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Energy and latency performance of geographic
random forwarding for ad hoc and sensor networks
Michele Zorzi †^ and Ramesh R. Rao ‡
†UdR CNIT, Universit`a di Ferrara – via Saragat, 1 – 44100 Ferrara, Italy ph.: +39-0532-974840 – fax: +39-0532-974870 – e-mail: zorzi@ing.unife.it ‡Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093-0407, USA
Abstract — In this paper, we describe a novel forwarding technique based on geographical location of the nodes involved and random selection of the relaying node via contention among receivers. A collision avoidance scheme based on this idea is described in detail, and an approximate analysis is provided. The proposed scheme is compared with STEM, and is shown to perform significantly better for sufficient node density.
I. I NTRODUCTION
In ad hoc and sensor networks, it is critically important to save energy. 1 Many papers have recently appeared which propose MAC, routing, and topology maintenance schemes which try to save energy based on aggressive power-off strategies. In fact, it has been recognized that the only way a node can save substantial energy is to power off the radio, since transmitting, receiving and listening to an idle channel are functions which require roughly the same amount of power. As a consequence of this key observation, MAC and routing strategies need to be revisited since, for example, CSMA-based access schemes need all nodes to continuously listen to the channel while, on the other hand, nodes which power off their radio may end up not being reachable and/or aware of activity in the network. The main problem in this scenario is therefore that of combining protocols which minimize the amount of time the radio is on with effective strategies for MAC and routing. An example of how topology can be maintained in the presence of sleeping nodes is provided by SPAN in [1], where the authors propose that in a dense network several disjoint sets of nodes be identified, each able to guarantee connectivity and bandwidth to all nodes. As long as one of these sets is active at any given time, the network is connected; on the other hand, since when one set is active the others can sleep, the percentage of time a node must be active is drastically reduced. STEM [2] provides a way to establish communications in the presence of sleeping nodes. Each sleeping node wakes up peri- odically to listen. If a node wants to establish communications, it starts sending out beacons polling a specific user. Within a bounded time, the polled node will wake up and receive the poll, after which the two nodes are able to communicate. An interesting feature of STEM is that a dual radio setup is envisioned, with separate frequencies used for wakeup and actual data transmission.
This work has been partially supported by the European Commission under contract IST-2001-34734 “EYES.” (^1) While in this paper we will mostly refer to sensor networks, many of the ideas presented can also be applied to ad hoc networks.
GAF [3] is similar to SPAN in a sense, since it envisions the use of only a fraction of nodes at any given time. The specific approach of GAF is to divide the area in square regions, called grids, in such a way that any two nodes in neighboring grids are within range of each other. With this provision, grids can be treated as equivalent (or virtual) nodes, in the sense that all nodes in the same grid can be interchangeably used for routing purposes. The price to pay for this guarantee is that the hop length is significantly smaller than the radio range (by a factor of
5 [3]). This may result in inefficiency in terms of latency and energy consumption (more hops than possibly needed). A common characteristic of the above schemes is that, at the MAC layer and often also at the routing layer, when a node decides to transmit a packet (as the originator or a relay) it specifies the MAC address of the neighbor to which the packet is being sent. Knowledge of the network topology (though in many cases only local in extent) is required since a node needs to know its neighbors and possibly some more information related to the availability of routes to the intended destination. This topological information can be acquired at the price of some signaling traffic, and becomes more and more difficult to maintain in the presence of network dynamics (e.g., nodes which move or turn off without coordination). In this document, we describe a transmission scheme based on geographical routing where packets are relayed on a best- effort basis, i.e., the actual node which acts as a relay is not known a priori by the sender, but rather is decided after the transmission has taken place. This idea leverages on the fact that in the wireless environment broadcast is free (from the sender’s point of view) and that in the presence of randomly changing topologies a node may not be aware of which of its current neighbors is in the best position to act as a relay. In a sense, this is like doing contention at the receiver’s end, which is untraditional because in classic schemes it is the transmitter which contends for the channel. Here, since the intended recipient is not specified, multiple nodes may be able to receive the packet, and a receiver contention scheme is therefore needed to avoid duplication.
