Delivery-Date: Sun Sep 21 09:21:03 2008
Message-Id: <200809211623.m8LGNDBv000979@bourbon.usc.edu>
To: cs551@merlot.usc.edu
Subject: Re: cs551-warmup#2
Date: Sun, 21 Sep 2008 09:23:13 -0700
From: Bill Cheng <william@bourbon.usc.edu>

Someone wrote:

  > Can you kindly explain how shud we calculate the avg no. of customers in Q1
  > using measured quantities like enqueue_time,dequeue_time of each customer
  > and no. of customres in queue(every time a customer is added ro removed from
  > the queue).

You should take a look at the last slide of lecture 5.  As
I've mentioned in class, you need to calculate the area under
the curve divide by the total time.  There is more than one
way to calculate the area under the curve.  Here's one way
I've mentioned in class.

Let's use the last timeline as an example.  You can draw
vertical lines at each transition and divide the timeline
into many regions:

  In the first region, there was 0 customer in Q1.
  In the 2nd region, there was 1 customer in Q1.
  In the 3rd region, there were 2 customers in Q1.
  In the 4th region, there was 1 customer in Q1.
  In the 5th region, there was 0 customer in Q1.
  In the 6th region, there was 1 customer in Q1.
  In the 7th region, there were 2 customers in Q1.
  In the 8th region, there were 3 customers in Q1.
  and so on

Let V1 be the time interval length of region 1, V2 be the
time interval length of region 2, V3 be the time interval
length of revion 3, and so on.  The total aread under the
curve is just (sum of (Vi * Hi)) where Hi is the height
of region i.

Your Q1 should know the values of Vi and Hi and it can
keep a running sum.  You should figure out the details.
--
Bill Cheng // bill.cheng@usc.edu <URL:http://merlot.usc.edu/william/usc/>