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

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

A critical performance measure in serial production lines is the variability of inter-departure times of a single-server queue. Increasing upstream inter-departure time variability generates greater downstream variability, diminishing overall line performance. Theory suggests that the variability of inter-departure times of a single-server queue is reduced by decreasing the variance of inter-arrival and service times. This study investigates the effects of the skewness of inter-arrival and service time distributions on the variability of inter-departure times. Contrary to previous results suggesting that mean waiting times of a GI/G/1 queue can be reduced by increasing inter-arrival time skewness, this experimental study of a GI/G/1 queue with triangular inter-arrival and service times shows that the inter-departure time coefficient of variation is reduced through a combination of negative inter-arrival time skewness and positive service time skewness. These results also suggest that the absolute value of the negative autocorrelation between consecutive departures is reduced by the same combination of negative inter-arrival time skewness and positive service time skewness for low values of server's utilization, while positive skewness for both inter-arrival and service times reduces this value for high values of server's utilization. Finally, it was found that queue capacity constraints increase the coefficient of variation of inter-departure times, as has been previously suggested, as well as the skewness and the absolute correlation values of the inter-departure time distribution

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

A critical performance measure in serial production lines is the variability of inter-departure times of a single-server queue. Increasing upstream inter-departure time variability generates greater downstream variability, diminishing overall line performance. Theory suggests that the variability of inter-departure times of a single-server queue is reduced by decreasing the variance of inter-arrival and service times. This study investigates the effects of the skewness of inter-arrival and service time distributions on the variability of inter-departure times. Contrary to previous results suggesting that mean waiting times of a GI/G/1 queue can be reduced by increasing inter-arrival time skewness, this experimental study of a GI/G/1 queue with triangular inter-arrival and service times shows that the inter-departure time coefficient of variation is reduced through a combination of negative inter-arrival time skewness and positive service time skewness. These results also suggest that the absolute value of the negative autocorrelation between consecutive departures is reduced by the same combination of negative inter-arrival time skewness and positive service time skewness for low values of server's utilization, while positive skewness for both inter-arrival and service times reduces this value for high values of server's utilization. Finally, it was found that queue capacity constraints increase the coefficient of variation of inter-departure times, as has been previously suggested, as well as the skewness and the absolute correlation values of the inter-departure time distribution