Consider a single channel queue system (a bank with one teller, a shop with one drill press, a switchboard with one attendant, etc.). Entities (customers, order for drilled part, phone calls, etc.) arrive to the system with a mean rate of 12 per hour following a Poisson distribution. There is one FIFO waiting line (queue) for the entities to wait when service is not immediately available. There is no balking and no reneging. Service time is exponential with a mean of 4 minutes.

We are interested in determine the average waiting time in the queue and resource utilization over a time horizon.

Perform a hand simulation of this process for 20 minutes using the following Interarrival times and service times:

Interarrival Times: 1, 2, 1, 3, 4, 7, 4, 1, 5, 10

Service Times: 5, 7, 2, 4, 8, 3, 1, 4

Define your variables (what may be needed at time zero). Your first arrival occurs based on the samples given for the Interarrival Times. Draw a graph of the resource utilization in addition to the algebraic computation.