Packet Radio Networks Packet Radio Networks are multiaccess networks - - PowerPoint PPT Presentation

Packet Radio Networks

Packet Radio Networks are multiaccess networks in which not all nodes can hear the transmission of all

• ther 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

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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

• nly 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

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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 lth component of a CFV is 1 if and only if the lth link is in the corresponding collision-free set

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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 1 1 1 1 1 1 1 1 1 1 1 1 1

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TDM for Packet Radio Nets

Choose some collection of CFVs {xi} and cycle between them by TDM, i.e. in the ith slot of a TDM cycle all links with a 1 in xi 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 J

• i

xi

is the fraction of time each link can be used

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TDM for Packet Radio Nets

By repeating a CFV xi a certain number of times in a TDM 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 is

called a convex combination of the vectors {xi} 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

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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 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 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

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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

• f link utilizations is a convex combination of a given set
• f CFVs has a computational time that increases very

rapidly with the number of links in the network

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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

• ther to avoid interference

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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

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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

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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

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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

• utgoing 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

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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 qij be the probability that node

i transmits a packet to node j in any given slot

Let Qi =

j qij be the probability that node i transmits

to any node We let qij = 0 if (i, j) ∈ L

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Slotted Aloha for Packet Radio Nets

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

pij = (1 − Qj)

• k:(k,j)∈L,k=i

(1 − Qk)

Finally, the rate fij of successful transmissions per slot

• n link (i, j) is fij = qijpij

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Slotted Aloha for Packet Radio Nets

Given the attempt rates qij we can now compute the link throughputs fij under the heavy-loading assumptions, but we would rather be able to find the attempt rates qij 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 fij, we start with an initial q0

ij = 0,

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

Qn

i = j qn ij (which thus will all be 0 when n = 0) and

then pn

ij = (1 − Qn j ) k:(k,j)∈L,k=i(1 − Qn k) (which thus will

all be 1 when n = 0), and then we get next iteration of

qij by qn+1

ij

= fij

pn

ij

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Slotted Aloha for Packet Radio Nets

Using this iterative procedure we get q1

ij ≥ q0 ij, thus

Q1

i ≥ Q0 i and p1 ij ≤ p0 ij, and q2 ij ≥ q1 ij, and so on, as long

as none of the Qn

i exceed 1

Thus as long as none of the Qn

i exceed 1 we get that qn ij

is nondecreasing and pn

ij is nonincreasing with

successive iterations n It follows that either some Qn

i exceed 1 at some iteration

n or else qn

ij 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 the

throughput fij

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Slotted Aloha for Packet Radio Nets

If any Qn

i > 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 the routes over which the sessions flow, we can in principle determine the steady-state rates f ′

ij at which the links

must handle traffic We would like to choose the throughputs of each link under heavy load to exceed these steady-state rates so the backlogs do not build up indefinitely

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Slotted Aloha for Packet Radio Nets

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

ij is feasible under heavy-load

assumptions, given this largest fij, and the corresponding attempt rates qij, we can empty out the backlog as it develops One problem here is that if some nodes are backlogged and others are not, the unbacklogged nodes no longer choose their transmission times independently, so it is possible in some odd cases that some backlogged nodes build up more backlog when other nodes are unbacklogged than they do when all nodes are backlogged

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Slotted Aloha for Packet Radio Nets

One way to avoid this difficulty is for new packets at a node to join the backlog immediately rather than being able to transmit in next slot, this increases delay under light-loading conditions The other way is to hope for the best, to some extent

• ne has to do this anyway since with a changing

topology one cannot maintain carefully controlled attempt rates One reason for focusing on the heavily loaded case is that the number of links entering each node is usually small so the attempt rates can be moderately high even under heavy-loading assumption

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Slotted Aloha for Packet Radio Nets

The other reason is that stabilization is much harder here since a node cannot help itself too much by adjusting its own attempt rates, since other nodes may cause congestion without experiencing congestion themselves So far, we have viewed the set of links as given, however, if a node increases its transmitter power, its transmission will reach a larger set of nodes, it is however desirable to keep the power level relatively low so that each node has a moderately small set of incoming and outgoing links, somewhere around 8 could be good according to a theoretical analysis (although with some questionable assumptions)

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Carrier Sensing and Busy Tones

We have previously seen that carrier sensing yielded a considerable improvement in the situation where all nodes could here all other nodes and the propagation delay is small For line-of-sight radio, the propagation delay is typically small relative to packet transmission times, so it’s reasonable to explore how well it will work here We have the hidden node problem, if node i is transmitting to node j and node k also wants to transmit to node j there is no guarantee that node k can hear i, so carrier sensing can prevent some collisions but not all

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Carrier Sensing and Busy Tones

With carrier sensing we lose the uniform slotting structure and thus lose some of the advantage that slotted Aloha has over unslotted Aloha Also, radio transmission is subject to fading and variable noise so detecting another transmitting node is hard to do in a short time For all these reasons carrier sensing is not very effective for packet radio One approach to improving the performance of carrier sensing is to use a busy tone, whenever any node detects a packet being transmitted, it starts to send a signal, called a busy tone, in a separate frequency band

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Carrier Sensing and Busy Tones

When node i starts to send a packet to node j, then node 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 avoid transmitting, and assuming that the nodes that can hear

j 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 thus every node within range of any node in range of i will be inhibited from transmitting

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Carrier Sensing and Busy Tones

Assuming transmission radius of R, when node i starts to transmit most nodes within radius of 2R of i will be inhibited, this is typically about 4 times the number of nodes within radius R from the receiving node, which is the set of nodes that should be inhibited, thus from throughput standpoint this is not very promising Another variation is for a node to send busy tone only after it receives the address part of the packet and recognizes itself as the intended recipient, this has besides more complexity also the disadvantage of increasing the time β over which another node could start transmission before hearing the busy tone

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Packet Radio Networks

In summary, for packet radio many more questions than answers exist, both in terms of desirable structure and how to analyze In addition questions about modulation and detection make the situation even more complex It is often desirable to use spread-spectrum techniques for sending packets, one of the consequences of this is that if two packets are being received at once, the receiver can often lock on to one with the other acting

• nly as wideband noise

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Packet Radio Networks

If different spread-spectrum codes are used for each receiver, the receiver can look for only its own sequence and thus reject simultaneous packets sent to other receivers, but unwanted packets can arrive with much higher power levels than desired packets and still cause a collision

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