Studying the Effects of the Skewness of Inter-Arrival and Service Times on the Probability Distribution of Waiting Times

Previous studies have shown that the mean queue length of a GI/G/1 system is significantly influenced by the skewness of inter-arrival times, but not by the skewness of service times. These results are limited because all the distributions considered in previous studies were positively skewed. To address this limitation, this paper investigates the effects of the skewness of inter-arrival and service times on the probability distribution of waiting times, when a negatively skewed distribution is used to model inter-arrival and service times. Subsequent to a series of experiments on a GI/G/1 queue using discrete-event simulation, results have shown that the lowest mean waiting time and the lowest variance of waiting times can be attained with a combination of positive inter-arrival skewness and negative service skewness. Results also show an interesting effect of the skewness of service times in the probability of no-delay in environments with a higher utilization factor

Serial production line performance under random variation:Dealing with the ‘Law of Variability’

Many Queueing Theory and Production Management studies have investigated specific effects of variability on the performance of serial lines since variability has a significant impact on performance. To date, there has been no single summary source of the most relevant research results concerned with variability, particularly as they relate to the need to better understand the ‘Law of Variability’. This paper fills this gap and provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance, i.e. throughput, inter-departure time and flow time, under random variation

Studying the effects of skewness of inter-arrival and service times on the probability distribution of waiting times

Previous studies have shown that the mean queue length of a GI/G/1 system is significantly influenced by the skewness of inter-arrival times, but not by the skewness of service times. These results are limited because all the distributions considered in previous studies were positively skewed. To address this limitation, this paper investigates the effects of the skewness of inter-arrival and service times on the probability distribution of waiting times, when a negatively skewed distribution is used to model inter-arrival and service times. Subsequent to a series of experiments on a GI/G/1 queue using discrete-event simulation, results have shown that the lowest mean waiting time and the lowest variance of waiting times can be attained with a combination of positive inter-arrival skewness and negative service skewness. Results also show an interesting effect of the skewness of service times in the probability of no-delay in environments with a higher utilization factor

Approximations for manufacturing networks of queues with overtime

Includes bibliographical references.Gabriel R. Britan, Devanath Tirupati