packet radio networks

Packet Radio Networks

Packet Radio Networks are multiaccess networks inwhich not all nodes can hear the transmission of allother nodes, this feature is characteristic for radiocommunication

We will focus on the effect of partial connectivity on themultiaccess techniques rather than the physicalcharacteristics of the radio broadcast medium

The topology of a radio network can be described by agraph, G = (N,L), where N is a set of nodes and L is aset of links, each link correspond to an ordered pair ofnodes, (i, j), and indicates that transmission from i canbe heard at j

Information Networks – p.1/28


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) 6∈ L

2

1 3 4

5 6



Our assumption about communication in thismultiaccess medium is that if node i transmits a packet,that packet will be correctly received by node j if andonly if

There is a link from i to j, i.e. (i, j) ∈ L, andNo other node k for which (k, j) ∈ L is transmittingwhile i is transmitting, andj itself is not transmitting while i is transmitting

A large number of links in a graph is not necessarilydesirable, it does increase the number of nodes thatcan communicate directly but also increases thelikelihood of collision



The question is now how much traffic can be carried insuch a network?

We define a collision-free set as a set of links that cancarry packets simultaneously with no collisions at thereceiving ends of the links

We can order the links and represent each collision-freeset as a vector of 0’s and 1’s called a collision-freevector (CFV), where the lth component of a CFV is 1 ifand only if the lth link is in the correspondingcollision-free set



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


TDM for Packet Radio Nets

Choose some collection of CFVs {xi} and cyclebetween them by TDM, i.e. in the ith slot of a TDM cycleall links with a 1 in xi can carry packets

There are no collisions and the fraction of time that agiven link can carry packets is the fraction of the CFVsthat contain a 1 in the position corresponding to thatlink, so with J CFVs

f =1

J

∑

i

xi

is the fraction of time each link can be used



By repeating a CFV xi a certain number of times in aTDM frame, with αi the fraction of frame slots using xi

we get

f =∑

i

αixi

as the fractional utilization of each link

A vector of the form∑

i αixi with∑

i αi = 1 and αi ≥ 0 iscalled a convex combination of the vectors {xi}

We can state the above result as; any convexcombination of CFVs can be approached arbitrarilyclosely as a fractional link utilization vector through theuse of TDM



Suppose we are using some sort of collision resolutionmethod in the network, at any given time, the vector oflinks that are transmitting successfully is a CFV

By averaging this vector over time we get a vectorwhose lth component is the fraction of time that the lth

link is carrying packets successfully

This is also a convex combination of CFVs, thus we seethat any link utilization that is achievable with collisionresolution is also achievable by TDM

One disadvantage of TDM is that the delays are longerthan necessary for a lightly loaded network



However, if all nodes have only a small number ofincoming links, many nodes can transmitsimultaneously and the waiting time for TDM slot isreduced

Another problem with the TDM approach is that thenodes are usually mobile, and thus the topology of thenetwork is constantly changing, this means that theCFVs keep changing, requiring frequent updates of theTDM schedule

The problem of determining whether a potential vectorof link utilizations is a convex combination of a given setof CFVs has a computational time that increases veryrapidly with the number of links in the network


FDM for Packet Radio Nets

FDM can also be used for packet radio networks in asimilar way to TDM, all links in a CFV can use the samefrequency band simultaneously, so in principle the linkscan carry the same amount of traffic as in TDM

This approach is used in cellular radio networks formobile voice communication

The area covered by the network is divided into a largenumber of local areas called cells, each cell has anumber of frequency bands for use within that cell

The frequency bands used by one cell can be reusedby other cells that are sufficiently separated from eachother to avoid interference


Collision Resolution for Packet Radio Nets

One complication in packet radio nets is obtainingfeedback information, suppose that the links (3, 5) and(4, 6) contain packets in a given slot, then node 6perceives a collision and node 5 correctly receives apacket

If nodes 5 and 6 send feedback information, node 3 willexperience a feedback collision

