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One of the difficulties about probability is realizing when two different looking problems are…


One of the difficulties about probability is realizing when two different looking problems are the same, in this case dealing cocaine and fighting fires. In Problem 2.19, calls to a fire station arrive according to a Poisson process with rate 0.5 per hour, and the time required to respond to a call, return to the station, and get ready to respond to the next call is uniformly distributed between 1/2 and 1 hour. If a new call comes before the Dryden fire department is ready to respond, the Ithaca fire department is asked to respond. What fraction of calls must be handled by the Ithaca fire department

Problem 2.19

Calls to the Dryden fire department arrive according to a Poisson process with rate 0.5 per hour. Suppose that the time required to respond to a call, return to the station, and get ready to respond to the next call is uniformly distributed between 1/2 and 1 hour. If a new call comes before the Dryden fire department is ready to respond, the Ithaca fire department is asked to respond. Suppose that the Dryden fire department is ready to respond now. Find the probability distribution for the number of calls they will handle before they have to ask for help from the Ithaca fire department.