Packet Radio Networks Packet Radio Networks are multiaccess networks in which not all nodes can hear the transmission of all other nodes, this feature is characteristic for radio communication We will focus on the effect of partial connectivity on the multiaccess techniques rather than the physical characteristics of the radio broadcast medium The topology of a radio network can be described by a graph, G = ( N, L ) , where N is a set of nodes and L is a set of links, each link correspond to an ordered pair of nodes, ( i, j ) , and indicates that transmission from i can be heard at j Information Networks – p.1/28
Packet Radio Networks In some situations node j might be able to hear node i but i is unable to hear j , in such a case ( i, j ) ∈ L but ( j, i ) �∈ L 2 1 3 4 5 6 Information Networks – p.2/28
Packet Radio Networks Our assumption about communication in this multiaccess medium is that if node i transmits a packet, that packet will be correctly received by node j if and only if There is a link from i to j , i.e. ( i, j ) ∈ L , and No other node k for which ( k, j ) ∈ L is transmitting while i is transmitting, and j itself is not transmitting while i is transmitting A large number of links in a graph is not necessarily desirable, it does increase the number of nodes that can communicate directly but also increases the likelihood of collision Information Networks – p.3/28
Packet Radio Networks The question is now how much traffic can be carried in such a network? We define a collision-free set as a set of links that can carry packets simultaneously with no collisions at the receiving ends of the links We can order the links and represent each collision-free set as a vector of 0’s and 1’s called a collision-free vector (CFV), where the l th component of a CFV is 1 if and only if the l th link is in the corresponding collision-free set Information Networks – p.4/28
Packet Radio Networks Some CFVs for our example graph is (1,2) (1,5) (2,1) (3,2) (3,4) (3,6) (3,5) (4,6) (5,3) (6,3) (6,4) 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 Information Networks – p.5/28
TDM for Packet Radio Nets Choose some collection of CFVs { x i } and cycle between them by TDM, i.e. in the i th slot of a TDM cycle all links with a 1 in x i can carry packets There are no collisions and the fraction of time that a given link can carry packets is the fraction of the CFVs that contain a 1 in the position corresponding to that link, so with J CFVs f = 1 � x i J i is the fraction of time each link can be used Information Networks – p.6/28
TDM for Packet Radio Nets By repeating a CFV x i a certain number of times in a TDM frame, with α i the fraction of frame slots using x i we get � f = α i x i i as the fractional utilization of each link A vector of the form � i α i x i with � i α i = 1 and α i ≥ 0 is called a convex combination of the vectors { x i } We can state the above result as; any convex combination of CFVs can be approached arbitrarily closely as a fractional link utilization vector through the use of TDM Information Networks – p.7/28
TDM for Packet Radio Nets Suppose we are using some sort of collision resolution method in the network, at any given time, the vector of links that are transmitting successfully is a CFV By averaging this vector over time we get a vector whose l th component is the fraction of time that the l th link is carrying packets successfully This is also a convex combination of CFVs, thus we see that any link utilization that is achievable with collision resolution is also achievable by TDM One disadvantage of TDM is that the delays are longer than necessary for a lightly loaded network Information Networks – p.8/28
TDM for Packet Radio Nets However, if all nodes have only a small number of incoming links, many nodes can transmit simultaneously and the waiting time for TDM slot is reduced Another problem with the TDM approach is that the nodes are usually mobile, and thus the topology of the network is constantly changing, this means that the CFVs keep changing, requiring frequent updates of the TDM schedule The problem of determining whether a potential vector of link utilizations is a convex combination of a given set of CFVs has a computational time that increases very rapidly with the number of links in the network Information Networks – p.9/28
FDM for Packet Radio Nets FDM can also be used for packet radio networks in a similar way to TDM, all links in a CFV can use the same frequency band simultaneously, so in principle the links can carry the same amount of traffic as in TDM This approach is used in cellular radio networks for mobile voice communication The area covered by the network is divided into a large number of local areas called cells, each cell has a number of frequency bands for use within that cell The frequency bands used by one cell can be reused by other cells that are sufficiently separated from each other to avoid interference Information Networks – p.10/28
