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Queueing theory
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== Service disciplines == Various scheduling policies can be used at queueing nodes: ; [[FIFO (computing and electronics)|First in, first out]]: [[File:Fifo queue.png|thumb|First in first out (FIFO) queue example]] Also called ''first-come, first-served'' (FCFS),<ref name="Manuel">{{cite book|last1=Manuel|first1=Laguna|title=Business Process Modeling, Simulation and Design|date=2011|publisher=Pearson Education India|isbn=978-81-317-6135-9|page=178|url=https://books.google.com/books?id=d-V8c8YRJikC&q=%22First-come%2C+first-served%22+business&pg=PA178|access-date=6 October 2017|language=en}}</ref> this principle states that customers are served one at a time and that the customer that has been waiting the longest is served first.<ref name="penttinen">Penttinen A., ''Chapter 8 – Queueing Systems'', Lecture Notes: S-38.145 - Introduction to Teletraffic Theory.</ref> ; [[LIFO (computing)|Last in, first out]]: This principle also serves customers one at a time, but the customer with the shortest [[Mean sojourn time|waiting time]] will be served first.<ref name="penttinen"/> Also known as a [[Stack (data structure)|stack]]. ; [[Processor sharing]]: Service capacity is shared equally between customers.<ref name="penttinen"/> ; Priority: Customers with high priority are served first.<ref name="penttinen"/> Priority queues can be of two types: ''non-preemptive'' (where a job in service cannot be interrupted) and ''preemptive'' (where a job in service can be interrupted by a higher-priority job). No work is lost in either model.<ref>{{Cite book | last1 = Harchol-Balter | first1 = M.|author1-link=Mor Harchol-Balter | chapter = Scheduling: Non-Preemptive, Size-Based Policies | doi = 10.1017/CBO9781139226424.039 | title = Performance Modeling and Design of Computer Systems | pages = 499β507 | year = 2012 | isbn = 978-1-139-22642-4 }}</ref> ; [[Shortest job first]]: The next job to be served is the one with the smallest size.<ref>{{cite book|author1=Andrew S. Tanenbaum|author2=Herbert Bos|title=Modern Operating Systems|url=https://books.google.com/books?id=9gqnngEACAAJ|year=2015|publisher=Pearson|isbn=978-0-13-359162-0}}</ref> ; Preemptive shortest job first: The next job to be served is the one with the smallest original size.<ref>{{Cite book | last1 = Harchol-Balter | first1 = M. |author1-link=Mor Harchol-Balter| chapter = Scheduling: Preemptive, Size-Based Policies | doi = 10.1017/CBO9781139226424.040 | title = Performance Modeling and Design of Computer Systems | pages = 508β517 | year = 2012 | isbn = 978-1-139-22642-4 }}</ref> ; [[Shortest remaining processing time]]: The next job to serve is the one with the smallest remaining processing requirement.<ref>{{Cite book | last1 = Harchol-Balter | first1 = M.|author1-link=Mor Harchol-Balter | chapter = Scheduling: SRPT and Fairness | doi = 10.1017/CBO9781139226424.041 | title = Performance Modeling and Design of Computer Systems | pages = 518β530 | year = 2012 | isbn = 978-1-139-22642-4 }}</ref> ; Service facility * Single server: customers line up and there is only one server * Several parallel servers (single queue): customers line up and there are several servers * Several parallel servers (several queues): there are many counters and customers can decide for which to queue ; Unreliable server Server failures occur according to a stochastic (random) process (usually Poisson) and are followed by setup periods during which the server is unavailable. The interrupted customer remains in the service area until server is fixed.<ref>{{Cite journal | last1 = Dimitriou | first1 = I. | title = A Multiclass Retrial System With Coupled Orbits And Service Interruptions: Verification of Stability Conditions | journal = Proceedings of FRUCT 24 | volume = 7 | pages = 75β82 | year = 2019}}</ref> ; Customer waiting behavior * Balking: customers decide not to join the queue if it is too long * Jockeying: customers switch between queues if they think they will get served faster by doing so * Reneging: customers leave the queue if they have waited too long for service Arriving customers not served (either due to the queue having no buffer, or due to balking or reneging by the customer) are also known as ''dropouts''. The average rate of dropouts is a significant parameter describing a queue.
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