Ad Hoc Wireless Networks (A Communication-Theoretic Perspective) || Route Reservation in Ad Hoc Wireless Networks

Chapter 7

Route Reservation in Ad HocWireless Networks

7.1 IntroductionThe two principal switching techniques used in wired networks are circuit switching andpacket switching [2]. One of the main differences between them is the way resources areshared. Circuit switching provides exclusive access to the resources by means of reservation.In packet switching, on the other hand, resources are shared on-demand, without priorreservation. While it is obvious that packet switching is suitable for a wired data networksuch as the Internet, it is not clear whether this is true in the case of ad hoc wireless networks.On the basis of the ‘bottom-up’ approach introduced in the previous chapters, in this chapter,we investigate the performance of two switching paradigms: reservation-based (RB) andnon-reservation-based (NRB) switching. The concepts of reservation and non-reservation areanalogous to those of circuit switching and packet switching in wired networks, respectively.However, there are some important differences, which can be summarized as follows.

• In an NRB scheme, an intermediate node can simultaneously serve as a relay for morethan one source. Hence, the resources (in terms of relaying nodes) are shared in an on-demand fashion. This is typical for most of the routing protocols for wireless ad hocnetworks proposed in the literature [148].

• In an RB scheme, a source first reserves a multi-hop route to its destination, i.e.it reserves intermediate nodes before the actual transmission begins. The reservedintermediate nodes are required to relay only the message generated by the specificsource. This gives the source an exclusive access to the path to the destination.This particular route reservation approach for ad hoc wireless networks was firstintroduced in [81] and is described in Chapters 2 and 3.

In addition to posing the interesting question of whether and when RB switchingmakes sense in wireless ad hoc networks, in this chapter we develop novel analyticalmodels (queuing models) for analyzing the network performance (in terms of throughput,delay, goodput, and mobility) under the RB and NRB switching schemes. Although somesimplifying assumptions are made to keep the analysis tractable, the results presented in thischapter still provide significant insights and may stimulate further research in this area.

Ad Hoc Wireless Networks: A Communication-Theoretic Perspective Ozan K. Tonguz and Gianluigi Ferrari© 2006 John Wiley & Sons, Ltd. ISBN: 0-470-09110-X

168 Chapter 7. Route Reservation in Ad Hoc Wireless Networks

One of the important contributions of this work is to identify under which conditions(in terms of route discovery, MAC protocol, pipelining, etc.) the delay performance of RBscheme can be superior to the NRB scheme. While the conventional wisdom in currentwireless ad hoc networking research favors NRB switching, in this chapter we show, for thefirst time, when and under which conditions RB switching might be preferable. Our resultsshow that, even under these somewhat strict and futuristic conditions, while RB switchingprovides a better delay performance, NRB switching can generally achieve higher networkgoodput and throughput. It is important to understand that if these conditions are not satisfied,then NRB switching will probably be preferable.

The rest of this chapter is organized as follows. In section 7.2, we briefly discuss therelated work in this area. In section 7.3, we describe ad hoc wireless network communicationmodels and assumptions used in this chapter. We describe the basic principles of operation ofRB and NRB switching schemes in section 7.4. Performance of the two switching schemes isanalyzed in detail in section 7.5. Results and their implications are presented in section 7.6.Finally, concluding remarks are given in section 7.7.

7.2 Related WorkA number of routing protocols for ad hoc wireless networks have been proposed over the pastfew years. Most of these protocols can be categorized as variants of the NRB routing protocol,where packets are relayed on a route with best effort. Examples include [42], [5], [149] andmore references can be found in [148]. A number of studies related to the evaluation ofNRB switching schemes have also been reported. In [150–152], the performance of a fewrouting protocols for ad hoc wireless networks, in terms of throughput, end-to-end delay andthe number of overheads, are investigated using computer simulations. In [16], an analyticalmodel for evaluating the performance, in terms of capacity and throughput, of static ad hocwireless networks without a delay constraint is proposed. The achievable network throughputfor a given delay constraint is then studied in [122, 153]; however, the queuing delay at eachnode is not taken into consideration. In [154], the authors consider NRB switching in ad hocwireless networks and derive delay bounds for a two-hop relay case and a multi-hop relaycase with packet flooding.

Many reservation-based routing protocols are also proposed in the literature. Theserouting protocols are designed to guarantee quality of service (QoS) such as bandwidthand delay. In [155], a ticket-based probing algorithm is used for searching routes whichsatisfy bandwidth and delay constraints. In [156], a time division multiple access (TDMA)-based QoS routing algorithm is considered. An IP-based QoS framework for mobile ad hocnetworks is presented in [157]. Adaptations of ReSerVation Protocol (RSVP) [158], a well-known resource reservation protocol used in the Internet, for mobile wireless networks areproposed in [159], [160]. However, to the best of our knowledge, none of these resourcereservation protocols has considered a reservation of intermediate nodes on a multi-hoproute as presented in this chapter (and introduced in Chapters 2 and 3). In addition, whilea few analytical models exist for NRB switched ad hoc wireless networks, similar modelshave not been reported for RB schemes. The performance analysis of RB schemes was firstconsidered in [58] where the effects of interference and retransmission were not taken intoaccount. In this chapter, we provide a more rigorous interference analysis and also include aretransmission model.

7.3. Network Models and Assumptions 169

Tier 1 Tier 2 Tier 3 …

Tx Rx

Figure 7.1 Tier structure of a grid network.

7.3 Network Models and AssumptionsIn this section, we describe network models and assumptions considered in this chapter.

7.3.1 Network TopologyThroughout the chapter, we consider a scenario where N nodes are distributed over a surfacewith finite area A. The node spatial density is defined as the number of nodes per unit areaand denoted as ρs � N/A (dimension [m−2]). To avoid edge effects, we assume the networksurface to be the surface of a torus [41] – however, the analytical technique presented in thischapter can be applied to other types of surfaces as well. The torus assumption allows usto treat any node in the network the same, whether it is at the edge or at the center of thenetwork. In a real scenario, the performance predicted by our analysis may not be extremelyprecise for nodes on the edge of the network surface. In this case, a more precise performanceevaluation may be obtained via simulations.

In this chapter, to gain fundamental insights into this important problem, we follow theapproach presented in Chapters 2 and 3, considering networks with a square grid topology,where each node has four nearest neighbors.48 An example of such a network topology isshown in Figure 7.1. Due to the structure of the square grid topology, the distance to thenearest neighbor, denoted by dlink, is fixed, and a route corresponds to a sequence of hopswith equal length. The distance dlink can be computed as follows. Note that constructing asquare lattice of N nodes over the surface of a torus with area A is equivalent to fitting N

small square tiles of area d2link into a large square of area A. Hence, it follows that Nr2

link = A.Finally, the distance between two nearest neighbors can be written as (see Chapter 2)

dlink =√

A

N= 1√

ρs.

48The analysis can also be extended for the case of a network with random topology by following the approachoutlined in [41].


7.3.2 Typical RoutesIn a peer-to-peer (P2P) ad hoc wireless network, where source–destination pairs are randomlyselected, the number of hops in each route is likely to be different. In this chapter, we considera route with an average number of hops as representative for average network performanceevaluation. In other words, we implicitly assume that routes with an average number of hopsare typical. We now estimate the average number of hops in a multi-hop route in a networkingscenario with grid topology.

