Diffusion approximation to a queueing system with time-dependent arrival and service rates (Q1892642)

The authors study the transient behavior of a Markovian single-server queueing system whose arrival and service rates vary over time and depend linearly on the current number of customers, and derive the asymptotic distribution in a special case. They construct a diffusion approximation for the scaled process. From the drift and variance functions they obtain the transition probability density, the asymptotic (gamma) distribution, and the first-passage density for the zero state. Finally, the accuracy of the approximation is discussed.