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picture1_Queuing Theory Ppt 75765 | Ch6queue2021


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File: Queuing Theory Ppt 75765 | Ch6queue2021
plan introduction classification of queueing systems little s law single stage queuing systems queuing networks non markovian queueing systems 2 introduction 3 definition of a queueing system customer departure of ...

icon picture PPTX Filetype Power Point PPTX | Posted on 02 Sep 2022 | 3 years ago
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                               Plan
     • Introduction
     • Classification of queueing systems
     • Little's law
     • Single stage queuing systems
     • Queuing networks
     • Non Markovian queueing systems
      
                                                                2
                     Introduction
                                                         3
                 Definition of a queueing system
       Customer                                       Departure of 
       arrivals                                       served customers
                 Departure of impatient 
                 customers
       •  A queueing system can be described as follows:
       "customers arrive for a given service, wait if the service cannot start 
          immediately and leave after being served"
       •  The term "customer" can be men, products, machines, ...
                                                                      4
                     History of queueing theory 
      •  The theory of queueing systems was developed to provide 
         models for forecasting behaviors of systems subject to random 
         demand.
      •  The first problems addressed concerned congestion of 
         telephone traffic (Erlang, "the theory of probabilities and 
         telephone conversations ", 1909)
      •  Erlang observed that a telephone system can be modeled by 
         Poisson customer arrivals and exponentially distributed 
         service times
      •  Molina, Pollaczek, Kolmogorov, Khintchine, Palm, 
         Crommelin followed the track
                                                                           5
                   Interests of queueing systems 
      Queueing theory found numerous applications in:
      – Trafic control (communication networks, air traffic, …)
      – Planing (manufacturing systems, computer programmes, …)
      – Facility dimensioning (factories, ...) 
                                                                            6
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...Plan introduction classification of queueing systems little s law single stage queuing networks non markovian definition a system customer departure arrivals served customers impatient can be described as follows arrive for given service wait if the cannot start immediately and leave after being term men products machines history theory was developed to provide models forecasting behaviors subject random demand first problems addressed concerned congestion telephone traffic erlang probabilities conversations observed that modeled by poisson exponentially distributed times molina pollaczek kolmogorov khintchine palm crommelin followed track interests found numerous applications in trafic control communication air planing manufacturing computer programmes facility dimensioning factories...

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