unnecessarily high control overhead. We analyze the tradeoff between routing delay and control overhead and determine that the minimum routing overhead can be achieved by increasing the timeout to at least twice the expected path residual time, without significant increase in routing delay, given exponentially or Rayleigh distributed link residual times.
In a low bandwidth MANET, a good caching strategy has to maintain low routing overhead in order to utilize precious network resources efficiently, which is also the major advantage of on-demand routing. Therefore, we argue that the best way to optimize route cache timeout is to jointly take into account the minimum routing delay and the routing control overhead. We consider a trade-off strategy for these components in this chapter.
The chapter is organized as follows. We first illustrate the challenges to im- plementing the route cache theoretical analysis from [54] in a real ad hoc network environment in Section 4.2. In Section 4.3, we propose our route caching scheme by setting the route cache timeout to a mobility metric, the expected path resid- ual time, in order to minimize routing delay. Three special cases are studied. In Section 4.4, we compare our cache timeout selection to other timeout values. In Section 4.5, we illustrate the relationship between route cache timeout and flood- ing probability. The average routing overhead is analysed in Section 4.6. How to achieve minimum routing overhead by setting the timeout is considered in Section 4.7. Simulation results, in Section 4.8, validate that the proposed mobility metric timeouts are a good approximation to the optimal route cache timeout. 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 4.9.
4.2
Review of Previous Work
This section provides an overview of the work in [54] which presents a route caching scheme for optimal routing delay. We demonstrate the challenge to implementing this scheme in practice. Since routing delay is the major issue in on-demand routing protocols, Liang and Haas in [54] determined the optimal route cache timeout, which was denoted as Time-To-Live (TTL), to minimize routing delay. In this scheme, every mobile node maintains a route cache table where every entry has a cache timeout. When a route request is generated at a given source node, ns,
it first checks all cache timeouts, purging the expired routes, and then searches the cache for a route to destination node, 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 ndin the cache table, the predefined
58 Choice of Timeout for Route Caching
4.1 illustrates how the routing delay time is calculated.
It is assumed that all links are either “up” or “down” at any point in time, and that all link states are statistically independent. Importantly, it is demonstrated that the timeout value which minimises routing delay is independent of the traffic distribution. We show that our choice of timeout 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 cumulation distribution function, Fa(t). The time taken for a data or control packet to be
transmitted across a link is assumed to be randomly distributed with a mean value of L seconds. It is assumed that the delay time 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 timeout of an h-hop cached route be T between ns and nd, due to the
last route request, and let the next route request to nd arrive at time ta. Given
the timeout T, the expected routing delay time is denoted as C(T). For ta < T
or ta > T, the expected delay is Cta<T(T) or Cta>T(T), respectively. In [54], the expected routing delay is shown to be
C(T) = Fa(T)Cta<T(T) + [1−Fa(T)]Cta>T(T) (4.1) = 2L[h+Fa(T) h X i=1 i(Qi−1(T)−Qi(T))−hFa(T)Qh(T)],
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 timeout has expired.
Now assume that all link up-times are identically distributed with CDF FR(t).
The i.i.d. assumption greatly simplifies the analysis of the optimal timeout. Then the survival function q(T) = 1−FR(T) is the probability that any given one of the
links in a cached route is still up at time T [26,52]. Note that the survival function is a non increasing function of its argument with a value of 1 at the origin and 0 as t→ ∞. It is determined in [54] that the optimal T in (4.1) satisfies
2hq(Topt)h −q(Topt)h−1 q(Topt)−1 = 0 0≤q(Topt)<1. (4.2)
Apparently, there is no closed-form solution for the optimal value, Topt. Moreover,
there are h roots of the h-order equation, and only the root corresponding to 0≤q(Topt)<1 gives the actual Topt.
4.2 Review of Previous Work 59
(a) Initial routing delay for broken link
(b) Additional routing delay for new route rediscovery
Figure 4.1: When an invalid cached route is employed to transfer data packets, routing delay consists of the initial routing delay for the broken link plus the addi- tional routing delay for new route rediscovery.
60 Choice of Timeout for Route Caching
cally distributed. Then, if the ith link has CDF FRi(t), (4.2) is replaced by:
2hQhi=1qi(Topt)−1− Ph−1 i=1 Qi j=1qj(Topt) = 0 0≤qi(Topt)<1,