M/D/1 queue: Difference between revisions

Revision as of 20:20, 19 December 2023

Latest revision as of 14:59, 20 December 2023

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==Application==

Includes applications in wide area [[network planning and design|network design]],<ref>{{cite journal|last1=Kotobi|first1=Khashayar|last2=Bilén|first2=Sven G.|title=Spectrum sharing via hybrid cognitive players evaluated by an M/D/1 queuing model|journal=EURASIP Journal on Wireless Communications and Networking|volume=2017|date=2017|pages=85 |doi=10.1186/s13638-017-0871-x|url=https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/s13638-017-0871-x |access-date=2017-05-05|doi-access=free}}</ref> where a single central processor to read the headers of the packets arriving in exponential fashion, then computes the next adapter to which each packet should go and dispatch the packets accordingly. Here the service time is the processing of the packet header and cyclic redundancy check, which are independent of the length of each arriving packets. Hence, it can be modeled as a M/D/1 queue.<ref>{{Cite book|title=Wide Area Network Design: Concepts and Tools for optimization.|last=Chan|first=Robert S.|publisher=Morgan Kaufmann Publishers Inc.|year=1998|isbn=1-55860-458-8|pages=319}}</ref>

== Software ==

=== Ciw ===

Ciw is a Python package for simulating queueing networks.<ref>{{Cite web |title=Welcome to Ciw’s documentation! — Ciw 3.1.0 documentation |url=https://ciw.readthedocs.io/en/latest/ |access-date=2023-12-19 |website=ciw.readthedocs.io}}</ref> A M/D/1 queue can be implemented and simulated using Ciw in the following way.<syntaxhighlight lang="python3">

import ciw

ciw.seed(2018)

ARRIVAL_TIME = 1

SERVICE_TIME = 1 / 2

HORIZON = 365

network = ciw.create_network(

arrival_distributions = [ciw.dists.Exponential(ARRIVAL_TIME)],

service_distributions = [ciw.dists.Deterministic(SERVICE_TIME)],

number_of_servers = [1]

)

simulation = ciw.Simulation(network)

simulation.simulate_until_max_time(HORIZON)

records = simulation.get_all_records()

</syntaxhighlight>

==References==