Infinitesimal perturbation analysis for queueing networks with general service time distributions

We study infinitesimal perturbation analysis (IPA) for queueing networks with general service time distributions. By ‘general’ we mean that the distributions may have discrete components. We show that in the presence of service time distributions with discrete components commuting condition (CC) is no longer sufficient for unbiasedness of IPA. To overcome this difficulty, we introduce the notion of separability of real-valued random variables, and show that separability of service times together with CC establishes unbiasedness of IPA for queueing systems with general service time distributions. It turns out that the piecewise analyticity of service times is a sufficient condition for separability.