Due to the spatial invariance on a torus, we can assume without any loss of generalitythat a source node is at the center of the network (see Figure 7.1). If a destination node isselected at random, the minimum number of hops to reach the destination can range from1 to 2imax, where imax is the maximum tier order. In other words, it takes one hop to reach adestination which is a neighbor of a source node in Tier 1, and it takes 2imax hops to reach thefarthest node from the center in Tier imax. The average number of hops can be obtained bycounting the number of hops on a route from the source to each destination node and findingthe average value. Assuming that each destination is equally likely, the average number ofhops in a route can be written as

nh = 1

N − 1

[4

imax∑i=1

i + 4imax∑i=1

2i + 8imax∑i=1

i−1∑j=1

(i + j)

]. (7.1)

The first summation term in (7.1) corresponds to the number of hops to reach any of the fournodes in alignment with the source at the center of the network in all possible tiers; the secondsummation corresponds to the number of hops to reach nodes on the four corners of each tier;finally, the third term (double summation) corresponds to the number of hops to reach theother nodes in each tier. With straightforward algebra, (7.1) can be simplified to

nh = 2

N − 1

(2i3

max + 3i2max + imax

). (7.2)

Since there are 8i nodes in tier i, it can be shown that if the number of nodes is sufficientlylarge, imax � √

N/2. Therefore, the average number of hops given by (7.2) can beapproximated as

nh �√

N

2+ 1√

N+ 3

2�

√N

2.

7.3.3 Bit Error Rate at the End of a Multi-hop RouteIn this subsection, we derive an expression for the bit error rate (BER) at the end of a multi-hop route, which is essential for the performance analysis presented in the next section.As indicated in the previous subsection, we assume that a communication route is givenby a sequence of links between nearest neighbors, i.e. with equal length. The BER at the endof a link between two neighboring nodes, denoted by BERlink, depends on the signal-to-noiseratio (SNR) at the receiving node (see Chapters 2 and 3). Generally, the link SNR is a functionof the transmit power, the distance between the transmitter and the receiver, the path loss, thethermal noise power and the interference power. In Chapter 3, a rigorous detection-theoreticapproach to the evaluation of the impact of the interference is proposed. In this chapter, forease of analytical treatment, we relax this treatment, since the focus in on route reservation.

7.3. Network Models and Assumptions 171

Assuming that the interfering signals are independent of each other, the SNR at the receivingnode of a link can be written as49

SNRlink = [GtGrc2/(4πfc)

2]Pt

dγ

link(Rb/B)(Pthermal + Pint)= αPt

dγ

link(Rb/B)(Pthermal + Pint)(7.3)

where Gt and Gr are transmitter and receiver antenna gains, γ is the path loss exponent, fc isthe carrier frequency, Pt is the transmit power, Pthermal is the additive white Gaussian thermalnoise power, Pint is the interference power, Rb is the data-rate (dimension [b/s]), and B isthe bandwidth (dimension [Hz]). The ratio Rb/B corresponds to the spectral efficiency of themodulation format used [40]. The thermal noise power Pthermal at the receiver can generallybe written as FkT0B, where F is the noise figure, k = 1.38 × 10−23 J/K is Boltzman’sconstant and T0 = 300 K is the room temperature [161].

The theoretical worst-case interference power, corresponding to a scenario where allnodes transmit simultaneously, in a network with grid topology can be expressed as [162]

Pint = αPt

dγ

link

imax∑i=1

[4

iγ+ 4

(√

2i)γ+

i−1∑j=1

8

(√

i2 + j2)γ

](7.4)

where i is the tier order. Comparing expression (7.4) for the average interference powerwith expression (3.12) in Chapter 3 in a scenario where the reserve-and-go (RESGO) MACprotocol is used, the reader can observe that the average interference power with the RESGOMAC protocol is obtained by scaling expression (7.4) with the transmission probability1 − e−λL/Rb . The worst-case interference assumption considered in this chapter correspondsto having no MAC protocol at all, i.e. to having the transmission probability equal to 1. Morediscussion on MAC protocols is given in section 7.6.6. Since the total interference noise isthe sum of many random signal components (all nodes are interfering), by the central limittheorem (CLT) the total interfering noise is approximately Gaussian50 [163]. For simplicity,in this chapter, we consider binary phase shift keying (BPSK) signaling – however, theproposed approach can be straightforwardly extended to any modulation format [40]. In thiscase, the link BER can be written as

BERlink = Q(√

2 SNRlink

)where Q(x) � 1√

2π

∫∞x

e−u2/2 du.

Assuming that uncorrected errors accumulate in successive links (a conservative assump-tion which is accurate at large link SNR values), the BER at the end of an nh-hop route canbe written as

BERroute � 1 − (1 − BERlink)nh . (7.5)

Given that a message is divided into packets of fixed length lp (dimension [b/pck]), in thecase of independent bit transmissions (as is the case for uncoded BPSK signaling) the packeterror rate (PER), denoted as PERlink, is related to the link BER as follows:

PERlink = 1 − (1 − BERlink)lp .

49The reader is referred to Chapter 3 for more details on the applicability of expression (7.3) for the link SNR.50The reader is referred once more to Chapter 3 for the applicability conditions of this assumption.


7.3.4 Retransmission ModelFor network communications to be reliable, retransmission of packets in error is needed.In this chapter, we consider a simple retransmission scheme where a packet in error will beretransmitted up to a maximum number of times kmax. If a packet is still received erroneouslyafter kmax retransmissions, then we assume that the receiver will have to take that packet inits current status.

The maximum number of retransmissions kmax is clearly an important parameter.In particular, in this chapter, it reflects the QoS in terms of the link PER. If the maximumnumber of retransmissions is too small, then the PER may not satisfy the desired QoS.The desired QoS will depend on the type of applications. For example, for the transmissionof very sensitive data, one may impose a QoS such that every packet must be ‘error-free’.However, for some applications, such as image transmission, every packet may not need tobe perfect – some errors in a packet might alter the colors of the image, but the image maystill be recognizable. We now derive an expression for kmax.

Let PERmaxlink be the maximum tolerable PER required by an application. The objective is

to guarantee that after kmax retransmissions, the link PER is lower than PERmaxlink . Assuming

that different packet retransmissions are independent of each other, the value kmax is theminimum possible value such that a packet is transmitted successfully with fewer than kmaxretransmissions. In other words, kmax is the smallest integer for which the following inequalityis satisfied:

kmax∑j=0

(PERlink)j (1 − PERlink) ≥ 1 − PERmax

link . (7.6)

Solving (7.6) for the lowest possible integer value of kmax, one obtains:

kmax =⌈

ln(PERmaxlink )

ln(PERlink)− 1

⌉(7.7)

where �·� is the ceiling operation. Without considering this operation, i.e. simply considering

kmax = ln(PERmaxlink )

ln(PERlink)− 1, it follows that kmax may not be an integer. However, a non-integer

value of kmax can be interpreted as follows. If, for example, kmax is equal to 0.01, it meansthat 1 retransmission in every 100 packet transmissions is required to satisfy the imposedQoS. In addition, (7.7) only makes sense if PERmax

link is lower than PERlink; that is, if PERmaxlink

is larger than PERlink, then no retransmission is required because the QoS is already satisfied.

