scholarly journals Mathematical Models of Mb/M/1 Bulk Arrival Queueing System

2014 ◽  
Vol 10 (1) ◽  
pp. 184-191 ◽  
Author(s):  
Sushil Ghimire ◽  
R. P. Ghimire ◽  
Gyan Bahadur Thapa
Keyword(s):  
Mathematical Model ◽  
Function Method ◽  
Queueing System ◽  
Batch Size ◽  
Queueing Model ◽  
Mean Waiting Time ◽  
Bulk Arrival ◽  
Number Of Customers ◽  
The Mathematical Model ◽  
Mean Time

 This paper deals with the study of bulk queueing model with the fixed batch size ‘b’ and customers arrive to the system with Poisson fashion with the rate λ and are severed exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers/work pieces in the queue and in the system by using generating function method. Some numerical illustrations are also obtained by using MATLAB-7 so as to show the applicability of the model under study.DOI: http://dx.doi.org/10.3126/jie.v10i1.10899Journal of the Institute of Engineering, Vol. 10, No. 1, 2014, pp. 184–191

scholarly journals M(t)/M/1 Queueing System with Sinusoidal Arrival Rate

2016 ◽  
Vol 11 (1) ◽  
pp. 120-127
Author(s):  
A. P. Pant ◽  
R. P. Ghimire
Keyword(s):  
Mathematical Model ◽  
Waiting Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Rate Function ◽  
Recursive Method ◽  
Mean Waiting Time ◽  
Number Of Customers ◽  
The Mathematical Model ◽  
Mean Time

This paper deals with the study of M (t)/M/1 queueing system with customers arrive to the system with sinusoidal arrival rate function λ (t) and are served exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers in the queue and in the system by using recursive method. Some numerical illustrations are also obtained by using computing software so as to show the applicability of the model under study.Journal of the Institute of Engineering, 2015, 11(1): 120-127

Fault Forecast Technology of Machine Based on Grey Theory for Aero-Engine Product Line

2011 ◽  
Vol 338 ◽  
pp. 718-722 ◽  
Author(s):  
Bing Chen ◽  
Ting Yang ◽  
Jun De Qi
Keyword(s):  
Mathematical Model ◽  
High Accuracy ◽  
Product Line ◽  
Grey Theory ◽  
Mean Time Between Failures ◽  
Time Between Failures ◽  
Aero Engine ◽  
Machine Fault ◽  
The Mathematical Model ◽  
Mean Time

Facing to the dynamic process of machine running, grey theory is introduced to increase the accuracy of forecast on machine fault. Firstly the mathematical model of the machine fault is constructed according to the life cycle of machine. Mean time between failures is defined as a tool to describe the fault on the machine. Moreover the fault is predicted respectively according to amount of data sample. And the produce to build the grey information model is given in this paper in detail. Finally an actual aero-engine casing production line is presented as an example to validate the algorithms in this paper. The results show that the fault forecast based on grey theory has high accuracy.

scholarly journals Discrete- Time Queueing Model Geox/G/ꚙ with Bulk Arrival Rule

2020 ◽  
Vol 9 (3) ◽  
pp. 2585-2589
Keyword(s):  
Discrete Time ◽  
Geometric Distribution ◽  
Transient State ◽  
State Solution ◽  
General Distribution ◽  
Queueing Model ◽  
Service Times ◽  
Bulk Arrival ◽  
Number Of Customers

A discrete time queueing model is considered to estimate of the number of customers in the system. The arrivals, which are in groups of size X, inter-arrivals times and service times are distributed independent. The inter-arrivals fallows geometric distribution with parameter p and service times follows general distribution with parameter µ, we have derive the various transient state solution along with their moments and numerical illustrations in this paper.

On a property of the variance of the waiting time of a queue

1968 ◽  
Vol 5 (3) ◽  
pp. 702-703 ◽  
Author(s):  
D. G. Tambouratzis
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Mean Waiting Time ◽  
Queue Discipline ◽  
The Mean ◽  
Number Of Customers

In this note, we consider a queueing system under any discipline which does not affect the distribution of the number of customers in the queue at any time. We shall show that the variance of the waiting time is a maximum when the queue discipline is “last come, first served”. This result complements that of Kingman [1] who showed that, under the same assumptions, the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in the order of their arrival.

