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Some questions in Queueing Theory

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data
    In$$ M/M/1/FCFS/c/\infty $$
    I don't know what is offered load and effective load.
    Wiki say offered load is equal to the expected number in the system, and I found offered load is equal to the ρ=λ/μ, where λ is the average arrive rate. And the μ is the average service time. And I don't know which one is true , and I can't find the information about effective load.
    Thank you . :^)
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 11, 2013 #2

    Ray Vickson

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    Please clarify: some authors use the notation A/B/C/D?E/F is slightly different order, so you need to tell us what the ##c## stands for. My guess is that you have an infinite calling population but a finite queue capacity; is that correct?

    You need to show your work; it is not enough to just say you don't know what to do. In particluar, if the 'c' means that a total of c customers can be accommodated (one in service and c-1 waiting) then some 'arriving' customers will not enter the system because it is full. In particular, you need to be careful when using such results as ##L = \bar{\lambda} W,## etc.
     
  4. Dec 11, 2013 #3

    haruspex

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    I believe the definition of offered load is mean arrival rate * mean service time, so λ/μ. Looks to me that for a queue of finite capacity the effective load is based on the effective arrival rate, which discounts arrivals when the queue is full. See e.g. http://www.engr.sjsu.edu/udlpms/ISE 265/set4 queuing theory.ppt.
    However, care must be taken in using this. You can't simply treat a queue of limited capacity as being an infinite queue with a reduced offered load.
     
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