Light traffic approximations in general stationary single-server queues

Light traffic approximations in general stationary single-server queues

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Article ID: iaor19941731
Country: Netherlands
Volume: 49
Issue: 1
Start Page Number: 151
End Page Number: 158
Publication Date: Jan 1994
Journal: Stochastic Processes and Their Applications
Authors: ,
Keywords: queues: theory
Abstract:

This paper complements two previous studies, by indicating the extent to which characteristics of a general stationary point process taken as the arrival process of a single-server queue influence light traffic limit theorems for the two essentially distinct schemes of dilation and thinning as routes of the limit. Properties of both the work-load and the waiting-time processes are derived, reflecting respectively the stationary time-sampling frame that may be appropriate for monitoring the system as a whole, and the customer-sampling frame (Palm distributions). Substantially different results can come from these two different views, and when compounded with the different approaches to the light traffic limits, no single light traffic scenario emerges.

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