7.3.5 MobilityAlthough the main body of our analysis refers to ad hoc wireless networks with fixed nodes(e.g. sensor networks [34] and wireless mesh networks [164]), it is also important to studyhow our results could be extended to a scenario with mobile nodes. While the impact ofmobility is the subject of Chapter 6, in this chapter we derive bounds on the maximum nodespeed which can be tolerated by the considered ad hoc wireless networks for a given packetsize, in order for the results derived for a scenario with stationary nodes to still apply.

Intuitively, the transmission of a message along a multi-hop route can be successfullyaccomplished, without route maintenance [4, 140], if every node in the route does not move‘too far’ from its neighbors during message transmission. In other words, a route does not

7.4. The Two Switching Schemes 173

break as long as each node does not move out of its range of its neighbors. In this section,we quantify the maximum node speed at which a message transmission on a route is notdisrupted. We use a simple and conservative mobility scheme. In particular, we assume that aroute breaks if a node moves, regardless of the direction, by more than a distance dmax, whichcorresponds to a fraction δ < 1 of the hop length dlink, i.e. dmax = δ dlink. Assuming that eachnode moves at the maximum speed vmax, the minimum time it takes for a link to break is

tbreak = dmax

vmax= δ dlink

vmax= δ

vmax√

ρs. (7.8)

A transmission is not disrupted as long as the transmission time of a message is not longerthan tbreak. Hence, given a desired value for the time tbreak to deliver an entire message fromsource to destination, from (7.8) the maximum tolerable speed vmax for each transmissionscheme can then be determined as

vmax = δ

tbreak√

ρs.

In section 7.5, we will evaluate the time it takes for a message to propagate from source todestination in a multi-hop route, for both RB and NRB schemes. Considering this value astbreak, we will then derive bounds on the maximum tolerable speed (or for a given maximumspeed, the message size that can be transmitted before a route breaks).

7.4 The Two Switching Schemes7.4.1 Reservation-Based SwitchingThe principle of operation of an RB scheme is fairly simple. Prior to data transmission, asource node reserves a multi-hop route to the destination through a route discovery phase [4]– this phase is discussed in detail in Appendix C. Once an intermediate node agrees to relaytraffic for a particular source in the network, it cannot initiate a session or relay messagesfor any other source until the on-going session is over. The source node releases the routeafter the session ends. We emphasize that this reservation pertains to node processing but notto the shared common radio channel. In other words, the intermediate nodes dedicate theirprocessing time only to the source which reserved the route; however, reservation of a multi-hop route does not give any node an exclusive access to the shared radio channel (in termsof frequency bands, time slots or spreading codes). Figure 7.2 (a) illustrates an example ofreserved routes in a network where an RB scheme is used.

In order to evaluate the performance of an RB switching scheme, we make the followingassumptions.

• Each node in the network generates messages according to a Poisson process withaverage arrival rate λm (dimension [msg/s]). While a node is acting as a relay, it stillgenerates its own messages, which are buffered for future transmission.

• The message length Lm is exponentially distributed51 with average value Lm(dimension [b]). Considering a fixed transmission data-rate Rb, the message durationis therefore exponentially distributed with mean value equal to Lm/Rb.

51Note that message lengths, in bits, should be characterized by a discrete probability distribution. However, foranalytical convenience, in this chapter we describe them with a continuous (exponential) probability distribution. Anon-integer value should realistically correspond to its closest integer value.


D1

S3

S2

S1

D2

D3

λ

λ

λ

λ

λ

λλ

λ

λλ

R’3R”3

S3R’3 R”3 D3

(a)

(b)

Virtual Server

λ

Figure 7.2 RB ad hoc wireless network model. (a) General scheme: each node has its ownqueue, and there are disjoint multi-hop routes in the network. (b) Equivalent conceptual modelfor the multi-hop route between S3 and D3 – observe that the queues of the relay nodes R′

3and R′′

3 and the destination node D3 are suppressed: in other words, the relay nodes and thedestination nodes do not involve new queues.

• Since intermediate nodes on a multi-hop route serve only one source node at a time,simultaneously active multi-hop routes are disjoint. In addition, given that each multi-hop route has a certain average length, there exists a maximum average number,denoted by Cs, of simultaneously active routes (an expression for Cs will be providedin section 7.5.1).

• If the number of nodes wishing to activate a multi-hop route is larger than Cs, thensome nodes have to wait before they can activate the route. The amount of time that anode has to wait before it can activate a route will be referred to as the ‘access delay’.

• The route activation process can be described by a conceptual ‘virtual request queue’which regulates requests from all sources (see Figure 7.3). In this sense, one canimagine that the first message of the queue at each source node is immediatelyforwarded to the virtual request queue. As will be shown later, the virtual server modelsthe waiting time that a source experiences, after discovering a route, before being ableto activate it. Each possibly active multi-hop route corresponds, in this conceptualmodel, to a virtual server which takes care of the messages in the virtual request queue.The number of servers corresponds to the maximum average number Cs of disjointmulti-hop routes in the network.

• The time spent by a message in the virtual request queue corresponds to the timenecessary for intermediate nodes to become available. Therefore, a message in

7.4. The Two Switching Schemes 175

Virtual Server 1

Virtual Server 2

Queue at node 1

Queue at node 2

Queue at node N-1

Virtual Request Queue

Queue at node N

Virtual Server Cs-1

Virtual Controller

λ

λ

λ

λ

Virtual Overlay System

Virtual Server Cs

Figure 7.3 Conceptual queuing model for a reservation-based wireless network: realqueues at each node are connected to an overall virtual request queue. Each virtual servercorresponds to a possible multi-hop route. (Reproduced by permission of © 2005 IEEE.)

the virtual request queue might not be served in the order in which it arrives.However, according to Little’s theorem, the average delay in the system will be thesame regardless of the specific queuing discipline employed [165].

• The total delay between generation and complete transmission of a message, at eachsource node, is obtained by adding three terms: (i) the time spent in the node’s ownqueue (denoted by WRB

o ); (ii) the time spent in the virtual request queue (denoted byWRB

v ); and (iii) the time spent in the server (denoted by T RBs ). In particular, the queue at

each node can be modeled as an M/G/1 queue with service time τRB = WRBv + T RB

s .

• The combination of the virtual request queue and the Cs virtual servers will be denotedas a ‘virtual overlay system’. In particular, there are N flows of information at its input,coming from the N nodes. Invoking Kleinrock’s independence approximation [2], thetotal arrival process at the input of the request queue can be modeled as being Poissonwith rate Nλm. Hence, it follows that the virtual overlay system shown in Figure 7.3can be modeled as an M/M/Cs/∞/N system [166].

7.4.2 Non-reservation-Based SwitchingIn the case of NRB switching, there is no reservation of a route prior to data transmission.As opposed to an RB scheme, in an NRB network communication scenario, multi-hop routescan overlap. In particular, a node can serve as a relay node for more than one route. In otherwords, when a node receives a message from another node (i.e. it acts as a relay), it placesthat message in its own queue (intermingled with its own generated messages). The messagesin the queue are transmitted sequentially (i.e. the priority given to relay and new locallygenerated messages is the same). An example of routes in a network with an NRB scheme isshown in Figure 7.4. As in the case of RB switching, we assume that the message generationprocess is Poisson and that the message length is exponentially distributed with averagevalue Lm.

