Practical Scheme for Optimizing Route-Cache TTL in MANETs

Practical Scheme for Optimizing Route-Cache TTL in MANETs Sanlin Xu Kim Blackmore Haley Jones Department of Engineering, Australian National University

Abstract

routing protocol that employs a FIFO route cache mechanism [6, 7] to ensure cache freshness. In this scheme, routes are stored by each node in a route cache table which incorporates a primary cache and a secondary cache. The 30-element FIFO primary cache stores routes that have been used or returned directly to this node in a route reply. A separate 34-element FIFO secondary cache stores other routes, such as routes obtained via overheard packets. The total capacity of the route cache is 64 elements. On-demand routing suffers from very high routing latency. Liang and Haas [8] have shown how to choose the cache TTL in order to minimize routing latency, by analyzing the expected routing delay in terms of source route caching and intermediate route caching. However, their calculation of the optimal TTL, Topt in [8], is very complex, particularly when the link durations are nonidentically distributed, which is the reality in MANETs. Hence, it is difficult to implement this analytical scheme in practical on-demand routing protocols. In this paper, we propose a more practical method to realize an almost optimal route cache, by setting the route TTL equal to the path residual time or the expected path duration [9, 10, 11]. Note that we use the terms ‘route’ and ‘path’ interchangeably in this paper. For a random distribution of nodes, these mobility metrics can be estimated as the average of past values. The proposed TTL is derived in closed-form for exponentially distributed, Rayleigh distributed, or deterministic links. We compare the expected routing delay achieved by our scheme to analysis results [8]. Calculated results show the expected routing delay for our TTL compared to TTL = Topt is no more than 2.5% greater, being less than 0.5% in most cases. In addition, these results are independent of the transmission traffic load and inter-request statistics. Our scheme can be readily implemented in the DSR routing protocol, and extendable to other on-demand routing protocols. It is a concern that choosing cache TTL to minimize routing delay introduces unnecessarily high control overhead. We analyze the tradeoff between routing delay and

Stale route cache information and frequent route discovery processes in MANETs generate considerable routing delay and overhead when on-demand routing protocols are employed. This paper proposes a practical route caching strategy to minimize routing delay and/or overhead by setting the cache Time-To-Live value to one of two mobility metrics, the path residual time or the expected path duration. The strategy is independent of network traffic load and adapts to various non-identical link duration distributions, so it is feasible to implement in a real-time route caching scheme. Calculated results show that the routing delay achieved by our route caching scheme is only marginally more than the theoretically determined minimum. Simulation in ns-2 demonstrates that the end-to-end delay from DSR routing can be remarkably reduced by our caching scheme. We also demonstrate that the minimum routing overhead can be achieved by increasing the TTL to around twice the expected path duration, without significant increase in routing delay.

1 Introduction In mobile ad hoc networks (MANETs), on-demand routing protocols [1, 2, 3, 4, 5] aim to conserve network resources by only initiating a route discovery procedure in reaction to a request to send a packet. To avoid the need to repeat the discovery process once the route has been found, on-demand routing protocols utilize route caches to store previously discovered routes. If the route cache Time-ToLive (TTL) is set too large for a given route, the amount of stale routing information in the cache is increased with a commensurate increase in the generation of invalid routing information. On the other hand, if the TTL is set too small, there will be a large number of route request packets flooding the network as valid routes are more likely to have been discarded. Dynamic Source Routing (DSR) [2] is an on-demand 1

control overhead and determine that the minimum routing overhead can be achieved by increasing the TTL to twice the expected path duration, without significant increase in routing delay, given exponentially distributed link durations The rest of this paper is organized as follows. We first illustrate the challenges to implementing the route cache theoretical analysis from [8] in a real ad hoc network environment in Section 2. In Section 3, we propose our route caching scheme by setting the route cache TTL to a mobility metric: the path residual time or the expected path duration, in order to minimize routing delay. Three special cases are studied. In Section 4, we argue that, when using optimal TTL to minimize routing delay, we need to consider the tradeoff between minimum control routing overhead and minimum routing delay. Simulation results, in Section 5, validate that the proposed mobility metric TTLs are a good approximation to the optimal route cache TTL. We present ns-2 simulation results that support the validity of our proposed scheme in DSR. Finally, conclusions are drawn and future work is discussed in Section 6.

is dominated by queuing delay in the MAC layer if traffic is at medium to high load, though packets may vary in length. Let the TTL of an h-hop cached route be T between nodes ns and nd , due to the last route request, and let the next route request to nd arrive at time ta . The expected routing delay is shown in [8] to be C(T )