A second problem is that if a node perceives a collision,it does not know if any of the packets were addressedto it

Thus we cannot assume perfect (0, 1, e) feedback andthe splitting algorithms cannot be used and thestabilization techniques require substantial revisions


Collision Resolution for Packet Radio Nets

Slotted and unslotted Aloha are still applicable, and to acertain extent, some of the ideas of carrier sensing andreservation can still be used

We start by analyzing how slotted Aloha works in thiscase

When an unbacklogged node receives a packet totransmit (either a new packet entering the network or apacket in transit that needs to be forwarded to anothernode), it transmits the packet in the next slot

If no acknowledgment (ack) of correct reception arriveswithin some time-out period, the node becomesbacklogged and the packet is retransmitted after arandom delay


Slotted Aloha for Packet Radio Nets

A backlogged node becomes unbacklogged when all itspackets have been transmitted and acked successfully

The simplest way to return acks to the transmitting nodeis that if i sends a packet to j that must be forwarded onto some other node k, then if i hears j’s transmission tok that serves as an ack of the (i, j) transmission

This however needs to be complemented with someway to ack packets from i that are destined for j

Further, if j successfully relays the packet to k but i failsto hear this due to a collision, an unnecessaryretransmission from i to j is done and j need to ack thisretransmission in some other way since j has alreadyforwarded the packet to k



Another approach is for each node to include explicitacks for the last few packets it has received in eachoutgoing packet

This requires a node to send a dummy packet carryingack information if the node has no data to send forsome period

A third approach is to provide time at the end of eachslot for explicit acks of packets received within the slot

We will now analyze what happens in slotted Aloha fora heavily loaded network



Assume that all nodes are backlogged all the time andhas packets to send on all outgoing links at all times

We assume that the nodes have infinite buffers to storethe backlogged packets

For all nodes i and j, let qij be the probability that nodei transmits a packet to node j in any given slot

Let Qi =∑

j qij be the probability that node i transmitsto any node

We let qij = 0 if (i, j) 6∈ L



Let pij be the probability that a transmission on (i, j) issuccessful

Under our assumption of heavy loading each nodetransmits or not in a slot independently of all othernodes

Since pij is the probability that none of the other nodesthat can reach j, including j itself, is transmitting we get

pij = (1 − Qj)∏

k:(k,j)∈L,k 6=i

(1 − Qk)

Finally, the rate fij of successful transmissions per sloton link (i, j) is fij = qijpij



Given the attempt rates qij we can now compute thelink throughputs fij under the heavy-loadingassumptions, but we would rather be able to find theattempt rates qij that will yield a desired set ofthroughputs (if that set of throughputs is feasible)

This latter problem can be solved iteratively, given adesired throughput fij, we start with an initial q0

ij = 0,and for each iteration n = 0, 1, 2, . . . we first computeQn

i =∑

j qnij (which thus will all be 0 when n = 0) and

then pnij = (1 − Qn

j )∏

k:(k,j) 6∈L,k 6=i(1 − Qnk) (which thus will

all be 1 when n = 0), and then we get next iteration ofqij by qn+1

ij = fij

pnij



Using this iterative procedure we get q1ij ≥ q0

ij, thusQ1

i ≥ Q0i and p1

ij ≤ p0ij, and q2

ij ≥ q1ij, and so on, as long

as none of the Qni exceed 1

Thus as long as none of the Qni exceed 1 we get that qn

ij

is nondecreasing and pnij is nonincreasing with

successive iterations n

It follows that either some Qni exceed 1 at some iteration

n or else qnij approaches a limit, q∗ij, and in this limit, with

corresponding Q∗i and p∗ij we have a solution to our

equations that for the attempt rate q∗ij gives thethroughput fij



If any Qni > 1 for some n then there is no solution to our

equations and the given throughput fij is infeasible

If we know the input rates to the network, and theroutes over which the sessions flow, we can in principledetermine the steady-state rates f ′

ij at which the linksmust handle traffic

We would like to choose the throughputs of each linkunder heavy load to exceed these steady-state rates sothe backlogs do not build up indefinitely



