Priority queues with Gaussian input: a path space approach to loss and delay asymptotics

Michel Mandjes; Petteri Mannersalo; Ilkka Norros

Priority queues with Gaussian input: a path space approach to loss and delay asymptotics

Michel Mandjes
, Petteri Mannersalo
, Ilkka Norros

Centrum voor Wiskunde en Informatica

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

Abstract

Priority queueing is the basic technique for providing real-time Quality of Service to packet-based networking. The mathematical analysis of priority queues with general traffic models is, however, prohibitively difficult, in particular when the traffic is long-range dependent. This paper provides some important steps forward in this direction. Our analysis is the first mathematically rigorous treatment of path-space large deviations of priority queues with class-wise heterogeneous Gaussian input having an arbitrary correlation structure. This includes the computation of the most probable paths that lead to overflow in one of the queues. Compared with earlier work on the same topic, the paper provides three novel contributions: a new representation of the workload in the low-priority queues, an exact characterization of the most probable paths, and an extension of the analysis to virtual waiting times, in addition to queue lengths.

Original language	English
Title of host publication	Performance Challenges for Efficient Next Generation Networks
Subtitle of host publication	Proceedings of the 19th International Teletraffic Congress ITC19
Pages	1135-1144
Publication status	Published - 2005
MoE publication type	A4 Article in a conference publication
Event	19th International Teletraffic Congress, ITC 19 - Beijing, China Duration: 29 Aug 2005 → 2 Sept 2005 Conference number: 19

Conference

Conference	19th International Teletraffic Congress, ITC 19
Abbreviated title	ITC19
Country/Territory	China
City	Beijing
Period	29/08/05 → 2/09/05

Keywords

priority queue
large deviations
Gaussian processes
fractional Brownian motion

Access to Document

https://publications.vtt.fi/julkaisut/muut/2005/prioritc.pdf

Cite this

@inproceedings{f77696bb7d014b7b9ccd0750535ac980,

title = "Priority queues with Gaussian input: a path space approach to loss and delay asymptotics",

abstract = "Priority queueing is the basic technique for providing real-time Quality of Service to packet-based networking. The mathematical analysis of priority queues with general traffic models is, however, prohibitively difficult, in particular when the traffic is long-range dependent. This paper provides some important steps forward in this direction. Our analysis is the first mathematically rigorous treatment of path-space large deviations of priority queues with class-wise heterogeneous Gaussian input having an arbitrary correlation structure. This includes the computation of the most probable paths that lead to overflow in one of the queues. Compared with earlier work on the same topic, the paper provides three novel contributions: a new representation of the workload in the low-priority queues, an exact characterization of the most probable paths, and an extension of the analysis to virtual waiting times, in addition to queue lengths.",

keywords = "priority queue, large deviations, Gaussian processes, fractional Brownian motion",

author = "Michel Mandjes and Petteri Mannersalo and Ilkka Norros",

note = "Project code: 1214; 19th International Teletraffic Congress, ITC 19, ITC19 ; Conference date: 29-08-2005 Through 02-09-2005",

year = "2005",

language = "English",

isbn = "7-5635-1141-5",

pages = "1135--1144",

booktitle = "Performance Challenges for Efficient Next Generation Networks",

}

Mandjes, M, Mannersalo, P & Norros, I 2005, Priority queues with Gaussian input: a path space approach to loss and delay asymptotics. in Performance Challenges for Efficient Next Generation Networks: Proceedings of the 19th International Teletraffic Congress ITC19. pp. 1135-1144, 19th International Teletraffic Congress, ITC 19, Beijing, China, 29/08/05. <https://publications.vtt.fi/julkaisut/muut/2005/prioritc.pdf>

Priority queues with Gaussian input: a path space approach to loss and delay asymptotics. / Mandjes, Michel; Mannersalo, Petteri; Norros, Ilkka.
Performance Challenges for Efficient Next Generation Networks: Proceedings of the 19th International Teletraffic Congress ITC19. 2005. p. 1135-1144.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Priority queues with Gaussian input

T2 - 19th International Teletraffic Congress, ITC 19

AU - Mandjes, Michel

AU - Mannersalo, Petteri

AU - Norros, Ilkka

N1 - Conference code: 19

PY - 2005

Y1 - 2005

N2 - Priority queueing is the basic technique for providing real-time Quality of Service to packet-based networking. The mathematical analysis of priority queues with general traffic models is, however, prohibitively difficult, in particular when the traffic is long-range dependent. This paper provides some important steps forward in this direction. Our analysis is the first mathematically rigorous treatment of path-space large deviations of priority queues with class-wise heterogeneous Gaussian input having an arbitrary correlation structure. This includes the computation of the most probable paths that lead to overflow in one of the queues. Compared with earlier work on the same topic, the paper provides three novel contributions: a new representation of the workload in the low-priority queues, an exact characterization of the most probable paths, and an extension of the analysis to virtual waiting times, in addition to queue lengths.

AB - Priority queueing is the basic technique for providing real-time Quality of Service to packet-based networking. The mathematical analysis of priority queues with general traffic models is, however, prohibitively difficult, in particular when the traffic is long-range dependent. This paper provides some important steps forward in this direction. Our analysis is the first mathematically rigorous treatment of path-space large deviations of priority queues with class-wise heterogeneous Gaussian input having an arbitrary correlation structure. This includes the computation of the most probable paths that lead to overflow in one of the queues. Compared with earlier work on the same topic, the paper provides three novel contributions: a new representation of the workload in the low-priority queues, an exact characterization of the most probable paths, and an extension of the analysis to virtual waiting times, in addition to queue lengths.

KW - priority queue

KW - large deviations

KW - Gaussian processes

KW - fractional Brownian motion

M3 - Conference article in proceedings

SN - 7-5635-1141-5

SP - 1135

EP - 1144

BT - Performance Challenges for Efficient Next Generation Networks

Y2 - 29 August 2005 through 2 September 2005

ER -

Priority queues with Gaussian input: a path space approach to loss and delay asymptotics

Abstract

Conference

Keywords

Access to Document

Fingerprint

Cite this