= Fa (T )Cta T (T ) = 2L[h + Fa (T )

h X

i(Qi−1 (T )

i=1

−Qi (T )) − hFa (T )Qh (T )],

(1)

where Qi (T ) is the probability that the first i hops of the cached route have not failed when a route request arrives before the TTL expires. It is assumed that all link up-times are identically distributed with cumulative distribution function FD (t). The i.i.d. assumption greatly simplifies the analysis of the optimal TTL. Given the probability, q(T ), that any given link in an h-hop cached route is still up at time T , the optimal T satisfies  q(T )h −1 h   2hq(T ) − q(T )−1 = 0 (2)   0 ≤ q(T ) < 1,

2 Review of Previous Work This section provides an overview of the work in [8] which presents an optimal route caching scheme. We demonstrate the challenge to implementing this scheme in practice. Since routing delay is the major drawback for ondemand routing protocols, Liang and Haas in [8] determined the optimal route cache TTL to minimize routing delay. In this scheme, every mobile node maintains a route cache table where every entry has a cache TTL. When a route request is generated at a given source node, ns , ns first checks all cache TTLs, purging the expired routes, and then searches the cache for a route to destination, nd . If a route is found, it immediately sends the data packet via the cached route, resulting in no routing delay. If the cached route turns out to have expired, as evidenced via receipt of a route-error packet, or if there is no route between ns and nd in the cache table, the predefined routing protocol is employed to search for a new route between ns and nd . It is assumed in [8] that all links are “up” or “down” at any point in time, and that all links states are statistically independent. Importantly, it has been demonstrated in [8] that the optimal TTL to minimize routing delay is independent of the traffic distribution. We show that our choice of TTL also has this property. To describe the traffic load of a wireless network, route request times from source node ns to destination node nd are assumed to be randomly distributed. The inter-arrival intervals of route requests are assumed to have a distribution, Fa (t). The time taken for a data or control packet transmission across a link is randomly distributed with a mean value of L seconds. It is assumed that the delay time

where q(T ) = 1 − FD (T ). Apparently, there is no closedform solution for the optimal value, Topt . Moreover, there are h roots of the h-order equation, and only the root corresponding to 0 ≤ q(T ) < 1 gives the actual Topt . However, more realistically, the link up-times in a cached route are not identically distributed, whereby (2) is replaced by:  Ph−1 Qi Qh   2h i=1 qi (T ) − 1 − i=1 j=1 qj (T ) = 0 (3)   0 ≤ qi (T ) < 1. Since the number of hops in a route scales as the squareroot of the number of nodes, even in a small-scale mobile ad hoc network with just 50 nodes, route lengths above 7 hops occur frequently. For a large-scale ad hoc network, the hop number, h, can be much larger, significantly increasing the computation time for Topt when deriving the optimal root of the h-order equation. Therefore, in practice, it is a challenge to implement the optimal TTL caching scheme proposed in [8], particularly if the link uptimes are not identically distributed.

3

Proposed Route Caching Scheme - TTL to Minimize TTL

Ideally, the TTL of a given cached route should be set to coincide with the exact moment the communication be2

tween the source and destination nodes breaks. That is, the TTL is equal to the path residual time1 [9, 10], R(h), of the h-hop route, where the corresponding link residual times are denoted as R1 , R2 , · · · , Rh . In the ideal case, the cached route is removed from the cache exactly when it ceases to physically exist. However, due to the mobility of nodes in MANETs and the uncertainty of the radio propagation channel, it is often not possible to determine the exact residual time of a given link or a given path between two roaming mobile nodes. Therefore, we usually have to exploit the statistical information of link and path availability to estimate the optimal TTL. This leads us to choosing a mobility metric, the expected path duration 2 , as an estimation of the lifetime of a cached route. Given a route with h hops, the expected path duration, denoted as E{D(h)}, with corresponding link durations {D1 , D2 , · · · , Dh } [10, 11, 12], is E{D(h)} = E{min(D1 , D2 , · · · , Dh )}.

at moderate and high velocities, the exponential distribution with appropriate parameterizations is a good approximation of the path duration distribution for a range of mobility models such as Random Waypoint, Reference Point Group Mobility, Freeway and Manhattan Mobility models. Through theoretical analysis, our previous research [9] verifies that the link and path duration are also exponentially distributed in the Random Walk Mobility model. Therefore, we suggest that the exponential distribution is generally a good approximation of the link duration PDF. If an arbitrary link of an h-hop route has exponentially distributed duration with parameter λi , from (5), the distribution of min(D1 , D2 ) is given by fmin D1 ,D2 (t) = (λ1 + λ2 )e−(λ1 +λ2 )t U (t),

(6)

where U (t) is the unit step function. Iteratively, the distribution of D(h) is

(4)

fD(h) (t) = e−

Ph i=1

λi t

h X

λi U (t).

