Lecture 10 Collision resolution. Collision resolution

Transcription

1 Lecture 10 Collisio resolutio Collisio resolutio May applicatios ivolve a iquiry over a shared chael, which ca be ivoked for: discovery of eighborig devices i ad hoc etworks, coutig the umber of RFID tags that have a certai property, estimatig the mea value cotaied i a group of sesors etc. Such a iquiry solicits replies from possibly large umber of termials. This ecessitates the usage of algorithms for resolvig batch collisios (coflicts) with ukow coflict multiplicity

2 Collisio resolutio Collisio Resolutio Protocols (CRP) aim at resolvig collisios as soo as they occur. I most versios of these protocols, ew packets that arrive to the system are ihibited from beig trasmitted while the resolutio of collisios is i progress. This esures that if the rate of arrival of ew packets to the system is smaller tha the rate at which collisios ca be resolved (the maximal rate of departig packets), the the system is stable. The basic idea behid these protocols is to exploit i a more sophisticated maer the feedback iformatio that is available to the users i order to cotrol the retrasmissio process, so that collisios are resolved more efficietly ad without chaotic evets Biary tree CRP Basic Biary tree CRP Whe a collisio occurs, i slot k say, all users that are ot ivolved i the collisio wait util the collisio is resolved. The users ivolved i the collisio split radomly ito two subsets, by (for istace) each flippig a coi. The users i the first subset, those that flipped 0, retrasmit i slot k+1 while those that flipped 1 wait util all those that flipped 0 trasmit successfully their packets. If slot k+1 is either idle or cotais a successful trasmissio, the users of the secod subset (those that flipped 1) retrasmit i slot k+. If slot k+1 cotais aother collisio, the the procedure is repeated, i.e., the users whose packets collided i slot k+1 (the collidig users ) flip a coi agai ad operate accordig to the outcome of the coi flippig, ad so o

3 Biary tree protocol B { } Let deote the legth of the CRI whe packets collided ad let B = E B The fractio /B is the effective service rate for the of packets. It ca be show that uder Poisso arrival of rates as log as λ < /B the system is stable Biary tree protocol B is miimized by utilizig balaced coi that is the 0 ad 1 should be selected with equal probability. It ca be show that B α+ 1, α.886 Hece, the maximum throughput of the protocol is 1 λ < e B ad the maximum delay is αλ+ 1 αλ D + 1 ( 1 αλ)

4 Modified Biary tree protocol The biary tree algorithm ca be improved by otig that empty slot is always followed by collisio. This could be avoided by automatically splittig the users after empty slots Modified Biary tree protocol I case of modified Biary tree protocol, we have shorter B ad thus larger arrival rate ca be supported. α λ > e B This actually exceed the best that could be achieved with ALOHA

5 Epoch mechaism The collisio resolutio iterval i biary tree protocol is log if the umber of collidig packets is log. After oe CRI, the packets that arrived durig that period will collide. Sice the period was log, also the umber of collidig packets is expected to be large. To reduce the umber of collidig packets, the arrivals durig the CRI could be divided ito epocs. The epocs would the be served i cosecutive maer Iterval-Splittig epoch mechaism First all users that arrived durig (a,g) will trasmit. If there is collisio, istead of flippig a coi, the iterval is split ad users that arrived o (a,d) will be served. If there is further collisio, we split the iterval ito (a,b) ad (b,d) etc