On stochastic recursive equations and infinite server queues

Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies. ◽

10.1109/infcom.2005.1498355 ◽

2005 ◽

Cited By ~ 6

Author(s):

E. Altman

Keyword(s):

Infinite Server ◽

Infinite Server Queues ◽

Recursive Equations ◽

Stochastic Recursive Equations

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Two-parameter heavy-traffic limits for infinite-server queues with dependent service times

Queueing Systems ◽

10.1007/s11134-012-9303-0 ◽

2012 ◽

Vol 73 (2) ◽

pp. 119-146 ◽

Cited By ~ 19

Author(s):

Guodong Pang ◽

Ward Whitt

Keyword(s):

Heavy Traffic ◽

Infinite Server ◽

Infinite Server Queues ◽

Service Times ◽

Two Parameter

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Tandem of Infinite-Server Queues with Markovian Arrival Process

Communications in Computer and Information Science - Distributed Computer and Communication Networks ◽

10.1007/978-3-319-30843-2_34 ◽

2016 ◽

pp. 323-333 ◽

Cited By ~ 2

Author(s):

Alexander Moiseev ◽

Anatoly Nazarov

Keyword(s):

Markovian Arrival Process ◽

Arrival Process ◽

Infinite Server ◽

Infinite Server Queues

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Networks of infinite-server queues with multiplicative transitions

Performance Evaluation ◽

10.1016/j.peva.2018.03.003 ◽

2018 ◽

Vol 123-124 ◽

pp. 35-49 ◽

Cited By ~ 1

Author(s):

Dieter Fiems ◽

Michel Mandjes ◽

Brendan Patch

Keyword(s):

Infinite Server ◽

Infinite Server Queues

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Markov-modulated stochastic recursive equations with applications to delay-tolerant networks

Performance Evaluation ◽

10.1016/j.peva.2013.06.001 ◽

2013 ◽

Vol 70 (11) ◽

pp. 965-980 ◽

Cited By ~ 1

Author(s):

Dieter Fiems ◽

Eitan Altman

Keyword(s):

Delay Tolerant Networks ◽

Markov Modulated ◽

Delay Tolerant ◽

Recursive Equations ◽

Stochastic Recursive Equations

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Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds

Queueing Systems ◽

10.1007/s11134-017-9550-1 ◽

2017 ◽

Vol 88 (1-2) ◽

pp. 1-25 ◽

Cited By ~ 2

Author(s):

Guodong Pang ◽

Yuhang Zhou

Keyword(s):

Infinite Server ◽

Infinite Server Queues ◽

Service Times ◽

Two Parameter

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Time-Scaling Limits for Markov-Modulated Infinite-Server Queues

Stochastic Models ◽

10.1080/15326349.2013.750536 ◽

2013 ◽

Vol 29 (1) ◽

pp. 112-127 ◽

Cited By ~ 10

Author(s):

J. Blom ◽

M. Mandjes ◽

H. Thorsdottir

Keyword(s):

Scaling Limits ◽

Infinite Server ◽

Time Scaling ◽

Infinite Server Queues ◽

Markov Modulated

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A large-deviations analysis of Markov-modulated infinite-server queues

Operations Research Letters ◽

10.1016/j.orl.2013.01.009 ◽

2013 ◽

Vol 41 (3) ◽

pp. 220-225 ◽

Cited By ~ 12

Author(s):

J. Blom ◽

M. Mandjes

Keyword(s):

Large Deviations ◽

Infinite Server ◽

Infinite Server Queues ◽

Markov Modulated

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TRANSIENT ANALYSIS OF SOME INFINITE SERVER QUEUES

Recent Advances in Statistical Methods ◽

10.1142/9781860949531_0029 ◽

2002 ◽

Cited By ~ 3

Author(s):

GORDON E. WILLMOT ◽

STEVE DREKIC

Keyword(s):

Transient Analysis ◽

Infinite Server ◽

Infinite Server Queues

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Two-parameter Sample Path Large Deviations for Infinite-Server Queues

Stochastic Systems ◽

10.1287/12-ssy080 ◽

2014 ◽

Vol 4 (1) ◽

pp. 206-249 ◽

Cited By ~ 2

Author(s):

Jose Blanchet ◽

Xinyun Chen ◽

Henry Lam

Keyword(s):

Large Deviations ◽

Sample Path ◽

Infinite Server ◽

Infinite Server Queues ◽

Two Parameter ◽

Sample Path Large Deviations

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A new view of the heavy-traffic limit theorem for infinite-server queues

Advances in Applied Probability ◽

10.1017/s0001867800023399 ◽

1991 ◽

Vol 23 (01) ◽

pp. 188-209 ◽

Cited By ~ 11

Author(s):

Peter W. Glynn ◽

Ward Whitt

Keyword(s):

Heavy Traffic ◽

Rates Of Convergence ◽

Infinite Server ◽

Open Networks ◽

Heavy Traffic Limit ◽

Many Server Queues ◽

Finite Set ◽

Deterministic Service ◽

Infinite Server Queues ◽

Service Times

This paper presents a new approach for obtaining heavy-traffic limits for infinite-server queues and open networks of infinite-server queues. The key observation is that infinite-server queues having deterministic service times can easily be analyzed in terms of the arrival counting process. A variant of the same idea applies when the service times take values in a finite set, so this is the key assumption. In addition to new proofs of established results, the paper contains several new results, including limits for the work-in-system process, limits for steady-state distributions, limits for open networks with general customer routes, and rates of convergence. The relatively tractable Gaussian limits are promising approximations for many-server queues and open networks of such queues, possibly with finite waiting rooms.

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