(7)

i=1

The expected path duration can be determined from the PDF of D(h). Let fDi (t) be the PDF, and FDi (t) be the CDF of link duration of the ith link. If all links are independent, then the distribution of min(D1 , D2 ) is given by [13]

Thus, it can be shown that the expected path duration is given by 1 E{D(h)} = Ph i=1

fmin(D1 ,D2 ) (t) = fD1 (t) + fD2 (t) − fD1 (t)FD2 (t) −fD2 (t)FD1 (t). (5)

λi

= Ph

1

i=1

1/µi

,

(8)

where µi is the mean value of the ith link duration. Now, let us assume that the time between route requests is exponentially distributed with parameter λa . Following [8], the expected routing delay for non-identically exponentially distributed link durations can be shown to be:

This can be applied iteratively to derive the distribution of min(D1 , D2 , · · · , Dh ). Consequently, we can obtain the expected value E{D(h)}. This will be shown for particular distributions in subsequent sections. Three example distributions of the links are studied below: exponential distribution, Rayleigh distribution and deterministic. Note that in all three cases, we assume an exponential distribution for the route request arrival times, but this choice does not affect the choice of TTL.

C(T ) = 2Lh + 2λa L

h−1 X i=0

Pj

1 − e−(λa + j=0 λj )T Pj λa + j=0 λj Ph

1 − e−(λa + i=1 λi )T = −4λa Lh . Ph λa + i=1 λi

(9)

Given the expected path duration from (8), the corresponding expected routing delay is:

3.1 Exponential Link Duration The distributions of path and link duration in MANETs have been extensively studied. In [11, 12], the statistical results show that link and path duration PDFs vary with parameters such as the mobility model, relative speed, number of hops, and radio range. However, it is suggested that,

C(E{D(h)}) = 2Lh + 2λa L

h−1 X i=0

− 4λa Lh

1−e

−

λa + Ph

P λa + i j=0 λj Ph λ i=1 i

Pi

j=0

λj

1 − e−(1+λa i=1 λi ) . Ph λa + i=1 λi

(10)

If all link durations of an h-hop route are i.i.d. with fD (t) = λe−λt , then (7) can be rewritten as:

1 Given an active path with h hops between two nodes at time t0 (which may also have been active immediately prior to time t0 ), the path residual time, R(h), is the length of time for which the path will continue to exist until it is broken. 2 Given that a path becomes active at time t0 , the path duration, D(h), is the length of time for which the path will continue to exist until it is broken. The path duration is the path residual time from the instant the path first becomes available. It could be understood as the maximal value of the path residual time.

fD(h) (t) = hλe−hλt U (t).

(11)

It can be shown that E{D(h)} in this case is given by E{D(h)} = 3

1 µ = . hλ h

(12)

delay in [8] is not appropriate when h = 1. In [8] it is assumed that two end nodes do not move too far between route requests, so that a newly discovered route has the same mean route length as the previous route. But this is not true when h = 1, because the new route must be at least two hops long (i.e. twice the length) - the single hop has been broken, necessitating the route request. The destination node is now not the source node’s neighbor. However, no such problem exists using TTL = E{D(h)}.

Given the expected path duration from (12), the corresponding expected routing delay is: C(E{D(h)}) = 2Lh + 2λa L

h−1 X i=0

1−e λa + hλ

λa

.

(13)

12 0.03

11

0.025 0.02

10

0.015

9

0.01

C(T) / L

Normalized increase in expected routing delay

− 4λa Lh

a −(1+ λ hλ )

i

1 − e−( h + hλ ) λa + iλ

0.005 0 10

8 7

20 15

5

6

10 5

µa / µ

0

0

5

Route length (hops)

µa = 0.3 µa = 0.1

4 −2 10

Figure 1: Normalized increase in expected routing delay, as a function of route length and the ratio of the mean inter arrival time. All link durations are identically exponentially distributed with mean µ.

−1

10

0

10 γ: TTL = γ Topt

1

10

2

10

Figure 2: Comparison of the expected routing delay, normalized to L, for 5-hop paths, with exponential link duration, for exponentially distributed route request times with means µa = 1, 0.3 and 0.1. The up-pointing triangles represent C(E{D(h)}) from (13), and the down-pointing triangles represent C(Topt ) from (9).

