# Queueing System

Case 2: Analyzing Disaster Situations at Tech (50%)
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 gas mains explosion or 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
4Tech 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 analysing various queueing models, as follows. (Unless otherwise stated, arrivals are Poisson distributed, and service times are exponentially distributed).
A. First, consider a single-server queueing 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. Determine how long, on average, victims have to wait at the staging area. Next, assume that the distribution of service times is undefined, with a mean of 4.5 minutes and a standard deviation of 5 minutes. Determine how the average wait changes.
B. Next,consideramultiple-servermodelinwhichthereareeightemergency vehicles available for transporting victims to the hospitals, and the mean time required for a vehicle to pick up and transport a victim to hospital is 20 minutes. (Assume the same arrival rate as in part A). Compute the average number of victims waiting for transportation, the average time they wait, and the average time for a victim to reach hospital.
C. Forthemultiple-servermodelinPartBnowassumethatthereareafinite number of victims, 18. Determine the same measures for this situation.
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. Compute the average number of victims waiting for transportation, the average time they wait, and the average time for a victim to reach hospital.
E. Next, consider a single hospital, Montgomery Regional, which in an emergency disaster situation has five 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. Compute the average number of victims waiting for treatment, the average time they wait, and the average time until treatment is complete.
F. For the multiple-server model in part E, now assume that there a finite number of victims, 23. Determine the same measures for this situation.
I only need an Excel file with all solutions. I just need a calculation and queueing models (E.g M/M/1).

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