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

Abstract

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.

Reducing the variability of inter-departure times of a single-server queueing system – The effects of skewness

“…This result, leading to research question 2, suggests that CV ID could be reduced by implementing a combination of negative inter-arrival skewness and positive service skewness. This differs from previous conclusions (Johnson, 1993;Romero-Silva, Shaaban, Marsillac, & Hurtado, 2017;Whitt, 1984) suggesting that the waiting times of a GI/ G/1 queue increased by decreasing inter-arrival skewness and increasing service skewness for a system with CV < 1, similar to the results from the current study (see Tables A14 and A15 in the Appendix) which suggest that the probability of balking is increased by decreasing inter-arrival skewness and increasing service skewness.…”