We can then search for the largest number β > 1 forwhich fij = βf ′

ij is feasible under heavy-loadassumptions, given this largest fij, and thecorresponding attempt rates qij, we can empty out thebacklog as it develops

One problem here is that if some nodes are backloggedand others are not, the unbacklogged nodes no longerchoose their transmission times independently, so it ispossible in some odd cases that some backloggednodes build up more backlog when other nodes areunbacklogged than they do when all nodes arebacklogged



One way to avoid this difficulty is for new packets at anode to join the backlog immediately rather than beingable to transmit in next slot, this increases delay underlight-loading conditions

The other way is to hope for the best, to some extentone has to do this anyway since with a changingtopology one cannot maintain carefully controlledattempt rates

One reason for focusing on the heavily loaded case isthat the number of links entering each node is usuallysmall so the attempt rates can be moderately high evenunder heavy-loading assumption



The other reason is that stabilization is much harderhere since a node cannot help itself too much byadjusting its own attempt rates, since other nodes maycause congestion without experiencing congestionthemselves

So far, we have viewed the set of links as given,however, if a node increases its transmitter power, itstransmission will reach a larger set of nodes, it ishowever desirable to keep the power level relatively lowso that each node has a moderately small set ofincoming and outgoing links, somewhere around 8could be good according to a theoretical analysis(although with some questionable assumptions)


Carrier Sensing and Busy Tones

We have previously seen that carrier sensing yielded aconsiderable improvement in the situation where allnodes could here all other nodes and the propagationdelay is small

For line-of-sight radio, the propagation delay is typicallysmall relative to packet transmission times, so it’sreasonable to explore how well it will work here

We have the hidden node problem, if node i istransmitting to node j and node k also wants to transmitto node j there is no guarantee that node k can hear i,so carrier sensing can prevent some collisions but notall



With carrier sensing we lose the uniform slottingstructure and thus lose some of the advantage thatslotted Aloha has over unslotted Aloha

Also, radio transmission is subject to fading andvariable noise so detecting another transmitting node ishard to do in a short time

For all these reasons carrier sensing is not veryeffective for packet radio

One approach to improving the performance of carriersensing is to use a busy tone, whenever any nodedetects a packet being transmitted, it starts to send asignal, called a busy tone, in a separate frequency band



When node i starts to send a packet to node j, thennode j (along with all other nodes that can hear node i)will start to send a busy tone

All the nodes that can hear j will thus avoidtransmitting, and assuming that the nodes that can hearj is the same as then nodes j can hear it follows that j

will experience no collision

A problem is that when node i starts to send a packet,all nodes in range of i will send busy tones, and thusevery node within range of any node in range of i will beinhibited from transmitting



Assuming transmission radius of R, when node i startsto transmit most nodes within radius of 2R of i will beinhibited, this is typically about 4 times the number ofnodes within radius R from the receiving node, which isthe set of nodes that should be inhibited, thus fromthroughput standpoint this is not very promising

Another variation is for a node to send busy tone onlyafter it receives the address part of the packet andrecognizes itself as the intended recipient, this hasbesides more complexity also the disadvantage ofincreasing the time β over which another node couldstart transmission before hearing the busy tone



In summary, for packet radio many more questions thananswers exist, both in terms of desirable structure andhow to analyze

In addition questions about modulation and detectionmake the situation even more complex

It is often desirable to use spread-spectrum techniquesfor sending packets, one of the consequences of this isthat if two packets are being received at once, thereceiver can often lock on to one with the other actingonly as wideband noise



If different spread-spectrum codes are used for eachreceiver, the receiver can look for only its own sequenceand thus reject simultaneous packets sent to otherreceivers, but unwanted packets can arrive with muchhigher power levels than desired packets and still causea collision


packet radio networks

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