We compare the expected routing delay achieved when cache TTL = E{D(h)} from (13) with that achieved when cache TTL = Topt [8], in Fig. 1. The normalized increase in expected routing delay is defined as: C(E{D(h)}) − C(Topt ) . C(Topt )

µa = 1

(14)

Following [8], we introduce a route cache TTL scaling factor, γ, in Fig. 2, such that, when a new route is cached, its TTL is set to γTopt . In Fig. 2, C(T )/L is plotted for T = γTopt , where 0.1 ≤ γ ≤ 10. The minimum routing delay is expected to be achieved at γ = 1. The plots in Fig. 2 show that C(E{D(h)}) is a good approximation of C(Topt ).

In Fig.1, the range of route lengths has been chosen to be 1 ≤ h ≤ 20, as this covers the majority of paths found in a typical ad hoc network. All link durations are identically exponentially distributed with mean µ. Let µa be the mean of the route request timing distribution. If µa /µ is small, the network data traffic is heavy, and vise versa. Fig. 1 shows that the increase in expected routing delay is generally less than 2.5%, and it is less than 0.5% if the number of hops in a given route is > 1. This demonstrates that using a cache TTL = E{D(h)} has routing delay performance comparable with that for TTL = Topt . The difference in routing delay performance between them is in fact negligible. Note that the calculated normalized increase in Fig. 1 is largest when the route length is 1. The reason behind this is that the method for calculating the expected routing

One important property of choosing TTL this way is that its setting is independent of traffic load. This can be seen in Fig. 2 where the minimum routing delay is achieved at γ ≈ 1 for traffic loads with µa = 0.1, µa = 0.3 and µa = 1. Moreover, the expected routing delay per route request is a decreasing function of the route-request arrival time. If the link duration is exponentially distributed, it can be seen that the expected routing delay does not change much for TTL greater than the optimal TTL when the network traffic is heavy, e.g., µa = 0.1. 4

some period of time. By exploiting a mobile user’s nonrandom travelling pattern (and GPS location information), we can calculate the exact link residual time between a pair of mobile nodes. That is, we can assume the link residual time is deterministic instead of random. If mobile nodes move with constant velocity, route cache TTL should equal the path residual time, given by

3.2 Rayleigh Link Duration If the link durations in an h-hop route are now Rayleigh distributed with the ith link having PDF fDi (t) = t −t2 /2σi2 e , from (5), we obtain σ2 i

fmin D1 ,D2 (t) =

2 t −t2 /2σ12 e U (t), 2 σ12

(15)

R(h) = min(R1 , R2 , · · · , Rh ).

where σ12 = √σ12σ2 2 . Iteratively, the distribution and the σ1 +σ1

The residual time of the wireless link between two nodes

expected value of D(h) can be obtained. If all link durations of an h-hop route are identically 2 2 Rayleigh distributed with fD (t) = σt2 e−t /2σ , we obtain r π µ E{D(h)} = σ=√ . (16) 2h h

40 µa = 1, exponential µa = 0.1, exponential µa = 1, deterministic

30

µa = 0.3, deterministic

C(T) / L

25

µa = 0.1, deterministic

20 15 10 5 0

3.3 Deterministic Link Residual Time

0

5

10 Route Length (hops)

15

20

Figure 4: Comparison of the expected routing delay, normalized to L, with exponential link durations from (13) and deterministic links from (19), for exponentially distributed route request times with means µa = 1, 0.3 and 0.1.

11 Calculated:TTL=Topt, exponential

9

µa = 0.3, exponential

35

It can be seen that E{D(h)} for a Rayleigh distributed link duration is similar to that for the exponential distribution. Consequently, a similar analysis can be made, as in section 3.1. Unlike the exponentially distributed link durations, it is not possible to derive the closed-form of the expected routing delay, C(T ), for Rayleigh distributed link durations. We give simulation results in subsequent sections.

10

(17)

Simulated:TTL=E{D(h)}, exponential Simulated:TTL=E{D(h)}, Rayleigh Simulated:TTL=R(h), deterministic

8

C(T) / L

7

with transmission range r, which are moving with speed, Vi and Vj at angles θi and θj , respectively, can be estimated as [14]: p −(ab + cd) + (a2 + c2 )r2 − (ad − bc)2 R= (18) a2 + c2

6 5 4 3 2 1 −1 10

0

10 TTL scaling factor γ

where (xi , yi ) is the coordinate of mobile node i, a = Vi cos(θi ) − Vj cos(θj ), b = xi − xj , c = Vi sin(θi ) − Vj sin(θj ), and d = yi − yj . Let the route request time again be exponentially distributed with fa (t) = λa e−λa t . Then, the corresponding expected routing delay can be shown to be:

1

10

Figure 3: Comparison of the average routing delay for 5hop paths, where link durations are non-identically distributed, µ = [7 6 8 2 5], with exponential, Rayleigh and deterministic links, respectively. The calculated plot is from (9). The vertical lines indicate the 99.95% confidence intervals.

