scholarly journals Construction and Analysis of Queuing and Reliability Models Using Random Graphs

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2511
Author(s):  
Gurami Tsitsiashvili
Keyword(s):  
Planar Graphs ◽  
Random Network ◽  
Random Processes ◽  
Queuing Network ◽  
Reliability Models ◽  
Dual Graphs ◽  
Queuing Models ◽  
Probability Methods ◽  
Absorbing States ◽  
Multi Server

In this paper, the use of the construction of random processes on graphs allows us to expand the models of the theory of queuing and reliability by constructing. These problems are important because the emphasis on the legal component largely determines functioning of these models. The considered models are reliability and queuing. Reliability models arranged according to the modular principle and reliability networks in the form of planar graphs. The queuing models considered here are queuing networks with multi server nodes and failures, changing the parameters of the queuing system in a random environment with absorbing states, and the process of growth of a random network. This is determined by the possibility of using, as traditional probability methods, mathematical logic theorems, geometric images of a queuing network, dual graphs to planar graphs, and a solution to the Dirichlet problem.

scholarly journals Intuitionistic Fuzzy Planar Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Noura Alshehri ◽  
Muhammad Akram
Keyword(s):  
Graph Theory ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Planar Graphs ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Dual Graphs ◽  
Intuitionistic Fuzzy

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

scholarly journals Mathematical analysis of single queue multi server and multi queue multi server queuing models: comparison study

2015 ◽  
Vol 3 (3) ◽  
pp. 97 ◽  
Author(s):  
Vijay Prasad ◽  
Badshah V.H ◽  
Tariq Ahmad Koka
Keyword(s):  
Mathematical Analysis ◽  
Comparison Study ◽  
Queuing Model ◽  
Total Cost ◽  
Queuing Models ◽  
Models Comparison ◽  
Mathematical Equations ◽  
Expected Total Cost ◽  
Multi Server ◽  
Better Than

<p>In the research paper entitled Mathematical Analysis of Single Queue Multi Server and Multi Queue Multi Server Queuing Model, Prasad and Badshah [7] were proved that single queue multi server model is better than multi queue multi server model, and discussed the relation between the performance measures of these two models, and derive the mathematical equations. In this paper we derive the total cost with assumption of certain Waiting cost in both cases. Also, prove that the expected total cost is less for single queue multi server model as comparing with multi queue multi server model.</p>

scholarly journals Single-valued Neutrosophic planar graphs

2016 ◽  
Vol 5 (2) ◽  
pp. 157 ◽  
Author(s):  
Muhammad Akram
Keyword(s):  
Planar Graphs ◽  
Neutrosophic Sets ◽  
Dual Graphs

We apply the concept of single-valued neutrosophic sets to  multigraphs, planar graphs and  dual graphs. We introduce the notions of  single-valued neutrosophic  multigraphs, single-valued neutrosophic planar graphs, and single-valued neutrosophic dual graphs. We illustrate these concepts with examples. We also investigate some of their  properties.

GAUGING PERFORMANCE OF A QUEUING SYSTEM USING MULTI-SERVER WAITING LINE MODEL (M/M/S): AN INVESTIGATION ON A LOCAL HOSPITAL’S OUTPATIENT DEPARTMENT

2016 ◽  
Vol 78 (6-4) ◽  
Author(s):  
Hendrik Lamsali ◽  
Mohamed Najib Salleh
Keyword(s):  
Queuing System ◽  
Outpatient Department ◽  
Operating Characteristics ◽  
Hospital Administrators ◽  
Queuing Models ◽  
Government Hospitals ◽  
Computational Work ◽  
The Government ◽  
Waiting Line ◽  
Multi Server

Healthcare is a fast growing industry demanding perfection, top notch services and optimal utilization of available resources. Despite shortages in doctors and nurses as well as frequent overcrowding, the number of incoming patients to the government hospitals is increasing every year. The outpatient department in Malaysian Government hospitals is consistently experiencing frequent congestion particularly in the morning. The challenge for hospital administrators is to rightly and timely allocate resources in relevant departments. Henceforth, this study aims to further gauge the performance of an outpatient department in a local hospital in Kedah. In particular, it aims to investigate the current efficiency level of a queuing system of the said department and to propose potential solutions. The study uses Multi-server Queuing Models (M/M/s) to measure the performance of the waiting line. A computational work is then presented to value the operating characteristics of the model. The findings exhibit the performance of existing queuing system and the need to re-examine the number of doctors on duty. In all, the study may be beneficial as a decision making aid to the administrator of the outpatient department particularly to re-look and improve existing queuing system in tandem with the center’s commitment for better customer satisfaction and minimal patients’ turnover.

scholarly journals Planar Graphs under Pythagorean Fuzzy Environment

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 278 ◽  
Author(s):  
Muhammad Akram ◽  
Jawaria Dar ◽  
Adeel Farooq
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Planar Graphs ◽  
Close Association ◽  
Substantial Role ◽  
Dual Graphs ◽  
Fuzzy Environment ◽  
Fuzzy Graphs ◽  
Network Problems ◽  
Weak Isomorphism

Graph theory plays a substantial role in structuring and designing many problems. A number of structural designs with crossings can be found in real world scenarios. To model the vagueness and uncertainty in graphical network problems, many extensions of graph theoretical ideas are introduced. To deal with such uncertain situations, the present paper proposes the concept of Pythagorean fuzzy multigraphs and Pythagorean fuzzy planar graphs with some of their eminent characteristics by investigating Pythagorean fuzzy planarity value with strong, weak and considerable edges. A close association is developed between Pythagorean fuzzy planar and dual graphs. This paper also includes a brief discussion on non-planar Pythagorean fuzzy graphs and explores the concepts of isomorphism, weak isomorphism and co-weak isomorphism for Pythagorean fuzzy planar graphs. Moreover, it presents a problem that shows applicability of the proposed concept.

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