Assignment:
Two area hospitals have jointly initiated several planning projects to determine how effectively their emergency facilities can handle disaster-related situations at nearby Tech University. These disasters could be weather related, such as a tornado, a fire, accidents (such as a gas main explosion or a building collapse), or acts of terrorism. One of these projects has focused on the transport of disaster victims from the Tech campus to the two hospitals in the area, Montgomery Regional and Radford Memorial. When a disaster occurs at Tech, emergency vehicles are dispatched from Tech police, local EMT units, hospitals, and local county and city police departments. Victims are brought to a staging area near the disaster scene and wait for transport to one of the two area hospitals. Aspects of the project analysis include the waiting times victims might experience at the disaster scene for emergency vehicles to transport them to the hospital, and waiting times for treatment once victims arrive at the hospital. The project team is analyzing various waiting line models, as follows. (Unless stated otherwise, arrivals are Poisson distributed, and service times are exponentially distributed.)
a. First, consider a single-server waiting line model in which the available emergency vehicles are considered to be the server. Assume that victims arrive at the staging area ready to be transported to a hospital on average every 7 minutes and that emergency vehicles are plentiful and available to pick up and transport victims every 4.5 minutes. Compute the average waiting time for victims. Next, assume that the distribution of service times is undefined, with a mean of 4.5 minutes and a standard deviation of 5 minutes. Compute the average waiting time for the victims.
b. Next, consider a multiple-server model in which there are eight emergency vehicles available for transporting victims to the hospitals, and the mean time required for a vehicle to pick up and transport a victim to a hospital is 20 minutes. (Assume the same arrival rate as in part a.) Compute the average waiting line, the average waiting time for a victim, and the average time in the system for a victim (waiting and being transported).
c. For the multiple-server model in part b now assume that there are a finite number of victims, 18. Determine the average waiting line, the average waiting time, and the average time in the system.
d. From the two hospitals' perspectives, consider a multiple-server model in which the two hospitals are the servers. The emergency vehicles at the disaster scene constitute a single waiting line, and each driver calls ahead to see which hospital is most likely to admit the victim first, and travels to that hospital. Vehicles arrive at a hospital every 8.5 minutes, on average, and the average service time for the emergency staff to admit and treat a victim is 12 minutes. Determine the average waiting line for victims, the average waiting time, and the average time in the system.