C( R(h) ) = 2Lh e−λa R(h) .

(19)

In Fig. 3, we use Matlab simulations to compare the average routing delay for exponentially distributed, Rayleigh distributed, and deterministic link durations, for a 5-hop path. In all cases, the mean link durations are [7 6 8 2 5], respectively. It can be seen that the deterministic links produce lower delay time than the Rayleigh links, regardless

In many mobile networks, nodes exhibit some degree of regularity in their mobility pattern [14]. For example, a car travelling on a highway or a tank travelling across a battle field is likely to maintain its direction and speed for

5

of TTL scaling factor, and both produce lower delay than the exponential link. This would be expected, since there is no variance in the link durations in the deterministic case, and the variance in the Rayleigh case is smaller than for exponentially distributed link durations with the same mean. In each case, the minimum average routing delay occurs at γ ≈ 1, that is, when TTL ≈ E{D(h)}, or R(h) respectively. Figure 4 presents the expected routing delay given TTL = E{D(h)} and TTL = R(h), for route lengths 1 ≤ h ≤ 20, for exponentially distributed link durations with µ = 1 and deterministic links, respectively. It can be observed that the minimum expected routing delay for deterministic links is less than that for exponentially distributed link durations, given the same route length and route request frequency. When the traffic request frequency is low, such that µa À 1, the optimal routing delay is so large that it approaches 2Lh, as can be seen by the slope of the top plot line in Fig. 4. This can also be seen from (19), as µa increases, λa decreases. If R(h) remains constant hen the exponential term goes to 1, leaving C(T ) → 2Lh. That is, it is similar to when no route cache is used, or TTL = 0.

2

Normalized expected routing delay

Normalized expected routing delay

µ = 0.1, deterministic a

µa = 0.3, deterministic µ = 1, deterministic a

µa = 0.1, exponential µ = 0.3, exponential a

µa = 1, exponential

10

1

10

0

10

0

5

10 Route length (hops)

15

µa = 0.3, exponential µa = 0.1, exponential

1.6 1.5 1.4 1.3 1.2

0

5

10 Route length (hops)

15

20

or R(h) reduces the routing delay for all scenarios considered. Ideally, if the link state is deterministic, the normalized routing delay can be very large compared to a system where no route cache is used, especially if µa is small, as shown in Fig. 5. Moreover, the normalized routing delay in Fig. 5 for deterministic links is constant with respect to varying route length, whereas with exponentially distributed link duration it is a decreasing function of route length. In Fig. 6, the normalized routing delay is less than in Fig. 5. This illustrates that using a route cache, even without a cache expiration mechanism, is better than not using a route cache at all. It is interesting to note that the plots for deterministic links overlap each other. This means that the normalized expected routing delay for deterministic links is independent of route request frequency. In this section, we have presented a practical method to choose the route cache TTL. In the next section, we examine the tradeoff between minimum routing delay and routing overhead.

4

2

µa = 1, exponential

Figure 6: Expected routing delay when TTL = ∞, divided by routing delay when TTL = E{D(h)} for exponential link duration from (13) and TTL = R(h) for deterministic link from (19).

5

3

µa = 0.1, deterministic

1.7

1

10

10

µa = 0.3, deterministic

1.8

1.1

3.4 Comparison to Other TTL Values

10

µa = 1, deterministic

1.9

20

Figure 5: Expected routing delay when TTL = 0, divided by routing delay when TTL = E{D(h)} for exponential link duration from (13) and TTL = R(h) for deterministic link from (19).

