[net.cse] Humorous Queuing Theory Problem

libes@nbs-amrf.UUCP (07/25/84)

Encountering problems like this make being a CS student all worth it.  This
problem actually appears in "Digital Computer Simulation", Chapter 3.

Xaviera operates an entertainment facility in Nevada.  Xaviera's standard
fee is $100.  Her employees perform their services for $50, $20 of which is
returned to Xaviera to cover operating expenses.  For all parts of this
problem, assume an 8-hour work night.  Model Xaviera's receipts and the
level of service offered her customers under the following alternative
conditions:

a.  Xaviera is the only server.  The average customer interarrival rate is
    10 minutes, exponentially distributed.  Determine the effects of the
    following service times:
    1.	Constant 15 minutes.
    2.	10 to 20 minutes, uniformly distributed.
    3.	Average of 15 minutes, exponentially distributed.

b.  Assume a second server is hired, and each server performs with a
    service time of 10 to 20 minutes, uniformly distributed.  What is the
    effect on service and profits?

c.  Assume that (within 10 minutes of) every hour, a customer arrives who
    requires both servers simultaneously.  Measure the impact of service.

d.  Suppose a third server is hired, who serves customers in an average of
    12 minutes (exponentially distributed).  What is the effect on business
    if there are separate queues with customers entering the shortest queue?
    Only one queue?

e.  Suppose 60% of the customers want Xaviera; the other 40% have no
    preference.  Investigate profits and queue behavior under these
    circumstances.

f.  If 10% of the customers require service that takes an average of 20
    minutes (exponentially distributed), for a 50% price increment, what is
    the effect on the business?

g.  Assume Xaviera has submitted to pressure from the Equal Employment
    Opportunity Commission to avoid the loss of Federal contracts.  She has
    hired a token male server who spends an average of 15 minutes
    (exponentially distributed) serving each of his customers.  After
    completing a service, he is obliged to rest for 2 hours before he can
    take on another customer.  Include this condition, assuming his
    customers arrive every 1 to 3 hours, uniformly distributed, and will not
    accept any of the other servers.

h.  A parking lot on the premises has a capactiy of 3 cars.  If the lot is
    full, arriving customers take their business elsewhere.  To what extent
    does this affect business?

Don Libes         {allegra,seismo}!umcp-cs!nbs-amrf!libes