Convergence of departures in tandem networks of ·/GI/[infinity] queues
By: Balaji Prabhakar, Tom Mountford, Nicholas Bambos.
Contributors: Mountford, Tom.; Bambos, Nicholas.; Hewlett-Packard Laboratories.
Series: [Technical report] / HP Laboratories Bristol. Basic Research Institute in the Mathematical Sciences -- HPL-BRIMS-96-15.; BRIMS technical report -- HPL-BRIMS-96-15.
Publisher: Hewlett Packard
Published: 1996
Place of publication: Bristol [England]
Language: eng
Number of pages: 12
Subjects: Queuing theory; Poisson processes
Description: Abstract: "We consider an infinite series of independent and identical ·/GI[infinity] queues fed by an arbitrary stationary and ergodic arrival process, A¹. Let A[superscript i] be the arrival process to the i[superscript th] node and let v[superscript i] be the law of A[superscript i]. Denote by T(·) the input-output map of the ·/GI/[infinity] node; that is, v[superscript i+1] = T(v[superscript i]). It is known that the Poisson process is a fixed point for T. In this paper, we are interested in the asymptotic distribution of the departure process from the n[superscript th] node, v[superscript n+1] = T[superscript n](v¹), as n -> [infinity]. Using couplings for random walks, this limiting distribution is shown to be either a Poisson process or a stationary v-Poisson process (defined below) depending on the joint distribution of A¹ and the service process. This generalizes a result of Vere-Jones [11] and is similar in flavour to [10] where Poisson convergence is established for departures from a series of exponential server queues using coupling methods."
Notes: Cover title.

"May, 1996."

Includes bibliographical references.