4

TTL to Minimize Overhead

Many of the existing on-demand routing protocols employ flooding of route request packets to discover new routes if no valid route is available in the cache [15]. Flooding of control packets causes a significant amount of redundancy, waste of bandwidth, collisions in the MAC layer, and broadcast storms due to frequent topology changes. Various schemes have been introduced to minimize the overhead produced by flooding. For example, the Pre-

We now compare our caching scheme to other schemes, such as, using no route cache or using a never-expiring cache. That is, TTL = 0 or TTL = ∞. Figures 5 and 6 illustrate the normalized expected routing delay in terms of these two strategies, respectively. Since all of the normalized routing delays in Figures 5 and 6 are always greater than 1, it can be concluded that setting TTL to E{D(h)}

6

Qh (T ) in (21) can be rewritten as

ferred Link-Based Routing (PLBR) protocol [16] allows only preferred neighbor nodes with strong links to forward the route request packets. In Section 3, we discussed how to choose TTL to minimize routing delay. Our route cache scheme with TTL = R(h) will also minimize routing overhead when the link residual time can be exactly determined (using GPS information, for example). However, for other scenarios, such as exponentially distributed link durations, the TTL necessary to minimize delay is unlikely to also achieve minimum control overhead. Since the routing overhead is mainly determined by the flooding message packets, minimizing the probability of flooding will also minimize overhead. Flooding will occur in two circumstances: if the next route request arrives at ta > T , where T is the cache TTL, the source node must discover a new route by flooding. If, instead, ta < T , the probability of flooding is 1 − Qh (T ), where Qh (T ) is the probability that all h hops of the cached route have not failed when a route request arrives before the TTL expires. Taking the two cases into account, the probability of flooding is given by,

Qh (T ) = −Ress=hλ =

λa (1 − e−(s+λa )T ) 1 hλ (1 − e−λa T )(s + λa ) s −s + hλ

λa 1 − e−(hλ+λa )T . hλ + λa 1 − e−λa T

(23)

Thus, we have Pr(T ) = 1 −

λa [1 − e−(hλ+λa )T ] . hλ + λa

(24)

When TTL is larger than 2E{D(h)}, the flooding probability will approach a lower bound, Pr{T |T ≥ 2E{D(h)}} → 1 −

λa . hλ + λa

(25)

For randomly distributed link durations, which are exponentially distributed, no matter how large the setting of the cache TTL is, the probability of flooding is not able to be less than 1 − λa /(hλ + λa ). 1

Pr(T ) = Fa (T )[1 − Qh (T )] + [1 − Fa (T )] = 1 − Fa (T )Qh (T ), (20)

0.9 0.8 Probability of flooding

where Fa (T ) is the distribution function of route request arrival times. Similarly to Qi (T ) in [8], we have Qh (T ) = Pr{ta < Xh |ta < T } (21) Z ∞ = Pr{ta < t|ta < T }fXh (t)dt 0 ¸ Z ∞ ·Z t = fc (t)dt fXh (t)dt 0 0 ¸ · Z ∞ 1 = L−1 fc∗ (s) fXh (t)dt s 0 ¸ Z c+j∞ ∗ Z ∞· fc (s) st 1 = e ds fXh (t)dt 2πj c−j∞ s 0 Z c+j∞ ∗ 1 fc (s) = fXh ∗ (−s)ds 2πj c−j∞ s X f ∗ (s) =− fXh ∗ (−s), Ress=ξ c s ξ∈poles offXh ∗ (−s)

0.6 0.5 0.4 0.3 µ =1

0.2

a

µa = 0.3

0.1 0

µa = 0.1 0

2

4 6 γ: TTL = γ E{D(h)}

8

10

Figure 7: Probability of flooding from (24) vs. TTL scaling factor, for 5-hop paths, with exponentially distributed link durations. The triangles represent the points where γ = 2. Flooding probabilities converge to the asymptotes, from (25), for γ > 2. Figure 7 illustrates that the probability of flooding approaches 1, for small γ, and is equal to 1 for γ = 0, corresponding to no route cache. The flooding probability decreases as γ is increased. The probability converges to a stable threshold for γ > 2, as in (25). This demonstrates that the minimum routing overhead can be effectively achieved if we simply double the optimal TTL, Topt , for minimum routing delay, given exponentially distributed link durations. Thus, we conclude that the TTL for minimum overhead is larger than the TTL for minimum routing delay, if the

where Ress=ξ denotes the residue at the pole s = ξ, L is the Laplace Transform operator, fc (t) is the conditional density function of ta given ta < T , and fXh (t) is the density function of Xh , being the minimum of the residual lifetimes of the first h hops in the cached route. If the route requests are of a Poisson process and the link durations are exponentially distributed, it is easy to obtain Fa (T ), which is Fa (T ) = 1 − e−λa T .