II. C OLLISION AVOIDANCE SCHEME
We consider a scheme which uses carrier sense before transmission, which partially avoids collisions but gives no guarantee against the hidden terminal problem. Notice that the fact that nodes are not always on makes traditional RTS/CTS- based collision avoidance mechanisms ineffective since a node may wake up after the CTS was issued. This could be solved
0-7803-7700-1/03/$17.00 (C) 2003 IEEE 1930
by requiring a long idle channel time to be detected before a transmission can start (essentially enough for the whole packet exchange to complete, which is of course very wasteful) or by synchronizing all nodes as in [4], which requires additional signaling and complexity. The solution we adopt here is the use of busy tones [5], [6]. It was observed in [2] that there exist sensor nodes equipped with two radios. In [2] the availability of separate channels for the data traffic and the wakeup signaling is useful to facilitate protocol operation, in particular to avoid that prolonged beacon periods interfere with data traffic. In our case, we use the second radio to let the receiving node issue a busy tone, which is a way to effectively prevent collisions at the receiver. Notice that we can trade off energy and latency as in [2] by using a pulsed busy tone with some duty cycle, with the requirement that the sensing time be increased in order to avoid that silent intervals of the busy tone are interpreted as idle channel. The protocol will then work as follows. When a node has a packet to send, it listens to both frequencies. If either is active, the node backs off. If both are inactive, the node transmits. The collision avoidance feature of this scheme is based on the RTS/CTS message exchange. However, unlike the traditional RTS message which is addressed to a specific node, in this case any node within range can respond to it, with nodes closer to the destination doing so with higher priority. Therefore, the CTS message is also subject to contention, since multiple nodes may decide to respond to the same RTS at the same time. A more detailed explanation of the protocol, including the contention mechanism, is given next.
A. Detailed description
We now describe in detail the protocol operation from the transmitter and the receiver side. The current description is for a specific solution, and many variants are possible which improve the performance while being more complicated to explain. In this section we choose a simple version to highlight the main points. 1) Transmitter: When a sleeping node has a packet to send, it transitions to the active state and monitors both frequencies for τ seconds. If either frequency is busy, the node backs off and reschedules an attempt at a later time. If on the other hand both frequencies are sensed idle during this entire interval, the node transmits a broadcast RTS message, which contains the location of the intended destination as well as that of the sender. After sending the RTS, the transmitting node listens for CTS messages from potential relays. In each of the CTS slots following the end of the RTS message, the transmitting node acts as follows: i) if only one CTS message is received, it starts transmission of the data packet, whose initial part acts as a CTS confirmation for the node which issued the CTS; ii) if it receives no CTSs, it will send a CONTINUE message and listen again for CTSs, timing out after Np empty CTS slots (which forces the node to abort the handshake and to reschedule it at a later time); iii) if it hears a signal but is unable to detect a meaningful message, it will assume that a collision took place, and will send a COLLISION message which will trigger the start of a collision resolution algorithm (to be described later) and will listen again for CTSs. After packet transmission, an immediate ACK is expected. If it is correctly received, it completes the transaction and the node can go back to sleep. If the transmitter does not get an ACK within a given time, it times out and declares
