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Two queues with random time-limited polling

Saxena M., Boxma O., Kapodistria S., Núñez-Queija R.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

257--289

In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously switches to the other queue, i.e., there is no switch-over time. For this polling model we derive the steady-state marginal workload distribution, as well as heavy traffic and heavy tail asymptotic results. Furthermore, we also calculate the joint queue length distribution for the special case of exponentially distributed service times using singular perturbation analysis.

Separation of time scales in the HCA model for sand

Niemunis A., Wichtman T.

Acta Geophysica

2014

Vol. 62, no. 5

1127--1145

Separation of time scales is used in a high cycle accumulation (HCA)model for sand. An important difficulty of the model is the limited applicability of the Miner’s rule to multiaxial cyclic loadings applied simultaneously or in a combination with monotonic loading. Another problem is the lack of simplified objective HCA formulas for geotechnical settlement problems. Possible solutions of these problems are discussed.

The order reduction and robust D-stability analysis of discrete uncertain time-delay systems by time-scale separation

Pan S.-T.

Control and Cybernetics

2003

Vol. 32, no 4

745-760

In this paper, the robust D-stability problem for discrete uncertain multiple time-delay systems is examined on the basis of their such reduced-order models (the slow and fast subsystems), which are obtained by time-scale separation method. Under the condition that the slow and fast subsystems of the nominal system are both -D(a,r)-stable, a D-stability criterion for the slow and fast subsystem of the original uncertain system is first derived. A delay-dependent criterion in terms of spectral radius is then proposed to guarantee the robust D-stability of the original uncertain system subject to structured perturbations. Moreover, the criterion for the robust asymptotic stability of the system subject to structured perturbations can be obtained from the proposed robust D-stability criterion. A numerical example is provided to illustrate our main results.