Unlike the case with RB switching (where the relay nodes give absolute priority to therelayed messages, stopping to serve their own messages), each multi-hop route is a tandem ofqueues, and the whole network can also be viewed as a tandem of queues. As a result, Burke’s


D1

S3

S2S1

D2

D3

λ

λ

λ

λ

λ λ

λ λ

λ

λ D’3

Figure 7.4 NRB ad hoc wireless network model: each node has its own queue and the multi-hop routes are not necessarily disjoint. In particular, two possible multi-hop routes betweenS1 and D1 are shown (dashed and dashed-dotted links). Observe that the same source cantransmit successive messages to a different destination (for example, source S3 might betransmitting to destinations D3 and D′

3).

r r

r

r

r r

r r

Tandem of Queues on a Multi-Hop route

Figure 7.5 Conceptual queuing model for a non-reservation-based wireless network: thequeues at the nodes of a multi-hop route constitute a tandem of queues. (Reproduced bypermission of © 2005 IEEE.)

theorem can be applied, and each individual node can be modeled as an M/M/1 queue [2].The conceptual model of an NRB network is shown in Figure 7.5.

7.5 Analysis of the Two Switching TechniquesAnalytical models for evaluating the performance, in terms of delay, goodput and throughput,of RB and NRB schemes are presented in the following two subsections.

7.5.1 Reservation-Based SwitchingMaximum Number of Disjoint Routes

One of the key factors that affects the performance of an RB scheme is the maximum numberof disjoint routes in the network. This corresponds to the number of virtual servers Cs inthe M/M/Cs/∞/N queuing model described in section 7.4.1. Given that each route has

7.5. Analysis of the Two Switching Techniques 177

an average number of hops nh, the maximum number of disjoint routes, corresponding toa scenario where each node belongs to a particular route (i.e. as the source, a relay orthe destination), can simply be written as

Cs � N

nh. (7.9)

Delay

With the assumptions specified in section 7.4.1, each node is modeled as an M/G/1 queue.The average delay that each message experiences is equal to the sum of the mean waitingtime in the source queue, denoted as E[WRB

o ], and the mean service time E[τRB], where, aspreviously defined, τRB = WRB

v + T RBs . The mean waiting time in an M/G/1 queue can be

computed using the Pollaczeck–Khinchin formula [2]:

E[WRBo ] = λmE[τ 2

RB]2(1 − λmE[τRB]) . (7.10)

It is clear from (7.10) that one needs to compute the first and second moments of theservice time τRB, which can be derived from the statistics of the total time spent in theM/M/Cs/∞/N virtual overlay system. The probability density function (PDF) of the timespent in the M/M/Cs/ ∞/N system is [166]

fτRB (x) = µe−µxCs−1∑n=0

an +N−1∑n=Cs

an

[µe−µx

(Cs

Cs − 1

)n−Cs+1

− µ

(Cs

Cs − 1

)n−Cs+1 n−Cs∑r=0

e−µx [µ(Cs − 1)x]rr!

]

where an is the probability that there are n ‘customers’ in the virtual overlay system (i.e. n

nodes are transmitting or waiting to start transmitting an already generated message) and µ

is the average service rate.The probability distribution {an} of the number of customers in an M/M/Cs/∞/N

system involves the computation of large factorials (e.g. N !), which leads to numericalproblems. To analyze a large-scale ad hoc network, we exploit the fact that when the numberof sources is large, the steady-state probability distribution of an M/M/Cs/∞/N systemfollows that of an M/M/Cs system [166]. The first and second moments of the time thateach message spends in the system are given by

E[τRB] = 1

µ+ (Cs, λm/µ)

µCs − λm(7.11)

E[τ 2RB] = 2

µ2 + 2 (Cs, λm/µ)

[µCs − λm]2 (7.12)

where

(Cs,

λm

µ

)�

[Cs−1∑n=0

(λm/µ)n

n! + (λm/µ)Cs

Cs! (1 − λm/µCs)

]−1(λm/µ)Cs

Cs! (1 − λm/µCs).


Since the route is reserved, it is possible to transmit a message from the source to thedestination using a pipelining method [167]. Assuming that the whole message of length Lmbits is divided into packets of fixed length lp bits, the total number of packets per messageis Lm/lp. Suppose there are nh links on a route from the source to the destination. The totaltime to transmit a message with a pipelining method can be computed as

T RBs = Lm

Rb+ (nh − 1)

lp

Rb. (7.13)

Consequently, the total transmission time T RBs , as given in (7.13), is not exponentially

distributed. This violates the exponential service time assumption. However, if Lm � nhlp,then the second term on the right-hand side of (7.13) is negligible, and the exponential servicetime assumption still holds.

In the case of retransmission, the message transmission time can be generalized as

T RBs = Lm

Rb(1 + K) + (nh − 1)

lp

Rb(1 + K) (7.14)

where K is the number of retransmissions per link. Since K is a discrete random variable, thetransmission time becomes a function of two random variables (Lm and K). The PDF of thetotal delay in this case can be written as

fT RBs

(t) =∞∑

j=0

[µ

1 + jeµt/(1+j)

] [(PERlink)

j (1 − PERlink)]u(t) (7.15)

where u(t) is the unit step function, defined as

u(t) �{

1t ≥ 00t < 0.

In particular, (7.15) can be derived directly from the total probability theorem [83]; theexpression in the first set of square brackets is the conditional PDF of the transmission timegiven that the number of retransmission is j , and the expression in the second set of squarebrackets is the probability mass function of the random variable K .

The PDF given in (7.15) is not exponential, and it may not have a closed-form expression.Fortunately, given that the number of retransmissions is j , the conditional PDF of thetransmission time has the following exponential structure:

fT RBs /j (t/j) = µ

1 + jeµt/(1+j)u(t). (7.16)

Consequently, even in the case of retransmissions, one can still analyze the delay performanceof the network communication system using the same queuing model, but with a modifiedservice time. From (7.16), it can easily be observed that the new mean service time is(1 + j)/µ. To take advantage of this, the number of retransmissions j must be specified.To be conservative, the number of per-link packet retransmissions which will be used in thefollowing is the maximum number of retransmissions kmax introduced in section 7.3.4. In thiscase, the service time is exponential with mean service time Lm(kmax + 1)/Rb.


Goodput

The goodput is the total number of bits received correctly per unit time at their respectivedestinations. Route goodput pertains to the amount of data transported correctly over timeon a single multi-hop route with an average number of hops. Network goodput, on the otherhand, is the aggregate amount of goodput due to all routes. It measures how much error-freedata can collectively be transferred in a network over time. Route goodput, denoted as β, andnetwork goodput, denoted as η, can be written as follows, respectively:

β � λmLm(1 − BERroute) (7.17)

η � β E[Nar] (7.18)

where E[Nar] is the expected number of active routes. The expected number of active routesis equal to the expected number of ‘busy servers’ in an M/M/Cs queuing model, which, inthis case, is equal to Nλm/(Rb/Lm).

Throughput

In order to capture the effects of packet retransmission according to the imposed QoS on linkPER (i.e. PERth), we use throughput instead of goodput. Throughput measures the rate atwhich a packet is received at its destination. In the case of no retransmission, the rate at whichthe packets are delivered to the destination is equal to the packet generation rate λp (dimension[pck/s]). In the case of retransmissions, the throughput decreases because multiple copies ofthe same packet are transmitted. The worst-case throughput, where each packet requires kmaxretransmissions, can be expressed as

ν � λp

nhkmax + 1. (7.19)

Note that when kmax is equal to zero, (7.19) corresponds to the case of no retransmission.The network throughput, denoted as ζ , can be computed by adding the throughput of all theactive routes, obtaining

ζ � ν E[Nar]. (7.20)

7.5.2 Non-reservation-Based SwitchingAverage Number of Routes per Node

In an NRB scheme, a node can relay traffic generated by multiple sources. However, thestability condition requires that the total incoming traffic rate is lower than the service rate.Consequently, it is important to know how much traffic a node carries for other sources.With the uniform traffic assumption (i.e. every node generates approximately the sameamount of traffic), in order to compute the average traffic relayed by a node, it is sufficientto compute the average number of routes passing through it. In this section, we derive anexpression for this number.