the transaction failed. It will then reschedule the same packet for future transmission. After NM axAtt failed attempts for the same packet, the transmitter will give it up and generate an error message for the higher layers. Notice that with the above rules the protocol does not lead to transmitter deadlock, as it will never wait indefinitely for CTSs or ACKs. Only in the case of completed transaction will the transmitter consider the packet as successfully passed to the next hop. A remaining problem with this scheme is that packet duplication may occur. In fact, if the final ACK is lost the relay node is now in charge of packet delivery whereas the transmitter will not be aware of this fact and will retry the packet transmission. This ambiguity does not compromise the correctness of the scheme and can be solved by intermediate nodes when an additional copy of the same packet is received and discarded. This requires that nodes keep memory of recent transmissions. If this is not possible or desirable, as well as in the case in which the duplicate packet goes through a different set of nodes, packet duplication will be detected at the destination, which leads to some inefficiency which on the other hand is mitigated by the fact that losing an ACK when the packet was successful is a low probability event and the overall performance impact may be expected to be limited. 2) Receiver: Each node will (more or less) periodically wake up and put itself in the listening mode. If nothing happens throughout the listening time, whose duration may be fixed or random, the node goes back to sleep. On the other hand, if the node detects the start of a transmission, it goes into the receiving state. Upon detecting the start of a message, a listening node starts receiving. At the same time, it activates the busy tone on the signaling frequency for a duration TRT S. If no valid RTS is received, the node goes back to the listening state, where it stays for the originally scheduled duration. On the other hand, if a valid RTS is received, the node reads the information in it and determines its own priority as a relay. This priority is based on the relative location of the node itself compared to the distance between the transmitter and the intended final destination. Specifically, assume the following: the portion of the coverage area of the transmitter which is closer to the intended destination than the transmitter itself is divided in Np regions A 1 ,... , ANp such that all points in Ai are closer to the destination than all points in Aj for j > i, i = 1,... , Np − 1. (Possible choices of these regions may be to take all with the same area or to quantize the advancement in Np equal levels.) In the first CTS slot after the RTS, all nodes in A 1 will send a CTS message, while all others will be silent. All nodes will then listen for the message from the transmitter in the latter part of the CTS slot. If a packet start is heard (which contains the identification of the node which sent the CTS), only the designated node will continue to receive, whereas all others will go back to sleep. Notice that going back to the listening state is not a good strategy since these nodes are in the coverage area of the transmitter and therefore will be unable to serve as relays for any other nodes. In the interest of energy saving, the best thing to do is to go back to sleep regardless of any previous schedule (if the listening interval is significantly longer than a complete transaction, nodes could just interrupt their listening and resume it at the end of the transmission). If in the second part of the first CTS slot a CONTINUE message is heard, it means that there are no nodes in A 1 , and all nodes in A 2 will contend in the second CTS slot. If an
area will start an RTS. Before being able to know whether it can be considered as a relay, the node must receive this RTS. Since the arrival time of this RTS is uniformly distributed within the listening interval, the actions involved are listening to the channel for TL/ 2 on average, and receiving for TRT S. Note that as soon as the node detects channel activity, it turns on its busy tone, so that a transmit activity for TRT S must be accounted for as well. Given that an RTS is started, with probability 1 − ξ the node will not be in the portion of the coverage area facing the destination, and will drop out immediately after receiving the RTS. In this case, there is no additional activity involved. On the other hand, with probability ξ the node will participate in the contention, along with other nodes whose number is a Poisson r.v. with mean ξM. Since all participating nodes have the same probability of being the winner, the probability that the node wins the contention is found as
∑^ ∞
k=
k + 1
e−ξM^ (ξM )k k!
