  We consider strategic arrivals to a FCFS service system that starts service
at a fixed time and has to serve a fixed number of customers, e.g., an airplane
boarding system. Arriving early induces a higher waiting cost (waiting before
service begins) while arriving late induces a cost because earlier arrivals
take the better seats. We first consider arrivals of heterogeneous customers
that choose arrival times to minimize the weighted sum of waiting cost and and
cost due to expected number of predecessors. We characterize the unique Nash
equilibria for this system.
  Next, we consider a system offering L levels of priority service with a FCFS
queue for each priority level. Higher priorities are charged higher admission
prices. Customers make two choices - time of arrival and priority of service.
We show that the Nash equilibrium corresponds to the customer types being
divided into L intervals and customers belonging to each interval choosing the
same priority level. We further analyze the net revenue to the server and
consider revenue maximizing strategies - number of priority levels and pricing.
Numerical results show that with only three queues the server can attain near
maximum revenue.