Considering a grid topology as shown in Figure 7.6, we want to find the average numberof routes passing through a generic node, say node V. We start by finding the probabilitythat node V belongs to a route of a particular source–destination pair. Let Si,j be a sourcenode at position (i, j) relative to the position of a node V, where i is the number of hops


Si,j

V

i

jimax

Figure 7.6 The node V represents a possible relay node for source node Si,j . (Reproducedby permission of © 2005 IEEE.)

in the horizontal direction and j is the number of hops in the vertical direction. Due to thespatial invariance on a torus, one can assume, without loss of generality, that the source isat the origin and node V is at position (i, j) relative to the source, as shown in Figure 7.6.We assume that a source can select any node in the network, at position (x, y) relative tothe source, as its destination. In addition, it is assumed that the shortest route between thesource and the destination is used. In the case where there is more than one shortest route, asource selects one of these routes randomly. For conciseness, let us denote the probability thatnode V is on a route of Si,j as P[V(i, j)], and let us denote the conditional probability thatV is on a route of Si,j , given that Si,j selects a destination at (x, y), as P[V(i, j)/D(x, y)].With these assumptions, one obtains:

P[V(i, j)/D(x, y)] =

0 x < i or y < j

np

ntotherwise

(7.21)

where np is the number of all possible shortest paths to the destination passing through nodeV and nt is the number of all possible shortest paths to the destination. In the case where x < i

or y < j , P[V(i, j)/D(x, y)] is equal to zero because V cannot possibly be on the shortestpath from Si,j to the destination node at (x, y). In the remaining cases, using combinatorics,it can be shown that

np =(

i + j

i

)(x + y − i − j

x − i

)nt =

(x + y

x

).

The next step is to find the probability that V is on a route of Si,j without conditioning on thedestination. Using the law of total probability [163], one obtains:

P[V(i, j)] =∑

∀(x,y)

P[V(i, j)/D(x, y)] P[D(x, y)] (7.22)


where P[D(x, y)] is the probability that a node at position (x, y) relative to Si,j is selected asthe destination. Assuming that a source randomly chooses a destination, P[D(x, y)] is simplyequal to 1/(N − 1). Combining the expressions given in (7.21) and (7.22), one gets

P[V(i, j)] = (i + j)!i!j !(N − 1)

imax∑x=i

imax∑y=j

(x + y − i − j)!x!y!(x + y)!(y − j)!(x − i)! .

By neglecting edge effects (according to the torus assumption), we can assume that node Vis at the center of the network. The average number of routes passing through V can now becomputed as

nr =∑∀(i,j)

P[V(i, j)].

Next, we assume that each node in the network generates approximately the same amount oftraffic according to a Poisson process with average rate λm (dimension [msg/s]). Then, theaverage rate of the traffic entering a node is given as

λtotal = λm +nr∑

i=1

λm = (nr + 1)λm.

Delay

Since each source does not have a dedicated route, a message transmitted in a route willexperience, in addition to the transmission delay, a queuing delay at each node it traverses.According to the assumptions in subsection 7.4.2 (in particular, the applicability of Burke’stheorem to an NRB switching network [2]), the average delay that a packet experiences ateach node it traverses corresponds to that of an M/M/1 queue and is given by

E[T NRB] = 1

Rb/Lm − λtotal. (7.23)

The total average delay for a message from the source node to the destination node of a multi-hop route is obtained as the sum of the average delays experienced at each intermediate node.In other words, E[T NRB

total ] = nhE[T NRB].As discussed earlier, given that the number of retransmissions is kmax, the service time for

transmitting a packet is still exponentially distributed. If a message (exponentially distributed)of size Lm bits is divided into packets of (fixed) length lp b/pck, the time it takes to transmita single packet is (1 + kmax)lp/Rb. Since there are Lm/lp packets in a message, the time atwhich the last packet will reach the next hop is (1 + kmax)Lm/Rb. Hence, in the case withretransmission, the expected per-link message transmission time in (7.23) can be generalizedas

E[T NRB] = 1

[Rb/Lm(1 + kmax)] − λtotal. (7.24)


Table 7.1 Major network parameters used in the scenarios considered

Parameters Values

Transmit power (Pt) 1 mWData rate (Rb) 1 Mb/sAverage message length (m) 106 bitsPacket length (lp) 103 bitsArea of the network (A) 106 m2

Path loss exponent (γ ) 3Carrier frequency (fc) 2.4 GHzRoom temperature (T0) 300 KNoise figure (F ) 6 dB

Goodput

Route goodput and network goodput of an NRB switching network can be computedin the same manner as that of an RB scheme. Note that, in the calculation of routegoodput, the amount of traffic should correspond to that generated only by source nodes(i.e. excluding the relay traffic). Since there are N sources, the network goodput of an NRBnetwork can then be written as

η = λLm(1 − BERroute)N. (7.25)

Throughput

The throughput of an NRB scheme can be computed in the same manner as in the case of anRB scheme.

7.6 Results and DiscussionNumerical results, along with their implications, are presented and discussed in this section.In all the considered scenarios, the main network parameter values used in the analysis areshown in Table 7.1, unless stated otherwise.

7.6.1 Switching Scheme and Traffic LoadIn this subsection, we discuss the tradeoff, in terms of goodput and delay, between the twodescribed switching schemes. In Figure 7.7, the network goodput of the considered switchingschemes, computed via (7.18) and (7.25), is shown as a function of the traffic load in (a) theideal case, where interference is neglected, and (b) the theoretical worst case, where allnodes transmit simultaneously, respectively. The worst-case interference power is computedvia (7.4). It is expected that the performance of a realistic ad hoc wireless network willbe somewhere between these two cases – in particular, case (b) is overly pessimistic, andperformance in a real scenario is expected to be definitely better. Two different values ofthe number of nodes in the network are considered, as indicated in the figure. Note that,

7.6. Results and Discussion 183

by keeping the area of the network fixed, increasing the number of nodes corresponds toa node spatial density increase. Generally, it is observed that the network goodput of anNRB switching scheme is higher than that of the corresponding RB scheme at every valueof traffic load and in each scenario (either ideal or worst case). This is due to the fact that anNRB scheme can support a higher number of routes (i.e. the disjoint routes constraint is notimposed in the NRB switching scheme). In addition, the performance difference between thetwo switching schemes increases, although not significantly, in each scenario (either ideal orworst case), as the network becomes denser.

To verify the analytical results, we also compute the network goodput via Monte Carlosimulations. Details of the simulations are given in Appendix D (section D.1). The simulationresults are shown in Figure 7.7 (a) and (b) with discrete symbols. It can be observed that in theideal case there is an excellent match between the simulation results and the analytical results.However, in the case with interference, the network goodput obtained from the simulationsis slightly lower than that predicted by the analysis. This may be due to the fact that whenone generates Gaussian random variables with a large variance, some samples might be verylarge (i.e. the tails of the distribution matter). However, the effect of the tails may not becaptured by the analysis, since in this case average values are considered. The problem isexacerbated for large noise variances, i.e. in the realistic case with interference, whereas thisis not a problem in the ideal case where the noise variance, associated with the thermal noise,is relatively small.

