Learning Goal: I’m working on a mathematics question and need guidance to help me learn.
St. Michael’s Hospital and Bridgepoint Hospital are in the process of developing an emergency response plan in the event of a major disaster at George Brown College. Disasters can be triggered by a number of event scenarios (i.e. weather, building collapse, fire, dangerous intruder, etc.) The main purpose of this emergency preparedness plan is focused on the transportation of disaster victims from the GBC campus to the two main hospitals in the area (St. Michael’s and Bridgepoint). When a disaster occurs on the GBC campus, vehicles can be dispatched from local fire and ambulance locations, as well as hospitals and police departments where victims are brought to a staging area near the scene and await 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 !.) 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 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, no 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. E. Next, consider a single hospital, S. Michael’s, which in an emergency disaster situation has 5 physicians with supporting staff available. Victims arrive at the hospital on average every 8.5 minutes. It takes an emergency room team, on average, 21 minutes to treat a victim. Determine the average waiting line, the average waiting time, and the average time in the system. F. For the multiple-server model in Part E., now assume that there are a finite number of victims, 23. Determine the average waiting line, the average waiting time, and the average time in the system. G. Which of these waiting line models do you think would be the most useful in analyzing a disaster situation? How do you think some, or all , of the models might be used together to analyze a disaster situation? What other types of waiting line models do you think might be useful in analyzing a disaster situation?
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