Approximating the Performance of a Batch Service Queue Using the ${\rm M/M}^{\rm k}/1$ Model

Batching plays an important role in semiconductor fabs, and it can lead to inefficiency if not treated with care. The performance of parallel batch processes is often approximated by the G/G/1-based approximate models. By carefully examining the existing models, the dependence between queueing time and wait-to-batch time has been identified. A new improved model for parallel batch systems is proposed to exploit this dependence. The computation of the new model is still simple and fast, but it gives better approximation by reducing the systematic error in earlier models which ignored the dependence between queueing time and wait-to-batch time.