Pierre, the owner of the famous restaurant ``Chez Pierre'' wants to simulate the flow of customers through his restaurant. Based on the simulation results, Pierre wants to, if necessary, make some changes to his restaurant.
Empirical study taught Pierre that customers typically arrive in groups of 1, 2, 3, or 4 customer with relative probabilities of 10%, 50%, 20% and 20%. The distribution of interarrival times between subsequent groups is exponential with an average of 5 minutes.
``Chez Pierre'' currently has 10 small tables and at each table, there is room for 2 customers. Tables can be joined to serve parties of more than 2 customers. When a group of hungry customers arrives, they have to wait until they get the undivided attention of Pierre who will seat them, if tables are available. If 10 groups of customers are already queueing, a new arriving group will find another restaurant.
Pierry is rather stingy and does not only receive incoming customers, but also acts as cashier.
If no customers are waiting to be seated, Pierre will go to the cash register. If customers are waiting to be seated, Pierre -who is shortsighted- tries to seat the first group of waiting customers. This, without taking into account the fact that this may block other groups of customers. It is namely possible that though there is no seating space for the first group of customers (as it is too large), one of the other waiting groups could be seated.
In the exclusive restaurant Chez Pierre, it is out of the question that more than one group would be put at the same table.
The time Pierre needs to re-arrange tables and seat a group of customers is uniformly distributed between 1 and 3 minutes.
When a group is seated, Pierre goes to the cash register while the group of customers waits uniformly distributed between 20 and 30 minutes to order and be served (taking customers' orders and serving is done by waiters -not by Pierre- who are not explicitly modelled here). The time to eat is uniformly distributed over 1h+-15min.
After seating the group, Pierre will serve all customers waiting to pay at the counter. This takes uniformly from 0.5 to 1 minute per group.
If there are no more waiting customers, Pierre looks for 15s at the proceeds of the evening. Then, he again waits for arriving customers.