Consider a single-server queueing system for which the interarrival times are independent and identically distributed. A customer who arrives and finds the server idle enters service immediately. The service time of the server is again an independent and identically distributed random variable. A customer who enters and finds the server busy joins the end of a single queue. Upon completing service for a customer, the server chooses a customer from the queue in a first-in first-out (FIFO) manner.
The MM1 examples illustrated in this package start with a simulator in "empty-and-idle" state. At t=0 we begin with waiting
for the first arrival which will occur after the first arrival time. We simulate the system until a fixed number of customers (n)
have completed their delays in queue. To measure the performance of this system, we will look at estimates of 3 quantities.
First we will estimate the expected average delay in queue of the n customers completing their service during the simulation.
This time delay is represented as d(n).
From a system based viewpoint we are going to look at the average number of
entities in the queue q(n) and to the average utilization of the server u(n).