question archive The manager of the reservations department for a small commuter airline is trying to determine how many reservations agents she needs to have on duty to answer incoming calls during the busiest part of the day
The manager of the reservations department for a small commuter airline is trying to determine how many reservations agents she needs to have on duty to answer incoming calls during the busiest part of the day
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The manager of the reservations department for a small commuter airline is trying to determine how many reservations agents she needs to have on duty to answer incoming calls during the busiest part of the day. The service times for calls are exponentially distributed with a mean service time of 4 minutes. Telephone calls to the reservations department follow a Poisson arrival process with an average 54 customers per hour.
a. What is the minimum number of agents that would be needed to have the utilization less than one?
b. What is the minimum number of agents that would be needed to assure that the average waiting time is less than 2 minutes?
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Solution
???? = 54, ???? = 15
a. Note that ???? = ????/ ????. In order to make ???? smaller than 1, at least 4 servers are needed.
b. First, calculate c = 4 using Kingman’s equation, and
we get Tq = 7.96
Then calculate c = 5,
we get Tq = 1.27.
So, we need at least 5 servers.
