scholarly journals Explicit Expression for Moment of Waiting Time in a DBR Line Production System with Constant Processing Times Using Max-plus Algebra

2015 ◽  
Vol 24 (2) ◽  
pp. 11-17
Author(s):  
Philip Park ◽  
Dong-Won Seo
1981 ◽  
Vol 11 (1) ◽  
pp. 99-104 ◽  
Author(s):  
C. H. Meng

The purpose of this study is to develop analytical formulae for special queuing situations which occur during the operations of the felling and processing devices of a tree harvester, and the pickup and processing devices of a tree processor. Analytical formulae are used to estimate mean waiting time and mean idle time; in case 1 both "input" times and processing times are normally distributed; in case 2 "input" times are normally distributed and processing times are Poisson distributed. "Input" time is a term used for convenience to denote time required to fell a tree by a harvester or time required to pick up a tree by a processor. Methods of choosing distributions for representing "input" times and processing times are provided. In addition, there are two examples, using historical data, which demonstrate the applications of the analytical formulae.


2012 ◽  
Vol 576 ◽  
pp. 714-717
Author(s):  
Mohammad Iqbal ◽  
Muhammad Ridwan Andi Purnomo ◽  
Muhammad Ammar Bin Mohd Imra ◽  
Mohamed Konneh ◽  
A.N. Mustafizul Karim

Material handling is one of major components in Flexible Manufacturing System (FMS). Any improvement of material handling capability is to affect the performance of the whole system. This paper discusses the simulation study on the effect of part arrival rate and dispatching rules to the average waiting time and production rate of the FMS. The facilities of the system were modeled into simulation environment by using Arena Simulation Software. The production parameters such as machine processing times, part transportation speed and type of products were put into the model to represent the behaviors of the real system. Two rules have been considered in the study, i. e. first come first served (FCFS), and shortest processing time (SPT). Average waiting time and productivity were taken into account as performance measures of the system. The result of the study showed that SPT rule gives shorter average waiting time and higher productivity. Based on this result, the SPT rules would be used to control part transporter in order to have a better performance of the FMS.


2017 ◽  
Vol 2 (4) ◽  
pp. 33-39
Author(s):  
Mohammad Annas

Objective - This research is a direct observation of initial queuing, using data that is categorised into two clusters: the number of people queuing at busy hours, and processing times in the same circumstances. Methodology/Technique - The raw data was converted for use in the Poisson distribution test, as well as the Kolmogorov-Smirnov exponential distribution options. An arena simulation model was also applied to identify the vendor's waiting time and to analyse receiving yard utilization. The average waiting time according to the Poisson distribution, the average serving time per vendor by an exponential distribution, and the number of receiving yards, are all essential factors effecting the utilization of receiving yards. Findings - The study compares the length of queues, serving times, arrival rate, and time in the system using dual and single receiving yard systems. However, the utilization rate on a two receiving yards system is less than the rate on single receiving yard system. As the aim of this study is to identify the utilization rate of the receiving yard, a single receiving yard operation is more representative of modern hypermarkets, and more efficient in terms of resource efficiency. Novelty - This study depends fully on the homogeneous operating hours of the retailers' receiving yards, the type of vehicle used by vendors to unload merchandises, procedures on moving the products to the inspections phase, a generalization of the products delivered by the vendors and the size of the modern hypermarkets business itself. Type of Paper: Empirical. Keywords: Receiving Yard Utilization; Hypermarket Receiving Yard; Queuing Simulation. JEL Classification: M1, M10, M19.


2005 ◽  
Vol 19 (3) ◽  
pp. 345-349 ◽  
Author(s):  
Geert Jan Franx

A surprisingly simple and explicit expression for the waiting time distribution of the MX/D/c batch arrival queue is derived by a full probabilistic analysis, requiring neither generating functions nor Laplace transforms. Unlike the solutions known so far, this expression presents no numerical complications, not even for high traffic intensities.


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