On average, six nurses work per shift at a community hospital emergency service. Patients arrive at the emergency service according to a Poisson distribution with a mean of six per hour. Service time is exponential, with a mean of thirty minutes per patient. Assume that there is one patient per nurse. Find each of the following performance measures.
A. Compute the average number of patients in queue
B. Compute the probability of zero units in the system.
C. Compute the average waiting time for patients in a queue and in the system
D. Compute the system utilization time.
E. On the weekend, emergency service averages four patients per hour, and the service rate is expected to be forty minutes. How many nurses will be needed to achieve an average time in line of forty minutes or less?