Abstract
This paper presents an analytical method to calculate the waiting time distribution for the G/G/1-queueing system with batch arrivals. Using the discrete time scale, it is possible to calculate the distribution of the waiting times and the idle times of a G/G/1-queueing system based on the Wiener–Hopf factorization. The influence of batch arrivals on the waiting time distribution is analyzed. The waiting time distribution is calculated for batch arrivals with both constant and stochastic batch sizes. The effect of stochastic batch sizes on the waiting process is highlighted. With the developed methods, it is possible to obtain congestion measures of high precision for logistic systems. The analytical results are evaluated by simulation. Several numerical examples are presented to emphasize the quality of the introduced methods.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
