Reference no: EM133396113

Assignment:

The village of Northlake provides ambulance service to its residents. Calls arrive at the dispatching office according to a Poisson process at an average rate of four per hour. The village has two ambulances on duty. The time it takes an ambulance to complete its services (the time required to drive to a house and take a person to the hospital) is exponentially distributed, with an average time of 12 minutes. (Once the patient is delivered to the hospital, the ambulance can respond to a new call without being at the dispatch site.)

1. On average, how many customers are waiting for the ambulance to be dispatched to their houses?

2. On average, how long does it take from the time a person calls the ambulance dispatcher until he or she is delivered to the hospital?

3. Northlake is adjacent to the village of Eastfork. Eastfork is identical to Northlake in the sense that it provides ambulance service using two ambulances, calls arrive according to a Poisson process at the rate of four per hour, and the average service times have the same distribution as those of Northlake. Northlake and Eastfork are considering a cooperative arrangement whereby all calls from both villages will come to one central dispatch site with four ambulances. Because the site will be on the border between the two villages, the average service time will increase to 15 minutes (exponentially distributed). Compute the average number of customers waiting, and the average time it takes from the moment a person calls the dispatch office until the person arrives at the hospital.