Barber simulation

A single-chair barbershop. From when it opens in the morning until it closes, customers arrive at random times. If the barber is not busy, he serves a customer immediately, otherwise they must wait in a queue (FIFO order). The time needed to serve each customer is also random.

The entities are:

• Server (idle or busy)
• customer (arrival and service times)

The events:

• customer arrives
• customer departs

The arrival and departure events encapsulate everything we care to know about a customer, so we don't need to track customers explicitly.

System state:

• Simulation time (starts at 0)
• event list (starts empty)
• server status (initially idle)
• customer queue (initial value empty)

The first two elements are properly part of the simulation program, rather than the system we're modelling. The last two are part of the barbershop simulation. There is always a single event list, since it represents the flow of time and all events end up there. There may be multiple event lists, depending on the system we're modelling.

Initialization:

• Schedule the first customer

Arrival event:

• If the server is idle, start service immediately (change server status to busy and schedule an end of service event). Otherwise the customer waits in queue (in some models they may ``balk'' and decide they don't have time to wait).
• Schedule the next customer arrival at random, given the desired distribution (more about this later).

Departure event:

• Change server status to idle
• If the customer queue is not empty, start service on the first customer in the queue (change the server status back to busy and schedule an end of service event).

Statistics

• Average delay: keep track of how long each customer waits (even if the waiting time is zero). At the end of the simulation, compute the average waiting time per customer (assuming >= 1 customer).
• Average server utilization: the fraction of the total time that the server was busy. Add up all the time the server was busy, divided by the total simulation time.
• Average number of customers in the queue: this could be a weighted sum: 0*(fraction of time the queue is empty) + 1*(fraction of time the queue has 1 person) + 2*(fraction of time the queue has 2 people) + ...
• To compute all of these statistics, we need to keep track of the following additional quantities during the simulation (the total simulation time is already stored in the system state): the total number of customers for the duration of the simulation, the total time spent waiting for all customers, the total amount of time that the server was busy, and the weighted sum of the number of customers waiting in the queue.
• At the end of the simulation, the server finishes working the the current request (if any), ignores anyone in the waiting list, except to record the size of the waiting list. No further statistics about the length of delay are collected, since this is unknowable (everybody goes home).