Collision Resolution for Packet Radio Nets One complication in packet radio nets is obtaining feedback information, suppose that the links (3 , 5) and (4 , 6) contain packets in a given slot, then node 6 perceives a collision and node 5 correctly receives a packet If nodes 5 and 6 send feedback information, node 3 will experience a feedback collision A second problem is that if a node perceives a collision, it does not know if any of the packets were addressed to it Thus we cannot assume perfect (0 , 1 , e ) feedback and the splitting algorithms cannot be used and the stabilization techniques require substantial revisions Information Networks – p.11/28
Collision Resolution for Packet Radio Nets Slotted and unslotted Aloha are still applicable, and to a certain extent, some of the ideas of carrier sensing and reservation can still be used We start by analyzing how slotted Aloha works in this case When an unbacklogged node receives a packet to transmit (either a new packet entering the network or a packet in transit that needs to be forwarded to another node), it transmits the packet in the next slot If no acknowledgment (ack) of correct reception arrives within some time-out period, the node becomes backlogged and the packet is retransmitted after a random delay Information Networks – p.12/28
Slotted Aloha for Packet Radio Nets A backlogged node becomes unbacklogged when all its packets have been transmitted and acked successfully The simplest way to return acks to the transmitting node is that if i sends a packet to j that must be forwarded on to some other node k , then if i hears j ’s transmission to k that serves as an ack of the ( i, j ) transmission This however needs to be complemented with some way to ack packets from i that are destined for j Further, if j successfully relays the packet to k but i fails to hear this due to a collision, an unnecessary retransmission from i to j is done and j need to ack this retransmission in some other way since j has already forwarded the packet to k Information Networks – p.13/28
Slotted Aloha for Packet Radio Nets Another approach is for each node to include explicit acks for the last few packets it has received in each outgoing packet This requires a node to send a dummy packet carrying ack information if the node has no data to send for some period A third approach is to provide time at the end of each slot for explicit acks of packets received within the slot We will now analyze what happens in slotted Aloha for a heavily loaded network Information Networks – p.14/28
Slotted Aloha for Packet Radio Nets Assume that all nodes are backlogged all the time and has packets to send on all outgoing links at all times We assume that the nodes have infinite buffers to store the backlogged packets For all nodes i and j , let q ij be the probability that node i transmits a packet to node j in any given slot Let Q i = � j q ij be the probability that node i transmits to any node We let q ij = 0 if ( i, j ) �∈ L Information Networks – p.15/28
Slotted Aloha for Packet Radio Nets Let p ij be the probability that a transmission on ( i, j ) is successful Under our assumption of heavy loading each node transmits or not in a slot independently of all other nodes Since p ij is the probability that none of the other nodes that can reach j , including j itself, is transmitting we get � p ij = (1 − Q j ) (1 − Q k ) k :( k,j ) ∈ L,k � = i Finally, the rate f ij of successful transmissions per slot on link ( i, j ) is f ij = q ij p ij Information Networks – p.16/28
Slotted Aloha for Packet Radio Nets Given the attempt rates q ij we can now compute the link throughputs f ij under the heavy-loading assumptions, but we would rather be able to find the attempt rates q ij that will yield a desired set of throughputs (if that set of throughputs is feasible) This latter problem can be solved iteratively, given a desired throughput f ij , we start with an initial q 0 ij = 0 , and for each iteration n = 0 , 1 , 2 , . . . we first compute Q n j q n ij (which thus will all be 0 when n = 0 ) and i = � then p n ij = (1 − Q n k :( k,j ) �∈ L,k � = i (1 − Q n j ) � k ) (which thus will all be 1 when n = 0 ), and then we get next iteration of = f ij q ij by q n +1 p n ij ij Information Networks – p.17/28
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