In Figure 7.8, the average packet delay, denoted as tp, is shown as a function of the averagepacket generation rate λp, for different values of the number of nodes N . The average delayper packet is defined as the arithmetic average between (i) the time the first packet in themessage arrives at the destination and (ii) the time that the last packet in the message arrivesat the destination. The message delays for RB and NRB switching schemes are computedvia (7.13) and (7.23), respectively. As expected, it is observed that the delay increases asthe traffic load increases. The results in Figure 7.8 show that an RB scheme performs betterthan an NRB scheme up to a critical load, which makes the delay of the RB scheme go toinfinity very rapidly. Below this critical load, the delay of an RB scheme is very insensitiveto the traffic load. The overall behavior of an RB scheme can therefore be characterized asbimodal: either almost constant, with respect to the traffic load, or infinite. Figure 7.8 showsthat the delay of an RB scheme is lower than that of an NRB scheme by more than one orderof magnitude for every considered node spatial density. Nonetheless, the maximum trafficload that an RB scheme can support is lower than that of an NRB scheme. This is due to thedisjoint routes constraint. It is important to observe, however, that the difference between themaximum traffic loads that the two schemes can support decreases as the node spatial densityincreases. In other words, an RB switching scheme becomes preferable, delaywise, in densead hoc wireless networks.

To verify the analytical results, we have simulated the delay of the queuing models usedfor RB and NRB schemes (i.e. the queuing models shown in Figures 7.3 and 7.5). Moredetails on the simulations can be found in Appendix D (section D.2). The simulation resultsare shown with discrete symbols (i.e. ◦, �, ♦ and �) in Figure 7.8. It can be observed thatsimulation and analytical results are in excellent agreement.

7.6.2 Effects of InterferenceIn this subsection, we discuss the impact of the interference on the network performance.Figure 7.9 illustrates the network goodput of an NRB scheme as a function of the traffic


0 20 40 60 80 10010

2

104

106

108

λp

lp

[kb/s]

η [b/s]

RB SchemeNRB Scheme

N = 529

N = 1089

(a)

0 20 40 60 80 10010

0

102

104

106

λp

lp

[kb/s]

η [b/s]

RB SchemeNRB Scheme

N = 529

N = 1089

(b)

Figure 7.7 Goodput of the two switching schemes in (a) the ideal case and (b) the worst case.The network goodput of the RB scheme and the NRB scheme obtained from the analysis areshown with the solid lines and with the dashed lines, respectively. The simulation results areplotted with discrete symbols (e.g. ×, •, ◦ and �). For (a), each simulation curve coincideswith the analytical curve, and for (b) each simulation curve corresponds to the analyticalcurve immediately above it. (Reproduced by permission of © 2005 IEEE.)

generation rate given by the product λplp (dimension [b/s]). Both the ideal case and the worst-case interference scenarios are considered. The network goodput of the RB and the NRBschemes obtained from the analysis are shown with the solid lines and the dashed lines,respectively, while the simulation results are shown with discrete symbols.

Generally, from Figure 7.9 it can be observed that the network goodput increases as thetraffic generation rate increases in both ideal and worst-case scenarios. This is due to our


0 20 40 60 80 10010

−1

100

101

102

103

104

λp [pck/s]

tp [s]

RB SchemeNRB Scheme

N = 529N = 1089

Figure 7.8 Delay comparison of the two switching schemes. The average route delay ofthe RB and the NRB schemes obtained from the analysis are shown with the solid lines andthe dashed lines, respectively. The route delay obtained from simulations are shown withdiscrete symbols (e.g. ◦, �, ♦ and �). Each simulation curve coincides with the analyticalcurve associated with it. (Reproduced by permission of © 2005 IEEE.)

0 20 40 60 80 10010

0

102

104

106

108

λplp

[kb/s]

η [b/s]

Ideal CaseWorst Case

N = 529N = 1089

Figure 7.9 Goodput of the NRB scheme compared at different node densities. The networkgoodput for the ideal case and the worst case obtained from the analysis are shown with thesolid lines and the dashed lines, respectively. The simulation results are plotted with discretesymbols (e.g. ×, •, ◦ and �). While ◦ and • denote the simulation results when N = 1089for the ideal case and worst case, respectively, � and × denote the simulation results forN = 529 for the ideal case and worst case, respectively.


0 10 20 30 40 50 60 7010

0

102

104

106

108

λp

lp

[kb/s]

η [b/s]

Ideal CaseWorst Case1/10 Interference

Figure 7.10 Goodput of the NRB scheme compared at different levels of interference.The simulation results are plotted with discrete symbols (e.g. ×, • and �). In the ideal case,the simulation curve coincides with the analytical curve. In the cases with interference, eachsimulation curve corresponds to the analytical curve immediately above it.

simplifying assumption that ‘none or all’ nodes interfere. However, in a real scenario, theinterference would certainly depend on the traffic generation rate. In fact, the interference isexpected to increase, as the traffic load increases. There would be a clear tradeoff betweensupporting high traffic load and keeping the interference low. The model proposed in thischapter does not take this aspect into account yet, but extensions in this direction are possible.However, the actual performance would still be bounded between those relative to ideal andworst cases, as shown here in Figure 7.9.

It is observed that the separation between the two bounds (ideal and worst cases) increasesas the number of nodes in the network increases. This is reasonable because, keeping the areafixed, the amount of interference is expected to increase as the number of interfering nodesincreases (i.e. the network becomes denser). For a large number of nodes (e.g. N = 1089),the two bounds are separated by almost four orders of magnitude. This clearly indicates thatthe network, especially if very dense, cannot function well without the use of a MAC protocoleffective at canceling or mitigating the interference. The same behavior is also observed inthe case of RB schemes.

In order to understand the impact of the interference on the network performance, we alsoconsider cases where the interference power is reduced. Figure 7.10 illustrates the networkgoodput of an NRB scheme computed via (7.25) as a function of the average bit generationrate, i.e. λplp. Three possible cases for the interference level are considered in this figure:(i) no interference (ideal case); (ii) worst-case interference; and (iii) a scenario where theinterference power is one-tenth of the worst case. The number of nodes is fixed at N = 1089.Interestingly, the network goodput increases by about two orders of magnitude when theworst-case interference power is reduced to one-tenth. A similar behavior is also observed inthe case of RB schemes.

Reduction of the total interference power could be obtained, for example, by dividingthe common (shared) communication channel into subchannels (e.g. in frequency, time or


0 10 20 30 40 50 60 7010

−1

100

101

102

103

104

λp [pck/s]

tp [s]

RB SchemeNRB Scheme

kmax

= 7.38 kmax

= 0.68 kmax

= 0

Figure 7.11 Delay of the two switching schemes compared at different levels ofinterference. (Reproduced by permission of © 2005 IEEE.)

code space). Only nodes using the same subchannel would interfere with one another. As aresult, the total interference power would decrease. In general, a MAC protocol shouldbe designed in such a way that the total interference is reduced and the network goodputbecomes close to the ideal performance bound. As an example, a MAC protocol which canguarantee a low interference level and is practical for an RB switching scheme could beone which uses code division multiple access (CDMA) and per-route spreading codes [67](see also Chapter 5). In this case, it is possible to show that the interference power is reducedproportionally to the spreading factor of the considered spreading codes.

