M/D/c queue: Difference between revisions

Revision as of 20:23, 19 December 2023

Latest revision as of 14:59, 20 December 2023

Line 20:

::<math>\mathbb P(W \leq x) = \sum_{n=0}^{c-1} P_n \sum_{k=1}^m \frac{(-\lambda(x-kD))^{(k+1)c-1-n}}{((K+1)c-1-n)!}e^{\lambda(x-kD)}, \quad mD \leq x <(m+1)D.</math>

== 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/c queue can be implemented and simulated using Ciw in the following way.<syntaxhighlight lang="python3" line="1">

import ciw

ciw.seed(2018)

ARRIVAL_TIME = 1

SERVICE_TIME = 1 / 2

HORIZON = 365

NUM_SERVERS = 2

network = ciw.create_network(

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

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

number_of_servers = [NUM_SERVERS]

)

simulation = ciw.Simulation(network)

simulation.simulate_until_max_time(HORIZON)

records = simulation.get_all_records()

</syntaxhighlight>

==References==