1 − e−ξM ξM
In this case, i.e., the node wins the contention, it is involved at most in sending x CTSs, receiving (x − 1) CTS replies, receiving the data packet and finally sending the ACK. When the node is receiving, i.e., for a time equal to (x − 1)TCT Sr + TD , the busy tone is on. If on the other hand the node participates in the con- tention but loses it (with conditional probability (ξM − 1 + e−ξM^ )/ξM ), the activity involved is upper bounded by receiving (x − 1) CTS replies and transmitting continuously (CTSs or busy tone) for (x − 1)(TCT S + TCT Sr). Note in fact that nodes losing the contention do not necessarily participate until the end, and with certainty do not transmit in the very last CTS slot (in which somebody else is successful). In summary, the total average active time of the radio (counting twice the times when both radios are on) can be found as
t = p 0 TL + (1 − p 0 )
[
TL
+ 2TRT S
1 − e−ξM M
(xTCT S + 2(x − 1)TCT Sr + 2TD + TACK )
ξM − (1 − e−ξM^ ) M
(x − 1)(TCT S + 2TCT Sr )
]
= TL + (1 − p 0 ) [ξ(x − 1)(TCT S + 2TCT Sr )
TL
1 − e−ξM M
(TCT S + 2TD + TACK )
]
For resonable scenarios, the probability that upon wakeup the node ends up being involved in a data exchange will have to be small (the whole idea being to avoid heavy load of the nodes). In order to have network stability we must have λN TDAT Aex < 1 , i.e., the average number of users in transmission state per coverage area must be less than unity (TDAT Aex is the total time for a data transfer from RTS to ACK). If we assume that TL TDAT Aex, we have that λN TL 1. In this case, we have p 0 1 and 1 − p 0 = 1 − e−λN TL^ λN TL. If once again we assume that an active radio consumes a power P regardless of its being in transmit, receive or listen mode, the total average contribution to the total average power consumption Etot/t can be found as EN/t. For an unloaded network, we would have N/t = d/TL, while in general it is
true that N/t ≤ d/TL, and the bound is tight for low traffic. In this case, we can write EN t
Ed TL
dP t TL
= dP + λP
[
M TL
]
where we used the fact that dP (1 − p 0 ) TL
dP λN TL TL
= λP M (10)
C. Sleeping The total amount of energy consumed while sleeping is given by TsPs, where Ts is the total amount of time the two radios are off. Notice that since in the above analysis we never accounted for sleeping times in between active periods of the radios, Ts must include those times as well. In any event, we can affirm that the contribution of sleeping time to the overall average power consumption is TsPs t
≤ Ps (11)
where Ps is the power consumed when both radios are off. In view of the fact that in the envisioned scenarios the radios must be sleeping most of the time, we have t − Ts t, and therefore the above bound is tight and can be used as a reasonable approximation.
D. Total average energy consumption We can find the total normalized average energy consump- tion to be
ψ 0 =
Etot P t
P
NT ET
t
EN
t
TsPs t
where the expressions for the three terms are given above. ψ 0 is the total energy consumed in time t, divided by the energy which would be consumed by a radio which is always on (transmitting, receiving or monitoring the channel).
E. Latency We define here latency as the time it takes from when a node starts the packet transmission handshake to when the transmission of the actual data packet starts. In our scheme, this corresponds to tT minus the time for data and ACK, i.e.,
T (^) S = (eξM^ − 1)−^1 (TRT S + Np(TCT S + TCT Sr)) +TRT S + xTCT S + (x − 1)TCT Sr (13)
F. Analysis of STEM A similar analysis can be carried out for the STEM scheme. We consider here STEM-B [2]. Energy consumption. The average energy consumption can still be divided into three terms. In a packet transmission, the sender sends beacons until the intended recipient wakes up and receives one. At that point, packet exchange takes place via 802.11-like MAC. Nodes wake up every T seconds for TL. The average time the beacon needs to be sent is then given by (T − TB )/2 + B 1 [2], and if we assume that TL = TB + B 1
we obtain (T − TL)/2 + 1. 5 B 1 , where T = TL/d. The total average amount of time the node is powered on is therefore given by
tT =
TL
2 d
TL
+ 1. 5 B 1 + TCT S + TD + TACK (14)
