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# 107.939 queueing theory This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2025S 2024S 2023S 2022S 2021S 2020S 2019S 2018S 2017S 2016S 2015S 2014S 2013S 2011W 2010W 2009W 2008W 2006W 2005W 2004W 2003W 2002W 2001W 2000W 1999W 1998W 1997W 1996W 1995W 1995S 1994S 1992W 1990W

2023S, VO, 2.0h, 3.0EC, to be held in blocked form

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to

• list and interpret the elements of a queueing model,
• define Kendalls notation,
• state the recursion for waiting times,
• state conditions for the stability in the G/G/1 model framework,
• cite Little's result,
• analyze the elementary queues M/M/1, M/M/m and M/M/m/m,
• apply the method of embedded Markov chain to M/G/1 and G/M/s queues,
• describe the spectral decomposition method for G/G/1 queues,
• provide estimates and approximations for queueing models,
• apply the elementary queues and approximations for queueing models in areas such as
computer science, financial mathematics or operations research.

## Subject of course

Introduction to the queueing theory, Kendall's notation, recursion for waiting times, stability, Little's law, elementary queueing theory including birth–death process and M/M/1, M/M/m as well as M/M/m/m queues, analysis methods and stationary distributions for M/G/1, G/M/1, G/G/1 queues, bounds, heavy traffic approximation, diffusion approximation.

Lecture

Oral

## Course dates

DayTimeDateLocationDescription
Thu11:00 - 14:0002.03.2023 - 27.04.2023Sem.R. DA grün 06B Queueing theory
queueing theory - Single appointments
DayDateTimeLocationDescription
Thu02.03.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Thu09.03.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Thu16.03.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Thu23.03.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Thu30.03.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Thu20.04.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Thu27.04.202311:00 - 14:00Sem.R. DA grün 06B Queueing theory
Course is held blocked

oral exam

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Fri10:00 - 11:3025.10.2024 Freihaus DA06B19oral15.10.2024 14:00 - 22.10.2024 23:59TISSWT_Prüfung
Thu08:30 - 09:3006.03.2025 DA06B19oral04.03.2025 12:00 - 05.03.2025 23:59TISSWT_Prüfung
Tue10:00 - 12:0003.06.2025 oral28.05.2025 17:00 - 02.06.2025 23:59TISSWT_Prüfung

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Not specified
860 GW Optional Courses - Technical Mathematics Not specified

## Literature

Recommended literature: "L. Kleinrock, Queueing Systems, Vol. I: Theory"

## Previous knowledge

probability theory and stochastic processes

## Language

if required in English