0.7

(22)

7

Table 1: ns-2 Simulation Parameters Parameters

Values

Parameters

Values

phyType

Phy/WirelessPhy

Mobility model

Random Waypoint

Routing protocol

Modified DSR

Number of nodes

50

Propagation

TwoRayGround

Mean node speed

10m/s

Radio transmission range

250m

Pause time

0

MAC

DCF of 802.11

Packets packed in a frame

512

ifq (Queue type)

Droptail priority

Maximum packets to sent

10,000

ifqlen (max packet in ifq)

50

Number of sources

20

Transmission rate

2Mbps

Traffic connection

CBR

Simulation time

900 seconds per trial

Network area

1000m × 1000m

link residual time is not deterministic. The principles balancing routing delay and overhead are: (1) TTL should be set to E{D(h)} to achieve the smallest routing delay for delay sensitive applications, such as audio and video transmissions; (2) TTL should be set to 2E{D(h)} to achieve the smallest overhead for radio bandwidth limited scenarios, such as sensor wireless networks; (3) in general, when E{D(h)} < TTL < 2E{D(h)}, a balance of minimum routing delay and overhead is achieved.

ing Overhead Rate is calculated by dividing the number of routing packets transmitted by the number of the successfully received data packets. It can be regarded as the average cost for each successful packet delivery. Figure 8 shows that near optimal results are obtained for packet delivery ratio, end-to-end delay, and routing overhead when TTL ≈ R(h). In each subplot, the performance of standard DSR is indicated by a horizontal line, and the performance metrics approach this value when TTL ≈ 10R(h). If the TTL is chosen too small, performance is much worse than original DSR, in general. Interestingly, the general trend for the average path length is increasing as TTL = γR(h) increases.

5 Mobility Metric TTL Simulations It is critical to verify if our proposed caching scheme can achieve practically minimum routing delay in a real ondemand protocol. We have done this via ns-2 simulations of DSR, where the route cache TTL is chosen to be R(h). The simulation model used in this paper is based on that used in [7, 17], for comparison purposes. The simulation parameters are recorded in Table 1. In the simulation, nodes move according to the Random Waypoint Mobility model, where every node selects a destination point uniformly distributed in the simulation area, and moves there with velocity uniformly distributed over [0, vmax ]. We choose a simulation area of 1000m× 1000m, so the nodes move, on average, for 521m before changing direction [18]. Such a large distance travelled in one direction implies that link residual time can most often be determined exactly by equation (18), making the link effectively deterministic. Once we have obtained all link residual times along a given route, the cache TTL is set to the path residual time, following equation (17). This could be implemented in practice if the node location and velocity of each mobile node could be obtained with GPS[19], or other methods (e.g., [20]). The performance metrics, Packet Delivery Ratio, Endto-end Delay, Routing Overhead Rate, and Average Path Length have been used, following [21]. Note that the Rout-

6

Conclusions

A key to achieving efficient MANET performance with ondemand routing protocols is to use a route cache. Liang and Haas [8] proposed setting the cache TTL to a calculated optimal value, Topt , with respect to minimizing routing delay. Unfortunately Topt is difficult to implement in practice. We have proposed setting the cache TTL to a mobility metric, the expected path duration, if link duration is randomly distributed, or path residual time if the link duration is approximately deterministic. Numerical and simulation results show that the increase in expected routing delay is less than 2.5% using the mobility metrics as TTL, rather than Topt . Further, we have shown that choosing the TTL to minimize routing delay does not necessarily minimize routing overhead, which contravenes the intent of on-demand routing protocols. For exponentially distributed links, practically minimum routing overhead is achieved for TTL more than twice the expected duration. 8

1

8

DSR: TTL = γ R(h) DSR: Original

0.9

7 End−to−end delay (seconds)

Packet delivery ratio (%)

0.8 0.7 0.6 0.5 0.4 0.3

6.5 6 5.5 5 4.5

0.2

4

0.1 0 −1 10

0

3.5 −1 10

1

10 TTL scaling factor γ

10

8

1

10

3.6

DSR: TTL = γ R(h) DSR: Original

DSR: TTL = γ R(h) DSR: Original

7

3.5 Average path length (hops)

Routing overhead rate

0

10 TTL scaling factor γ

(b)

(a)

6

5

4

3

2

1 −1 10

DSR: TTL = γ R(h) DSR: Original

7.5

3.4

3.3

3.2

3.1

3

0

10 TTL scaling factor γ

1

−1

10

10

0

10 TTL scaling factor γ

1

10

(d)

(c)

Figure 8: Comparison of the network performance between the modified DSR using γR(h) and the original DSR with no route cache expiration.

Acknowledgment

[3] Z. Haas and M. Pearlman, “Determing the Optimal Configuration for Zone Routing Protocol,” IEEE J. Selected Area in Commun., vol. 17, no. 8, pp. 1395– 1414, Aug. 1999.

