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slotted aloha probability problem

 
 
Reply Sun 28 Apr, 2013 03:09 pm
Hello.
I'd be very glad if someone could help me with the following question.

607 stations divided into two sets. The first set contains 100 stations, whose maximal distance is 1,000 km, and the second set contains the remaining stations, whose maximal distance is also 1,000 km. Each set will communicate between its stations using slotted ALOHA (bandwidth =100kbps, frame = 2000 bits) and a diff erent frequency. Frames that need sending between the first set to the second (or the other way around), will be sent via a special station which happens to be on both sets (and has inf inite memory). These frames will be sent once to the special station, which will then send it on the second network. Assuming all stations introduce frames with the same probability, and that the recipient is also distributed with equal probability among all stations, what is the throughput of the new
system?

Throughput S is defined as : S = GP
where G is transmission-attempts per slot-time(this I think I can find) and P is the probability of successful transmission of a frame in a network.
The problem for me is to define P for the given system. Because , as far as i see, there are three cases: frame might pass within first set, frame might pass within second set and frame might pass between sets.
I tried to define P using conditional probability but lost my way a bit.

Will be grateful for any help.
Thanks .
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markr
 
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Reply Sun 28 Apr, 2013 08:33 pm
@mynetwork,
I'm thinking it's something like (but not necessarily exactly) this:
Assuming P1 is the probability of a success in the first set, and P2 is the probability of a success in the second set:

(100*99*P1 + 507*506*P2 + 100*507*P1*P2 + 507*100*P2*P1) / (607*606)

Issues:
- Is the special station a 608th station?
- Does it only relay frames?
- Does it introduce frames with the same probability as the other stations?
- Are frames that pass between sets considered two frames or one for purposes of determining probability of success?
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