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picture1_Analysis Ppt 75536 | Dss L8


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File: Analysis Ppt 75536 | Dss L8
overview i what is queuing queuing theory why is it an important tool examples of different queuing systems components of a queuing system the exponential distribution queuing stochastic processes some ...

icon picture PPTX Filetype Power Point PPTX | Posted on 02 Sep 2022 | 3 years ago
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    Overview (I)
     •   What is queuing/ queuing theory?
          – Why is it an important tool?
          – Examples of different queuing systems
     •   Components of a queuing system
     •   The exponential distribution & queuing
     •   Stochastic processes
          – Some definitions
          – The Poisson process
     •   Terminology and notation
     •   Little’s formula
     •   Birth and Death Processes
                                                                                                  2
  Overview (II)
     • Important queuing models with FIFO dis-
       cipline
        – The M/M/1 model
        – The M/M/c model
        – The M/M/c/K model (limited queuing capacity)
        – The M/M/c//N model (limited calling popula-
         tion)
     • Priority-discipline queuing models
     • Application of Queuing Theory to system 
       design and decision making
                                                    3
   Overview (III)
   • Simulation – What is that?
      – Why is it an important tool?
   • Building a simulation model
      – Discrete event simulation
   • Structure of a BPD simulation project
   • Model verification and validation
   • Example – Simulation of a M/M/1 
     Queue
                                                        4
  What is Queuing Theory?
  • Mathematical analysis of queues and waiting 
    times in stochastic systems.
     – Used extensively to analyze production and servic
      e processes exhibiting random    variability in mar
      ket demand (arrival times) and service times.
  • Queues arise when the short term demand fo
    r service exceeds the capacity
     – Most often caused by random variation in service t
      imes and the times between customer arrivals.
     –                                          5
      If long term demand for service > capacity the qu
      eue will explode!
   Why is Queuing Analysis Im-
   portant?
   •   Capacity problems are very common in industry and 
       one of the main drivers of process redesign
        – Need to balance the cost of increased capacity against the 
          gains of increased productivity and service
   •   Queuing and waiting time analysis is particularly im
       portant in service systems
        – Large costs of waiting and of lost sales due to waiting
       Prototype Example – ER at County Hos
       pital
   •   Patients arrive by ambulance or by their own accord
   •   One doctor is always on duty                                               6
   •   More and more patients seeks help  longer waiting 
       times
   Question: Should another MD position be insta
       ted?
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...Overview i what is queuing theory why it an important tool examples of different systems components a system the exponential distribution stochastic processes some definitions poisson process terminology and notation little s formula birth death ii models with fifo dis cipline m model c k limited capacity n calling popula tion priority discipline application to design decision making iii simulation that building discrete event structure bpd project verification validation example queue mathematical analysis queues waiting times in used extensively analyze production servic e exhibiting random variability mar ket demand arrival service arise when short term fo r exceeds most often caused by variation t imes between customer arrivals if long for qu eue will explode im portant problems are very common industry one main drivers redesign need balance cost increased against gains productivity time particularly large costs lost sales due prototype er at county hos pital patients arrive ambula...

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