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To obtain insight in the quality of heavy-traffic approximations for queues with many servers, we consider the steady-state number of waiting customers in an M/D/s queue as s → ∞. In the Halfin-Whitt regime, it is well known that this random variable converges to the supremum of a Gaussian random walk. This paper develops methods that yield more accurate… (More)

We consider piecewise deterministic Markov processes that occur as scaling limits of discrete-time Markov chains that describe the Transmission Control Protocol (TCP). The class of processes allows for general increase and decrease profiles. Our key observation is that stationary results for the general class follow directly from the stationary results for… (More)

In [13] it is shown that the two-stage tandem queue with coupled processors can be solved using the theory of boundary value problems. In this paper we consider the issues that arise when calculating performance measures like the mean queue length and the fraction of time a station is empty. It is assumed that jobs arrive at the first station according to a… (More)

In commonly used approaches for the discrete-time bulk service queue, the stationary queue length distribution follows from the roots inside or outside the unit circle of a characteristic equation. We present analytic representations of these roots in the form of sample values of periodic functions with analytically given Fourier series coefficients, making… (More)