Exact and asymptotic solutions to a PDE that arises in time-dependent queues

Exact and asymptotic solutions to a PDE that arises in time-dependent queues

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Article ID: iaor20012992
Country: United States
Volume: 32
Issue: 1
Start Page Number: 256
End Page Number: 283
Publication Date: Mar 2000
Journal: Advances in Applied Probability
Authors:
Abstract:

We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection–diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

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