I've grabbed a queuing question from my operations research textbook (by W. Winston) which I am really struggling with and unfortunately haven't got a solutions manual for. Would really appreciate help in identifying what type of queue it is. I'm leaning towards M/M/2/NPRP/c/infinity, but we didn't cover those at university yet this question has been listed on the review sheet.
Anyway, here is the question:
Smalltown has 2 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 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 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 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 below:
Ambulance from College travelling to College: 4 minutes
Ambulance from College travelling to Noncollege: 7 minutes
Ambulance from Downtown travelling to College: 5 minutes
Ambulance from Downtown travelling to Noncollege: 4 minutes
a) What fraction of the time is the downtown ambulance busy?
b) What fraction of the time is the college ambulance busy?
c) What fraction of all calls will be lost to the system?
d) On average, who waits longer for an ambulance, a college student or a town person?
I'm sure I could answer the questions if I could only work out what type of queue I was looking at. The textbook covers both M/G/s/GD/s/inf queues, or the blocked customers cleared type, where people can get lost in the system, and also covers M/M/s/NPRP/inf/inf queues, where there are different probabilities of someone being served, but this would be a mixture of both, right?
Thanks in advance! And sorry for the long post.