metric) as supplementary variables leads to the notion of forward or backward Chapman–Kolmogorov equations, respectively. We further show that for a class of queueing systems, using remaining time as the supplementary variable makes analysis simpler.

Probabilistic assessment of complex system consisting three subsystems, multi-failure threats and copula repair approach

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abbas Bin Jibril ◽  
V.V. Singh ◽  
Dilip Kumar Rawal
Keyword(s):  
Research Work ◽  
System Failure ◽  
Supplementary Variable ◽  
System Availability ◽  
Content Type ◽  
Industrial Systems ◽  
Variable Approach ◽  
Series Configuration ◽  
Better Than ◽  
Operational Scheme

PurposeThe purpose of this paper is to deliberate the system reliability of a system in combination of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance.Design/methodology/approachProbabilistic assessment of complex system consisting three subsystems, multi-failure threats and copula repair approach is used in this study. Abbas Jubrin Bin, V.V. Singh, D.K. Rawal, in this research paper, have analyzed a system consisting of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance.FindingsIn this analysis, four different cases of availability are analysed for Gumbel–Hougaard family copula and also four cases for general repair with similar failure rates are studied. The authors found that when failure rates increase, the system availability decreases, and when the system follows copula repair distribution, the system availability is better than general repair.Research limitations/implicationsThis research may be implemented in various industrial systems where the subsystems are configured under k-out-of-n: G working policy. It is also advisable that copula repair is highly recommended for best performances from the system. On the basis of mean time to system failure (MTSF) computations, the failure rate which affects system failure more needs to be controlled by monitoring, servicing and replacing stratagem.Practical implicationsThis research work has great implications in various industrial systems like power plant systems, nuclear power plant, electricity distributions system, etc. where the k-out-of-n-type of system operation scheme is validated for system operations with the multi-repair.Originality/valueThis work is a new work by authors. In the previously available technical analysis of the system, the researchers have analyzed the repairable system either supplementary variable approach, supplementary variable and system which have two subsystems in a series configuration. This research work analyzed a system with three subsystems with a multi-repair approach and supplementary variables.

Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations

1997 ◽  
Vol 34 (2) ◽  
pp. 546-555 ◽  
Author(s):  
Wei Li ◽  
Dinghua Shi ◽  
Xiuli Chao
Keyword(s):  
Reliability Analysis ◽  
System Performance ◽  
Queueing Systems ◽  
Variable Method ◽  
Supplementary Variable ◽  
Transient Solution ◽  
Reliability Measures ◽  
Supplementary Variable Method ◽  
Insight Into

This note introduces reliability issues to the analysis of queueing systems. We consider an M/G/1 queue with Bernoulli vacations and server breakdowns. The server uptimes are assumed to be exponential, and the server repair times are arbitrarily distributed. Using a supplementary variable method we obtain a transient solution for both queueing and reliability measures of interest. These results provide insight into the effect of server breakdowns and repairs on system performance.

scholarly journals A non-Markovian queueing system with a variable number of channels

2003 ◽  
Vol 16 (4) ◽  
pp. 375-395
Author(s):  
Hong-Tham T. Rosson ◽  
Jewgeni H. Dshalalow
Keyword(s):  
Queueing System ◽  
Invariant Probability Measure ◽  
Variable Number ◽  
Time Parameter ◽  
Embedded Markov Chain ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Queueing Process ◽  
Variable Approach ◽  
Parallel Channels

In this paper we study a queueing model of type GI/M/m˜a/∞ with m parallel channels, some of which may suspend their service at specified random moments of time. Whether or not this phenomenon occurs depends on the queue length. The queueing process, which we target, turns out to be semi-regenerative, and we fully explore this utilizing semi-regenerative techniques. This is contrary to the more traditional supplementary variable approach and the less popular approach of combination semi-regenerative and supplementary variable technique. We pass to the limiting distribution of the continuous time parameter process through the embedded Markov chain for which we find the invariant probability measure. All formulas are analytically tractable.

Reliability analysis of M/G/1 queueing systems with server breakdowns and vacations

1997 ◽  
Vol 34 (02) ◽  
pp. 546-555 ◽  
Author(s):  
Wei Li ◽  
Dinghua Shi ◽  
Xiuli Chao
Keyword(s):  
Reliability Analysis ◽  
System Performance ◽  
Queueing Systems ◽  
Variable Method ◽  
Supplementary Variable ◽  
Transient Solution ◽  
Reliability Measures ◽  
Supplementary Variable Method ◽  
Insight Into

This note introduces reliability issues to the analysis of queueing systems. We consider an M/G/1 queue with Bernoulli vacations and server breakdowns. The server uptimes are assumed to be exponential, and the server repair times are arbitrarily distributed. Using a supplementary variable method we obtain a transient solution for both queueing and reliability measures of interest. These results provide insight into the effect of server breakdowns and repairs on system performance.

Distinguishing Adequate Versus Inadequate Cancer Health Literacy Levels: A Discrete Latent Variable Approach

2013 ◽  
Author(s):  
Levent Dumenci ◽  
Robin Matsuyama ◽  
Robert Perera ◽  
Laura Kuhn ◽  
Laura Siminoff
Keyword(s):  
Health Literacy ◽  
Latent Variable ◽  
Variable Approach ◽  
Latent Variable Approach

International Remittances and Private Healthcare in Kerala, India

2020 ◽  
Vol 17 (3) ◽  
pp. 445-460
Author(s):  
Mohd Imran Khan ◽  
Valatheeswaran C.
Keyword(s):  
Instrumental Variable ◽  
Capital Investment ◽  
Healthcare Expenditure ◽  
Healthcare Services ◽  
Private Healthcare ◽  
International Remittances ◽  
Variable Approach ◽  
Using Data ◽  
The Impact ◽  
Instrumental Variable Approach

The inflow of international remittances to Kerala has been increasing over the last three decades. It has increased the income of recipient households and enabled them to spend more on human capital investment. Using data from the Kerala Migration Survey-2010, this study analyses the impact of remittance receipts on the households’ healthcare expenditure and access to private healthcare in Kerala. This study employs an instrumental variable approach to account for the endogeneity of remittances receipts. The empirical results show that remittance income has a positive and significant impact on households’ healthcare expenditure and access to private healthcare services. After disaggregating the sample into different heterogeneous groups, this study found that remittances have a greater effect on lower-income households and Other Backward Class (OBC) households but not Scheduled Caste (SC) and Scheduled Tribe (ST) households, which remain excluded from reaping the benefit of international migration and remittances.

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