This study comprises a historical review of liver transplants performed in Canada during 2000--2004, and sensitivity analyses to assess the impact of possible changes in the operation of the waitlists. In the first part, overall statistics are reported, and the notable impact that blood type plays in affecting waiting time is discussed. Waiting times and numbers of transplants are also reported by gender, age, and geographic region (waitlist), and statistical analyses of the patient placement and cadaveric donations processes are performed. These analyses establish that the service times of an appropriate queuing model are closely approximated by an exponential distribution. Consequently, the resulting distribution for the waiting time from placement until transplant is well described by a different exponential distribution. The GI/M/1 queuing model is then used to perform a number of sensitivity analyses. The sensitivity analyses attempt to quantify the impact of no change in policy via a lottery system, and likely increases in cadaveric and/or living donor sources that would be needed to bring stability to the system. The results can be used by relevant authorities, together with information on success rates for publicity campaigns and living donor matching campaigns, to assess where further efforts should be made to reduce waiting times.