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To: cs551@merlot.usc.edu
Subject: Re: CS551: statistics calculation
Date: Fri, 15 Sep 2006 23:46:58 0700
From: william@bourbon.usc.edu
Someone wrote:
> I can understand doing it the queue, since we have actual events
> that come in discrete time.
> there for u can just have the freq of customers in the queue when
> a customer arrives.
>
> The issue with the servers is that there is no discrete time,
> since service time is continuous.
I don't know what you mean by "discrete" and "continuous".
There is no restriction on when a customer can be enqueued or
dequeued from Q1.
> there are no discrete time intervals that the server runs on. the
> server seamlessly works continuously, only stopping when the
> queue is empty.
>
> could you suggest a way to quantify the time as we can in the
> case of the queue.
Here's an example for S1:

1 + ++ ++ ++ ++
        
0 +++++++++++++++> time
0 1 2 3 4 5 6 7
Again, if the simulation ends at 8.315, you can still add up
the area under the curve and divide by 8.315.

Bill Cheng // bill.cheng@usc.edu
 Original Message 
From: william@bourbon.usc.edu
Date: Friday, September 15, 2006 10:51 pm
Subject: Re: CS551: statistics calculation
To: cs551@merlot.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
> >