The authors wish to thank Prof. Ben Liang of the University of Toronto for his helpful discussions during the development of this work.

[4] Y. Ko and N. Vaidya, “Location-Aided Routing (LAR) in Mobile Ad Hoc Networks,” in Proc. of MobiCom 98, Oct. 1998, pp. 66–75.

References

[5] C. E. Perkins and E. M. Royer, “Ad-Hoc On-demand Distance Vector Routing,” in Proc. of WMCSA ’99. Second IEEE Workshop on Mobile Computing Systems and Applications, Feb. 1999, pp. 90 – 100.

[1] V. D. Park and M. S. Corson, “A Highly Adaptive Distributed Routing Algorithm for Mobile Wireless Networks,” in Proc. of INFOCOM97, Apr. 1997, pp. 1405–1413.

[6] J. Broch, D. Maltz, D. Johnson, Y. Hu, and J. Jetcheva, “A Performance Comparison of MultiHop Wireless Ad Hoc Network Routing Protocols,” in Proc. of the 4th Int. Conf. on Mobile Computing and Networking, Oct. 1998, pp. 85–97.

[2] D. B. Johnson, D. A. Maltz, and Y. C. Hu, “The Dynamic Source Routing Protocol for Mobile Ad Hoc Networks (DSR),” IETF Draft, draft-ietfmanet-dsr10.txt, July 2004. 9

[7] Y. Hu and D. Johnson, “Caching Strategies in OnDemand Routing Protocols for Wireless Ad Hoc Networks,” in Proc. of MobiCom 2000, Aug. 2000, pp. 231–242.

[20] N. Priyantha, A. Chakraborty, and H. Balakrishnan, “The Cricket Location-support System,” in Proc. of ACM MOBICOM. Boston, MA, Aug. 2000, pp. 32– 43.

[8] B. Liang and Z. Hass, “Optimizing Route-Cache Lifetime in Ad Hoc Networks,” in Proceedings of IEEE INFOCOM, vol. 3, Apr. 2003, pp. 1745–1752.

[21] S. Jiang, Y. Liu, Y. Jiang, and Q. Yin, “Provisioning of Adaptability to Variable Topologies for Routing Schemes in Manets,” IEEE J. Select. Areas Commun., vol. 22, no. 7, pp. 1347 – 1356, Sept. 2004.

[9] S. Xu, K. Blackmore, and H. Jones, “Mobility Metrics for Manets Requiring Persistent Links,” in Proc. WiTMeMo ’05 of MobiSys 2005. Seattle, June 2005. [10] ——, “An Analysis Framework for Mobility Metrics in Mobile Ad Hoc Networks.” To be submitted. [11] F. Bai, N. Sadagopan, B. Krishnamachari, and A. Helmy, “Modeling Path Duration Distributions in MANETs and Their Impact on Reactive Routing Protocols,” IEEE J. Select. Areas Commun., vol. 22, no. 7, pp. 1357 – 1373, Sept. 2004. [12] N. Sadagopan, F. Bai, B. Krishnamachari, and A. Helmy, “PATHS: Analysis of PATH Duration Statistics and Their Impact on Reactive MANET Routing Protocols,” in Proc. of MobiHoc, June 2003, pp. 246–256. [13] A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes. McGraw Hill, 2002. [14] W. Su, S. Lee, and M. Gerla, “Mobility Prediction and Routing in Ad Hoc Wireless Networks,” Int. J. of Network Management, pp. 3–30, 2000. [15] C. Murthy and B. Manoj, Ad-Hoc Wireless Networks Architecture and Protocols. Prentice Hall, 2004. [16] R. Sisodia, B. Manoj, and C. Murthy, “A Preferred Link-based Routing Protocols for Ad Hoc Wireless Networks,” J. of Commun. and Networks, vol. 4, no. 1, pp. 14–21, Mar. 2002. [17] S. Xu, K. Blackmore, and H. Jones, “Cache Timeout Strategies for On-demand Routing in MANETs,” Accepted by WITSP’2005 of 8th International Symposium on DSP and Communication Systems, DSPCS’2005, Dec. 2005. [18] C. Bettstetter, G. Resta, and P. Santi, “The Node Distribution of the Random Waypoint Mobility Model for Wireless ad hoc Networks,” IEEE Trans. Mobile Comput., vol. 2, pp. 257–269, 2003. [19] W. Su and M. Gerla, “Ipv6 Flow Handoff in AdHoc Wireless Networks Using Mobility Prediction,” in Proc. of IEEE Global Commun. Conf., vol. 1, Dec. 1999, pp. 271–275. 10