Layered queueing network

In queueing theory, a discipline within the mathematical theory of probability, a layered queueing network (or rendezvous network^[1]) is a queueing network model where the service time for each job at each service node is given by the response time of a queueing network (and those service times in turn may also be determined by further nested networks). Resources can be nested and queues form along the nodes of the nesting structure.^[2]^[3] The nesting structure thus defines "layers" within the queueing model.^[2]

Layered queueing has applications in a wide range of distributed systems which involve different master/slave, replicated services and client-server components, allowing each local node to be represented by a specific queue, then orchestrating the evaluation of these queues.^[2]

For large population of jobs, a fluid limit has been shown in PEPA to be a give good approximation of performance measures.^[4]

External links

Tutorial Introduction to Layered Modeling of Software Performance by Murray Woodside, Carleton University

References

↑ Neilson, J. E.; Woodside, C. M.; Petriu, D. C.; Majumdar, S. (1995). "Software bottlenecking in client-server systems and rendezvous networks". IEEE Transactions on Software Engineering. 21 (9): 776. doi:10.1109/32.464543.
1 2 3 Franks, G.; Al-Omari, T.; Woodside, M.; Das, O.; Derisavi, S. (2009). "Enhanced Modeling and Solution of Layered Queueing Networks". IEEE Transactions on Software Engineering. 35 (2): 148. doi:10.1109/TSE.2008.74.
↑ Tribastone, M.; Mayer, P.; Wirsing, M. (2010). "Performance Prediction of Service-Oriented Systems with Layered Queueing Networks". Leveraging Applications of Formal Methods, Verification, and Validation (PDF). LNCS. 6416. p. 51. doi:10.1007/978-3-642-16561-0_12. ISBN 978-3-642-16560-3.
↑ Tribastone, M. (2013). "A Fluid Model for Layered Queueing Networks" (PDF). IEEE Transactions on Software Engineering. 39 (6): 744–756. doi:10.1109/TSE.2012.66.

Queueing theory

Single queueing nodes	D/M/1 queue M/D/1 queue M/D/c queue M/M/1 queue Burke's theorem M/M/c queue M/M/∞ queue M/G/1 queue Pollaczek–Khinchine formula Matrix analytic method M/G/k queue G/M/1 queue G/G/1 queue Kingman's formula Lindley equation Fork–join queue Bulk queue

Arrival processes	Poisson process Markovian arrival process Rational arrival process

Queueing networks	Jackson network Traffic equations Gordon–Newell theorem Mean value analysis Buzen's algorithm Kelly network G-network BCMP network

Service policies	FIFO LIFO Processor sharing Round-robin Shortest job first Shortest remaining time

Key concepts	Continuous-time Markov chain Kendall's notation Little's law Product-form solution Balance equation Quasireversibility Flow-equivalent server method Arrival theorem Decomposition method Beneš method

Limit theorems	Fluid limit Mean field theory Heavy traffic approximation Reflected Brownian motion

Extensions	Fluid queue Layered queueing network Polling system Adversarial queueing network Loss network Retrial queue

Information systems	Data buffer Erlang (unit) Erlang distribution Flow control (data) Message queue Network congestion Network scheduler Pipeline (software) Quality of service Scheduling (computing) Teletraffic engineering

Category

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