Lou Guzik  Telecom 2062  Fall 96 Homework #7 Due 11/12/96

1. A company has two leased overseas telephones lines
 connecting it's Pittsburgh and Paris offices. One line is
 dedicated to fax transmission, the other line is shared by
 telephones and fax machine. Documents to be faxed  have a
 exponentially distributed interarrival time with mean rate
 10 jobs per hour.  The time to transmit a fax is Poisson
 distributed with a mean of 5 minutes. The Fax machine with
 a dedicated line can store up to 2 faxes for transmission in
 memory (including the one currently in transmission). When
 the main fax machine is full, jobs are routed to the fax
 machine connected to the shared line and the job will wait
 until the machine is free.  The fax machine on the shared
 line can only begin transmision when the shared line is not
 busy with a phone call. Phone calls arrive to theshared line
 with an exponentially distributed interarrival timewith a
 mean of 8  minutes and the length of the calls are
 exponentially distributed with a mean of 4 minutes. A phone
 call arriving to a busy line is blocked and lost.

 Simulate the system and construct a 90% confidence interval
 with relative precision of 10% on the average number in the
 main fax queue. Also determine a 90% confidence interval on
 the utilization of the shared phone line, the percentage of
 blocked phone calls and the average number of jobs in the
 alternate fax machine. Compare the relative precision of
 these confidence intervals - why are they different?  Turn
 in all programs, calculations, etc... anything you want
 credit for.



2. For the random number generator below
(a) Compute Z_i and U_i for enough values of i to cover an
 entire cycle
   
(b) Compute the mean value of U_i across 1 cycle

    Z_i = (5Z_(i-1)  + 6)(mod 16) with Z_0 = 3