Plot the number in the system for exponential arrivals $/$ exponential service $/1$ server $($M$/$M$/1)$ and exponential arrivals $/$ deterministic service times $/1$ server $($M$/$D$/1)$ on the same graph as a function of utilization. You can use excel. Both formulas are simple. What are the policy implications of this graph.

What is the maximum reasonable utilization for a manufacturing system using the above graph.

What is the relationship between lead time and utilization? Please use Littles law and the graph in question $1.$

You have exponential arrivals and service times for a single machine system. The customers arrive at a rate of $9$ per hour and are serviced at a rate of $10$ per hour. What is the average time in system, wait time in queue, number in system and number in queue.

You have an arrival rate of $4$ per hour and a service rate of $4$ per hour at an oil change location. You have one machine $($changing station$).$ Customers will not wait if more than one customer is in line. You make $$10$ per oil change. You can increase your processing time to $6$ per hour by buying new equipment. The equipment upgrade costs $30,000.$ Should you buy the new equipment. Your center is open $40$ hours per week.

For the prior question, would the lower wait times and less balking potentially increase the department. Please discuss the impact. Is it easy to quantify this factor in the decision making?

Look up $3$ approximations for G$/$G$/1$ queue.

Look up and discuss the equations for m$/$m$/$n queue $($exponential arrivals $/$ exponential service $/$ m servers$).$