Figure 7.11 illustrates the impact of the interference on the delay performance of thetwo switching schemes. The message delays for RB and NRB schemes are first computedvia (7.14) and (7.24), respectively. Then, the average packet delay tp is computed using theapproach described earlier for Figure 7.8. Different values of the number of retransmissionskmax for keeping PERth above 10−2 are considered. An increase of kmax can be interpretedas an increase of the interference level. In other words, higher interference requires ahigher number of retransmissions per packet. In general, one can conclude that the averagepacket delay of the two schemes increases as the traffic load increases. In addition, asthe level of interference increases, the delay also increases due to a higher number ofretransmissions.

The results in Figure 7.11 show that the delay of an RB scheme is lower than thatof an NRB scheme by more than one order of magnitude for every considered value ofkmax. Nonetheless, the maximum traffic load that an RB scheme can support is lower thanthat of an NRB scheme. This is due to the constraint on disjoint routes. It is important toclarify, however, that the difference between the maximum traffic loads that the two schemescan support decreases as the number of retransmissions increases. In other words, an RBswitching scheme becomes preferable, delaywise, in an environment where the interferenceis high.

Figure 7.12 illustrates the impact of the interference on the throughput of the twoswitching schemes. The network throughput of the two schemes is compared for different


0 10 20 30 40 50 6010

−2

100

102

104

λp [pck/s]

ζ[pck/s]

RB SchemeNRB Scheme

kmax

= 0

kmax

= 0.68

kmax

= 7.38

Figure 7.12 Throughput of the two switching schemes compared at different levels ofinterference. (Reproduced by permission of © 2005 IEEE.)

values of the number of retransmissions kmax that keep PERth above 10−2. It can be observedthat the throughput of both schemes decreases as the number of retransmissions increases.However, the throughput of the NRB scheme is larger than that of the RB scheme, due to thehigher number of active multi-hop routes.

7.6.3 Effects of the Number of Simultaneously Active Disjoint Routes

In an RB switching scheme, the number of simultaneously active disjoint routes is animportant factor, which significantly affects network performance. Based on our analysis,the maximum number Cs of routes that can simultaneously be active is, on average, givenby (7.9). In reality, however, the maximum number of disjoint routes that can concurrentlybe active may not be as large as the average number obtained with our analysis. In thissubsection, we show how the number of active routes affects the performance of the RBswitching scheme. In other words, we try to understand what would happen in a realisticscenario where the number of active routes is lower than the theoretical maximum value.

In Figure 7.13, the delay of an RB switching scheme is evaluated for three differentvalues of the number of disjoint active routes: (i) the maximum average number Cs ofroutes estimated from the analysis; (ii) half of the maximum number, i.e. Cs/2; and (iii) one-tenth of the maximum number, i.e. Cs/10. It is observed that as the maximum number ofsimultaneously active routes increases, the total amount of traffic which can be supported bythe network also increases. In addition, it is interesting to see that the delay behavior of an RBscheme is still insensitive to the amount of traffic load – provided, of course, that the trafficload is sufficiently lower than the critical value. This is due to the fact that the waiting timein the system is much smaller than the message transmission time.

In Figure 7.13, the delay performance of an NRB scheme is also shown for comparison.In general, the delay of an RB scheme is smaller than that of an NRB scheme. However, an


0 10 20 30 40 50 6010

−1

100

101

102

103

λp [pck/s]

tp [s]

Cs

Cs/2

Cs/10

NRB Scheme

Figure 7.13 Delay of an RB scheme (in the ideal case without interference) comparedat different values of maximum number of simultaneous active routes. (Reproduced bypermission of © 2005 IEEE.)

NRB scheme can support a much higher traffic load compared to an RB scheme, especiallywhen the maximum number of simultaneously active routes is small. In a real network, theaverage number of simultaneously active routes is expected to be lower than that of the torusnetwork. From simulations, it is shown that the average number of simultaneously activeroutes in a real network is approximately

√N , which is about half of the number of active

routes in a torus network.52 Thus, in a real network, the performance of the RB scheme shouldbe more like the dotted curve (i.e. Cs/2) shown in Figure 7.13.

7.6.4 Effects of Node Spatial DensityAs previously observed (in particular, from Figures 7.8 and 7.11), the average delay providedby an RB scheme is insensitive to the traffic load up to a critical value of the packet generationrate, denoted by λcrit

p , beyond which the delay goes to infinity. This suggests that the critical

load λcritp of an RB scheme is approximately equal to the crossing value above which an NRB

scheme becomes delaywise more appealing than an RB scheme. In Figure 7.14 (a) and (b),the critical traffic load λcrit

p , at which the delay curves of RB and NRB schemes asymptoticallyapproach infinity, is shown as a function of the number of nodes N in the cases with Cs andCs/2 active routes, respectively. The top border of the grey area corresponds to λcrit

p for an

NRB scheme, whereas the line between grey and black areas is λcritp for an RB scheme. The

results in Figure 7.14 (a) and (b) should be interpreted as follows. For a given number of nodes(or node spatial density, since the area is fixed) and a given value of the packet generation rate,it is possible to locate the corresponding network operating point in the figure. The schemeto be preferred is the one associated with the region inside which the network operating pointfalls. In particular,

52Details about the simulations are given in Appendix D (section D.3).


1000 1500 2000 2500 30000

20

40

60

80

100

N

λp

[pck/s]

NRB

RB

λcritp

for NRB

λcritp

for RB

(a)

1000 1500 2000 2500 30000

20

40

60

80

100

N

λp

[pck/s]NRB

RB

λcritp

for NRB

λcritp

for RB

(b)

Figure 7.14 Critical load of the two switching schemes when the number of disjoint activeroutes allowed is (a) maximum average number estimated from the analysis and (b) half ofthe estimated number. ((a) Reproduced by permission of © 2005 IEEE.)

• the dark shaded region in these two figures represents the region where the delay of anRB scheme is smaller than that of an NRB scheme, i.e. the operative region where anRB scheme should be chosen to optimize the network delay performance;

• similarly, the light shaded area in these figures represents the region where the delay ofan NRB scheme is better than that of an RB scheme, i.e. the operative region where anNRB scheme should be chosen to optimize the network delay performance.


0 10 20 30 40 50 60 700

5

10

15

20

25

30

35

λp [pck/s]

vmax

[m/s]

Lm

= 1 Mb/msg

Lm

= 0.5 Mb/msg

Lm

= 0.1 Mb/msg

NRB Scheme RB Scheme

Figure 7.15 Effect of mobility.

7.6.5 Effects of Mobility

The performance of the two switching schemes, in terms of maximum tolerable speed vmax,as defined in section 7.3.5, is shown in Figure 7.15. Three different values of average messagelengths are considered: Lm = 1 Mb/msg, Lm = 0.5 Mb/msg and Lm = 0.1 Mb/msg,respectively. In this scenario, δ is equal to 0.1. It can be observed that, in general, anRB scheme is more robust to node mobility, i.e. it can tolerate a higher maximum nodespeed. More precisely, from the figure one can observe that an RB scheme can supportcommunication in a scenario where nodes move at a pedestrian speed (up to 3 m/s) or evenat a vehicle speed (up to 30 m/s for short message size), whereas an NRB scheme can hardlysupport any mobility. This behavior can be explained as follows. In an RB scheme, since theroute is reserved, it takes less time to transmit a message. Consequently, the total allowed timebefore a route breaks is longer than that allowed by an NRB scheme, in which an intermediatenode has to serve multiple routes.

