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Queueing Theory and its ApplicationsA Personal View
ICAI 2010, Eger, Hungary27 ‐ 30 January, 2010
János SztrikUniversity of Debrecen, Debrecen, Hungary
http://irh.inf.unideb.hu/user/jsztrik
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Outline
g Origin of Queueing Theory
g Classifications of Queueing Systems
g Applications
g Solution Methods
g Basic Formulas and Laws
g Recent Developments
g Hungarian Contributions
g References
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Origin of Queueing Theory
Agner Krarup Erlang, 1878‐1929
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g "The Theory of Probabilities and Telephone Conversations", Nyt Tidsskriftfor Matematik B, vol 20, 1909.
g "Solution of some Problems in the Theory of Probabilities of Significancein Automatic Telephone Exchanges", Elektrotkeknikeren, vol 13, 1917.
g "The life and works of A.K. Erlang", E. Brockmeyer, H.L. Halstrom and ArnsJensen, Copenhagen: The Copenhagen Telephone Company, 1948.
Queueing Theory Homepage
http://web2.uwindsor.ca/math/hlynka/queue.html
Murphy’s Law of Queue
g If you change queues, the one you have left will start to movefaster than the one you are in now.
g Your queue always goes the slowest
g Whatever queue you join, no matter how short it looks, willalways take the longest for you to get served.
Google search for “Queueing Theory “: 188 000
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Applications
g Telephony
g Manufacturing
g Inventories
g Dams
g Supermarkets
g Computer and Communication Systems
g Call Centers
g Infocommunication Networks
g Hospitals
g Many others
Kendall’s Notation
David G. Kendall, 1918‐2007
A/B/c/K/m/Z7
Performance Metrics
g Utilizations
g Mean Number of Customers in the System / Queue
g Mean Response / Waiting Time
g Mean Busy Period Length of the Server
g Distribution of Response / Waiting Time
g Distribution of the Busy Period
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Solution Methodologies
g Analytical
g Numerical
g Asymptotic
g Simulation
g Tools
Erlang Loss Formulas, M/G/c/c Systems
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Pollaczek‐Khintchine Formulas, M/G/1 Systems
Felix Pollachek, 1892‐1981 Alexander Y. Khintchine, 1894‐1959
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Mean Value Formulas
Transform Formulas
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Little’s Law
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Recent Developments
Boris Vladimirovich Gnedenko, 1912‐1995
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Recent Developments
Leonard Kleinrock, 1934 ‐
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Hot Topics
22nd International Teletraffic Congress
September 7‐9, 2010, Amsterdam, The Netherlands
• Performance of wireless/wired networks• Business models for QoS• Performance and reliability tradeoffs• Performance models for voice, video, data and P2P applications• Scheduling algorithms• Simulation methods and tools
Madrid Conference, 2010
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Hungarian Contributions
Lajos Takács, 1924 ‐
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Hungarian Contributions
g Eötvös Loránd University ( A. Benczúr, L. Lakatos, L. Szeidl )
g Budapest University of Technology and Economics( L. Györfi, M. Telek, S. Molnár )
g University of Debrecen ( J. Tomkó, M. Arató, B. Almási, A. Kuki, J. Sztrik )
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MyMost Cited Paper, 22 citations
On the finite‐source QueueEuropean Journal of Operational Research 20 (1985) 261‐268
Steady‐State Probabilities
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Performance Metrics
Utilizations
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Mean Values
Java Applets and Information
g http://irh.inf.unideb.hu/user/jsztrik/education/09/index.html
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http://irh.inf.unideb.hu/user/jsztrik/
Bibliography