Optimum Design of Planar Four-Bar Linkage for Scheduled Tracks

2012 ◽  
Vol 215-216 ◽  
pp. 395-398
Author(s):  
Tian Xiang Liu ◽  
Chun Wang
Keyword(s):  
Mathematical Model ◽  
Optimum Design ◽  
Penalty Function ◽  
Function Method ◽  
Penalty Function Method ◽  
Design Efficiency ◽  
Four Bar Linkage ◽  
The Mathematical Model

The mathematical model was established, the pragram was made to optimize the lengths and angles of each link by means of inner point penalty function method. Involving 12 scheduled points, the track of a certain point on the coupler of a planar four-bar linkage was realized and previewed using Matlab. The optimum program presented here could enhance the design efficiency and insure the design accuracy markedly. By this method the coupler-curve involving more than or less than 12 points could be realized, and more complex multi-linkage could be designed.

scholarly journals The use of Lambert function method for analysis of a multidimensional control system with delays and with structure of the complete graph

2012 ◽  
Vol 53 ◽  
Author(s):  
Irma Ivanovienė ◽  
Jonas Rimas
Keyword(s):  
Mathematical Model ◽  
Complete Graph ◽  
Function Method ◽  
Lambert Function ◽  
Mutual Synchronization ◽  
Delayed Argument ◽  
The Matrix ◽  
Matrix Differential ◽  
The Mathematical Model ◽  
Step Responses

The mathematical model of the mutual synchronization system with structure having form of the complete graph and composed of n  oscillators, is investigated. The mathematical model of the system is the matrix differential equation with delayed argument. The step responses matrix of the system is obtained applying the Lambert function method. The transition processes are investigated using obtained step responses of the system.

Dynamic Systems - Applications in Economy and in Technology

2021 ◽  
Vol 110 ◽  
pp. 9-14
Author(s):  
Dumitru Bălă
Keyword(s):  
Mathematical Model ◽  
Dynamic Systems ◽  
Function Method ◽  
Stability Study ◽  
Regression Method ◽  
Tourism Activity ◽  
The Stability ◽  
The Mathematical Model ◽  
The Way

In this paper, starting from recent data provided by the National Institute of Statistics, we analyze the tourism activity in Mehedinți County. We apply the regression method and analyze some models. We also compare the economic results with those of previous years. Also, in this paper we study the stability of dynamic systems with applications in economics. The stability study is done using the Leapunov function method. The originality of the paper consists in the way we choose the mathematical model in case of regression and in the way we choose the Leapunov function in case of dynamic systems in which we analyze stability.

On a property of the variance of the waiting time of a queue

1968 ◽  
Vol 5 (03) ◽  
pp. 702-703 ◽  
Author(s):  
D. G. Tambouratzis
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Mean Waiting Time ◽  
Queue Discipline ◽  
The Mean ◽  
Number Of Customers

In this note, we consider a queueing system under any discipline which does not affect the distribution of the number of customers in the queue at any time. We shall show that the variance of the waiting time is a maximum when the queue discipline is “last come, first served”. This result complements that of Kingman [1] who showed that, under the same assumptions, the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in the order of their arrival.

A Discrete-Time Queueing Model with Service Upgrade

2014 ◽  
Vol 513-517 ◽  
pp. 806-811
Author(s):  
Ivan Atencia ◽  
Inmaculada Fortes ◽  
Sixto Sánchez
Keyword(s):  
Discrete Time ◽  
Generating Functions ◽  
Busy Period ◽  
Queueing System ◽  
Queueing Model ◽  
Numerical Examples ◽  
Extensive Analysis ◽  
Number Of Customers ◽  
Incoming Message

In this paper we analyze a discrete-time queueing system where the server decides whento upgrade the service depending on the information carried by the incoming message. We carry outan extensive analysis of the system developing recursive formulae and generating functions for thestationary distribution of the number of customers in the queue, the system, the busy period and thesojourntimeas well as some numerical examples.

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