Sojourn-time Distribution for M/G^a/1 Queue with Batch Service of Fixed Size - Revisited

This paper presents an explicit and straightforward method for finding the sojourn-time distribution of a random customer in an M/G^a/1 queue with a fixed-size batch service. The exhibited process is much more straightforward than the approach discussed by Yu and Tang (Methodology and Computing in Applied Probability 20(4):1503–1514, 2018 ). We obtain two closed-form expressions for probability density functions by using the inside and outside roots of the underlying characteristic equation. Applying partial fractions and residue theorem, we determine an explicit form of sojourn-time distribution and evaluate the distribution function for any specific time. In illustrative examples, we compare the results obtained by both methods and find that the results match excellently.