Assignment #6 for Capacity Planning                                KJC (8/23/01)
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DUE: 12/04 in class

For this assignment you will compare a simulation of an M/M/1 queue with
analytical results.  You will also compare M/M/1 against M/D/1.

Download and build the program mm1_smpl.c from the Christensen tools page.

1) Simulate utilization values ranging from 10% to 98% (say, 10% to 90%
   in steps of 10% and then 90% to 98% in steps of 1%) for a mean service
   rate of 1.0 customers per second.  Plot the utilization versus mean
   customer delay (response time).  Plot also analytical results for
   response time (i.e., as computed using the M/M/1 formulas).  How close
   are the simulation versus analytical results?  What is the cause of
   the difference?  How might the difference be reduced?

2) Change mm1_smpl.c to have deterministic service times (this is now a
   model of an M/D/1 queue, call it md1_smpl.c).  Rerun part (1) above and
   plot the results on the same graph as the M/M/1 results.  Is the response
   time of an M/D/1 less or greater than that of an M/D/1?  Why?  Determine a
   "formula" for the difference in response time between M/M/1 and M/D/1.

HINT #1: Remember that utilization is arrival rate divided by service rate,
         which is the same as service time divided by interarrival time.  So,
         you simply need to set the values of Ta and Ts in mm1_smpl.c to
         achieve the desired utilization and service time.

HINT #2: The program mm1_smpl.c is a simulation.  You need to "tune" the value
         of Te to achieve "reasonable" run times (e.g., several million
         completions which should execute in a few minutes wall clock time
         on a modern PC).  If the simulation "runs too fast", increase Te.
         If the simulation "never finishes", decrease Te.

HINT #3: The "formula" for the difference between M/M/1 and M/D/1 response
         times is trivial (it is a simple relationship).  Look at your notes
         for analytical modeling and maybe you can see something there...

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