Ipswich has two ambulances. Ambulance 1 is based at the local college and ambulance 2 is based downtown. If a request for an ambulance comes from the local college, the college-based ambulance is sent if it is available. Otherwise, the downtown-based ambulance is sent if it is available. If no ambulance is available, the call is assumed to be lost to the system. If a request for an ambulance comes from anywhere else in the town, the downtown-based ambulance is sent if it is available. Otherwise, the college-based ambulance is sent if it is available. If no ambulance is available, the call is considered lost to the system. The time between calls is exponentially distributed. An average of 3 calls per hour are received from the college and an average of 4 calls per hour are received from the rest of the town. The average time (exponentially distributed) it takes an ambulance to respond to a call and be ready to respond to another call is shown in the following table.
Table
|
Ambulance comes from
|
Ambulance goes to
|
|
College
|
Non-college
|
|
College
|
4 minutes
|
7 minutes
|
|
Downtown
|
5 minutes
|
4 minutes
|
i) What fraction of the time is the downtown ambulance busy?
ii) What fraction of the time is the college ambulance busy?
iii) What fraction of all calls will be lost to the system?
iv) On the average, who waits longer for an ambulance, a college student or a town person?