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To: cs551@merlot.usc.edu
Subject: Re: CS551: statistics calculation
Date: Fri, 15 Sep 2006 22:51:14 0700
From: william@bourbon.usc.edu
Someone wrote:
> Could you please provide some hint in calculating the average
> number of customers in Q1 (and s1 and s2)? Do we need to consider
> the overlapping time (say customer is in the queue from time 15,
> and customer 2 is in the queue from 27 etc)?
In your example, you can plot the number of customers in Q1
vs. time and it should look like the following:

2 + ++
  
1 + ++ ++
  
0 ++++++++> time
0 1 2 3 4 5 6 7
If simulation ends at time 8, then the average number of
customers at Q1 is the area under the above curve divided by
the total time which is 9/8=1.125.
You can do the same plot with S1 (and S2). The only
difference is that the number of customers at S1 only
goes between 0 and 1.

Bill Cheng // bill.cheng@usc.edu
 Original Message 
From: william@bourbon.usc.edu
Date: Friday, September 8, 2006 2:53 pm
Subject: Re: CS551: statistics calculation
To: cs551@merlot.usc.edu
> Someone wrote:
>
> > Since the poisson distribution only corresponds to only inter
> arrival > times and service times, I'm not sure how to calculate
> the following
> > statistics:
> > Let me know if the following assumptions are correct. And how to
> > calculate 3 & 4.
> > 1. customer drop probability = (number of
> > customers dropped / total number of customers) ?
>
> This is correct.
>
> > 2. average number of customers in Q1 = (number of
> > customers/size of Q1) ?
>
> This is not correct. If 50% of the time Q1 is empty,
> 30% of the time Q1 has 1 customer, and 20% of the time
> Q1 has 2 customers, then the average number of customers
> in Q1 is:
>
> 0.5 * 0 + 0.3 * 1 + 0.2 * 2 = 0.7
>
> > 3. average number of customers at S1 =
> > 4. average number of customers at S2 =
>
> If 60% of the time S1 is empty and 40% of the time
> S1 has 1 customer, then the average number of customers
> at S1 is:
>
> 0.6 * 0 + 0.4 * 1 = 0.4
>
> This is the same as saying the probability that S1
> is busy or the utilization of S1.
> 
> Bill Cheng // bill.cheng@usc.edu
>
>