A New Approach to Compute Moments of Busy Period in

One of the main characteristics in optimization and performance evaluation in a queuing model is its busy period. Finding the exact distribution of this variables in queuing models which service distribution and or inter-arrival distribution is general, is so complicated and there is usually no closed formula for it. Traditionally, in these situations, Laplase–Stieltjes transform this variable computed and then by using that the moments it determined. In this paper while, we address using this approach to computemoments of the duration of the busy period in   / /1/ X M G K systems with vacation times and under the partial batch acceptance strategy is associated with some important practical limitations, we propose a new procedure to calculate the moments of this queuing system. The new approach relies on the number of customers that arrive to the system during the first vacation time of system and taking full advantage of the Markov-regenerative process property. Numerical results are presented to demonstrate the simplicity and efficiency of the new approach.