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Shear's Insurance Agents

The insurance department at Shear's has two agents, each working at a mean speed of 8 customers per hour. Customers arrive at the insurance desk at a mean rate of one every six minutes and form a single queue. Management feels that some customers are going to find the wait at the desk too long and take their business to Word's, Shear's competitor. In order to reduce the time required by an agent to serve a customer Shear's is contemplating installing one of two minicomputer systems: System A which leases for $18 per day and will increase an agent's efficiency by 25%; or, System B which leases for $23 per day and will increase an agent's efficiency by 50%. Agents work 8-hour days. If Shear's estimates its cost of having a customer in the system at $3 per hour, determine if Shear's should install a new minicomputer system, and if so, which one.

Solution Preview

Please see the attached file

The given problem is regarding an M/M/c queuing model with c = 2.

For an M/M/2 model with arrival rate  and service rate  we have the following characteristics.
If denotes the steady state probability distribution of the model, it can be easily seen that ...

Solution Summary

The expert estimates the costs of having a customer in the systems per hour.

$2.19