1. Consider a single channel queuing system with an infinite population, Poisson distributed arrivals and exponential departures. The mean arrivals are 15 units per period and mean departures are 22 units per period. Find the probability of greater than 4 units in the system. Express your answer as a percentage.
2. Consider an infinite population single channel queuing system with Poisson arrivals and exponential departures. The service level objective has been set such that there is less than a 48.15% chance that there will be one or more units in the system. Find the mean departure rate for a mean arrival rate of 38 units per period.
3. Consider an infinite population, single channel queuing system with Poisson arrivals and exponential departures. The arrival rate is 44 units per period, and the average number of units in the system is 9. Find the required departure rate.
4. Consider an infinite population, single channel queuing system with Poisson arrival distribution and exponential departure distribution. The arrival rate is 50 units per period, the waiting cost is is 4.25 dollars per period, and the facility cost is is 6.2 dollars per unit per period. Please find the minimum cost service rate.