Note that in the case of an RB scheme, the maximum tolerable speed is almost constant,with respect to the average packet generation rate, before dropping to zero. This can beexplained by considering the delay behavior shown in Figure 7.8. In fact, since the delayis almost constant with respect to the packet generation rate, and since the transmissiontime is relatively small, the robustness against speed becomes almost independent of thepacket generation rate. Note that the actual load where the maximum tolerable speed drops tozero corresponds to the load where the delay explodes. In addition, one can observe that themaximum tolerable speed to avoid route breaking increases as the message size decreases.

Alternatively, Figure 7.15 can also be interpreted as follows. For given maximum speedvmax and traffic load, there is a maximum tolerable average message length at which amessage can reach the destination before a communication route breaks. Depending on typesof nodes in ad hoc wireless networks (e.g. pedestrians, cars), vmax will be different. As vmaxincreases, the message length has to decrease correspondingly. One could argue that, incertain applications it may be impossible to control the speed vmax with which mobile nodesmove. The results in Figure 7.15 suggest that if vmax and the traffic generation rate are known,


then the message length Lm should be equal to or less than a fixed value so that the messagecan reach the destination before the route breaks.

Figure 7.15 also suggests that moderate mobility (corresponding to pedestrian or slowvehicle speed) does not significantly affect the goodput and delay performance of an RBscheme. In other words, the goodput and delay performance of an RB scheme presentedearlier does not change much if mobile nodes move at moderate speeds (lower than vmax).On the other hand, the performance of an NRB scheme, in terms of goodput and delay, willsignificantly degrade if mobile nodes move even slowly, since the maximum tolerable speedis basically zero.

7.6.6 Implications on Practical ScenariosIn the analysis presented in this chapter, we have made a number of simplifying assumptionsto keep the analysis tractable. Of course, these assumptions cannot completely reflect whatreally happens in a real ad hoc wireless network. In this section, we briefly discuss how theperformance of RB and NRB schemes will be affected in a realistic scenario.

• Network topology: we have assumed a square grid topology over the surface of a torus,which allows us to treat any node the same in the analysis. In a real ad hoc network,nodes near the edge of the network are likely to have higher number of hops to thedestination than nodes near the center of the network. Thus, the delay for these nodescould be higher than what is predicted by our analysis.

• MAC protocol: this protocol has not been taken into account in the analytical modelpresented in this chapter. This has implications for the interference and the delay.In terms of interference, we have considered the two extremes: (i) the ideal case wherethere is no interference and (ii) the worst case where all nodes transmit simultaneously.In an RB scheme, the ideal case could be realized if a CDMA scheme with per-route spreading codes is used. This would eliminate the interference among differentactive routes. However, interference can still occur among nodes within the same route.To reduce the intra-route interference, each node of the same route could transmit ondifferent frequencies. The same frequency can be reused for links in the route thatare sufficiently far apart. With this integration of spreading codes and frequencies, theinterference could be reduced to a level that is close to the ideal case. Similarly, in theNRB scheme, the ideal case could be realized if each link uses a spreading code that isdifferent from the other links. The same code can also be reused if the links using thesame code are sufficiently far apart. Distributed code assignment algorithms for multi-hop networks, for example, can be found in [168,169]. The same conclusions also holdif frequency reuse is considered.

The worst-case interference corresponds to having no MAC protocol at all. Obviously,a real ad hoc wireless network cannot function without a MAC protocol, and any MACprotocol employed should yield a higher goodput. Thus, the worst-case interferencecould be used as a benchmark for performance comparison.

Without any MAC protocol being considered, the queuing models in this chapter havenot yet taken multiple access delay into account. It remains to be seen how delayfrom a specific MAC protocol employed would affect the performance of RB andNRB schemes. However, for the RB scheme, with the ideal MAC protocol mentionedearlier (i.e. integration of the per-route spreading code and use of different frequencies

7.7. Concluding Remarks 193

on each hop of a route) it is possible to transmit packets with the pipelining method.This corresponds to the scenario considered in our queuing model, and thus the delaycan be predicted by the model. Similarly, for the NRB scheme, if the suggested idealMAC protocol (i.e. a different code for each link with possible code reuse) is employed,then the delay is already captured by our queuing model. If other MAC protocols areused, then one has to take the multiple access delay into account.

• Pipelining: the pipelining packet transmission is assumed in the RB scheme. A MACprotocol that could work under pipelining is suggested in the previous item. However,the pipelining assumption implies that a node has to be able to receive and transmitat the same time. This requires a node to have at least two air interfaces. Currently,some wireless communication devices, e.g. cellular phones, already have two airinterfaces: one for communicating with a base station in a cellular band and the otherfor communicating with a Bluetooth device in the unlicensed industrial, scientific andmedical (ISM) band. Thus, in the near future, nodes in ad hoc wireless networks couldalso have multiple wireless interfaces, making pipelining possible.

• Interference: in the analysis, we have pessimistically assumed the worst-case scenario,where all nodes transmit simultaneously. In addition, since the total interference noiseis the sum of many random signal components, by the CLT we assume that the totalinterfering noise is Gaussian. However, if the number of interfering nodes is small, thisGaussian assumption could lose its validity, as has been shown in detail in Chapter 3.

7.7 Concluding RemarksIn this chapter, we have posed and investigated an interesting question: namely, if and whenreservation-based switching makes sense in contemporary wireless ad hoc networks. Whileconventional wisdom in current ad hoc wireless networking research favors routing schemescorresponding to the NRB switching, it is shown that if the right requirements (in terms ofroute discovery, MAC protocol used, pipelining, etc.) are met, then RB switching schemes canprovide better delay performance than NRB switching schemes. In return, the throughput andgoodput performance of NRB schemes, even under these somewhat stringent requirements,seem to be superior to RB schemes.

Another major contribution of this chapter is the novel analytical framework and model(queuing models) developed for analyzing the network performance (in terms of throughput,goodput, delay, and mobility) under the RB and NRB switching schemes. This seemssignificant as such models, to the best of authors’ knowledge, do not exist (even for NRBschemes) in the open literature.

The results of the analytical framework (also supported by the Monte Carlo simulationsconducted) show that RB schemes are appropriate for real-time applications, such as voiceand video, whereas NRB schemes are more appropriate for delay-insensitive applications.While RB schemes can provide better delay performance, NRB schemes support higher trafficloads than RB schemes. In addition, it is found that NRB schemes can support a highernumber of routes because there is no constraint for the routes to be disjoint. Finally, it isshown that RB schemes are more robust to node mobility than NRB schemes.

We would like to emphasize that the foregoing conclusions are drawn based on theassumptions made in this chapter. It is important to understand that if one uses a differentMAC protocol (such as 802.11b) and/or one does not use a separate control channel for route


discovery, for instance, then the results obtained might be very different from those derivedin this chapter. In fact, if the requirements outlined in this chapter for RB switching are notmet, then NRB schemes will probably be preferable.

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Ad Hoc Wireless Networks (A Communication-Theoretic Perspective) || Route Reservation in Ad Hoc Wireless Networks