One of the main characteristics in optimization and performance evaluation in a Queueing Model is its busy period. Finding the exact distribution of this variables in Queueing Models which service distribution and or inter-arrival distribution is general is so complicated and there is usually no closed formula for that. Traditionally in these situations, Laplase-Stieltjes transform this variable computed and then by using that the moments it determined.
Mohammad Taremi and Mohammad Reza Salehi Rad. Analyze the Duration of Busy Period in M|X|/G/1/K Systems with Vacation Time and under the Partial Batch Acceptance Strategy.
DOI: https://doi.org/10.36478/jeth.2011.106.109
URL: https://www.makhillpublications.co/view-article/1994-8212/jeth.2011.106.109