where we assumed that the beacon acts as RTS. The con- tribution to the average energy consumption due to packet transmission is then given by λP tT. After waking up, a node will be addressed with probability 1 − p 0 , where p 0 is the probability that no activity is detected. Note that in this case nodes are explicitly addressed, and therefore the rate at which messages for a specific node are generated is lower than before (where on the other hand all nodes in the coverage area would receive the RTS). However, since a beacon is for a specific node, the interval of time during which a new message can be generated is now T rather than TL. The message arrival rate is then given by λN TN = λT dL. Notice that this is the average fraction of listening periods in which a node gets a message, and as before in the envisioned scenario we expect this number to be small. After waking up, a node will listen for TL and go back to sleep with probability p 0 = e−λTL/d. With probability 1 − p 0 λTL/d, the node will be involved in receiving a message. In this case, note that in STEM the listen time is TL = TB + B 1 , where TB is the period with which beacons are sent and B 1 is the length of a beacon. Since the beacon start time is uniformly distributed within TB , the average time to receive a beacon is TB /2+B 1 = (TL +B 1 )/ 2. After receiving a beacon, the node’s radio is involved in sending a CTS, receiving a data packet and sending an ACK. The total activity time for listening/receiving is therefore
t = p 0 TL + (1 − p 0 )
[
TL + B 1
+ TCT S + TD + TACK
]
TL +
λTL d
[
B 1 − TL
+ TCT S + TD + TACK
]
Finally, as before, we approximate the contribution of sleep mode to the overall average power as Ps. The total average energy consumption in STEM can there- fore be computed as
ψs =
Etot P t
≤ λtT +
dt TL
Ps P
Latency. If we define latency as the time from when a beacon is initiated to the time an ACK for it is successfully received (and therefore data exchange can start), we have as in [2] (we assume here ε = 0, which corresponds to minimum listening time TL)
T (^) S = B1+2 +
T − TB
T − TL
+ 1. 5 B 1 + B 2 (17)
IV. P ERFORMANCE COMPARISON
In this section, we give some numerical results for the schemes considered, and provide a comparison between them. First of all, notice that there are three types of parameters in the above formulas:
- fixed parameters , i.e., parameters which are expected to be decided once for all and will be considered as constant: in particular, we choose Np = 4, ξ = 0. 4 , TSIG/TD =
- 1 (we assume here for simplicity that all signaling packets are of the same length TSIG);
10 -3^10 -2^10 -1^100 duty cycle, d
10 -
10 -
10 -
10 0
normalized energy, psi_
traffic = 0.
proposed, N= STEM, N= proposed, N= STEM, N=
Fig. 1. Average normalized energy consumption, ψ 0 , vs. duty cycle, d. Proposed scheme and STEM compared. N = 20, 100 , network load 0.01.
- external parameters , i.e., parameters which are common to all schemes and provide the scenario in which those schemes are compared: in particular, the node density and the network traffic; here, we use the average number of nodes per coverage area, N , as a measure of the network density, and the average normalized traffic per coverage area, λN TD as a measure of the network load;
- parameters of the specific schemes , i.e., parameters which play different roles in different schemes and can be chosen differently according to the scheme selected; for example, the listening time or the duty cycle may not be the same in the proposed scheme and in STEM. In reality, these parameters would be subject of protocol optimization, and a fair comparison should take into account that they can be independently selected. As to the parameter optimization, note the following. In STEM, the minimum listening time is TB + B 1 = 3TSIG. Since it is obvious that the best choice is to select TL as small as possible, we set TL = 3TSIG here. The remaining independent parameter is the duty cycle. In our scheme, if we upper bound the energy consumption by neglecting the negative term −M TL/ 2 in (9), the listening time no longer appears explicitly in the expressions, and can therefore be ignored. In this case also, the duty cycle is the only remaining independent parameter. Results are shown in Figures 1 through 4, in which the performance of our proposed scheme is compared with that of STEM. Figures 1 and 2 show the normalized energy performance, ψ 0 , vs. the duty cycle, d. In both schemes, for large duty cycle, the energy consumption is dominated by the listening activity, as expected. As the duty cycle is decreased, other sources of energy consumption are important. In particular, the fact that the transmitter must spend energy to “find a neighbor” (either via the beacon as in STEM or by repeated attempts in our scheme) becomes dominant, and more so as the network load is higher. Note that in all cases our scheme outperforms STEM, with more significant gains when the node density is large. It should be noted that the choice of the duty cycle does not have to be the same in the two schemes, as they may
