A Maclaurin-series expansion approach to multiple paired queues

Motivated by kitting processes in assembly systems, we consider a Markovian queueing system with KK paired finite-capacity buffers. Pairing means that departures from the buffers are synchronised and that service is interrupted if any of the buffers is empty. To cope with the inherent state-space explosion problem, we propose an approximate numerical algorithm which calculates the first LL coefficients of the Maclaurin series expansion of the steady-state probability vector in O(KLM)O(KLM) operations, MM being the size of the state space.