On the packet loss overhead in buffer-limited ad hoc networks

Abstract

This paper focuses on the routing overhead analysis in ad hoc networks. Available work in this research field considered the infinite buffer scenario, so that buffer overflow will never occur. Obviously, in realistic ad hoc networks, the node buffer size is strictly bounded, which leads to unavoidable packet loss. Once a packet is dropped by a relay node, the bandwidth consumption for the previous transmission is actually wasted. We define the extra wasted bandwidth as the packet loss (PL) overhead. A theoretical analysis framework based on G/G/1/K queuing model is provided, to estimate the PL overhead for any specific routing protocols. Then, with this framework, we propose a distributed routing algorithm termed as novel load-balancing cognitive routing (NLBCR). The OPNET network simulator is further conducted to compare the performance among the NLBCR, AODV and CRP. The results indicate that NLBCR can reduce routing overhead to a considerable extent, as well as improve the network throughput and decrease the end-to-end delay.

Appendix: Convexity of the blocking probability

We use $J$ and $K$ to denote the queue length and buffer size respectively, $0\le J\le K$. The blocking occurs when the queue length reaches its upper bound $K$. Fixing the number of servers, buffer size and service process, for the arrival rates $g_{1}\le g_{2}$, the mean queue length usually satisfies

$$\begin{aligned} \overline{J}\left( g_{1}\right) \le \overline{J}\left( g_{2}\right) \end{aligned}$$

(24)

We denote by $\overline{K}$ the mean residual buffer size

$$\begin{aligned} \overline{K}\left( g_{1}\right) =K-\overline{J}\left( g_{1}\right) \ge K-\overline{J}\left( g_{2}\right) =\overline{K}\left( g_{2}\right) \end{aligned}$$

(25)

Imposing an increment $\triangle g$ on both $g_{1}$ and $g_{2}$, we investigate the corresponding blocking probability increment $\triangle P_{B}$. Since the mean residual buffer size satisfies $\overline{K}\left( g_{1}\right) \ge \overline{K}\left( g_{2}\right)$, thus the former has a better capability to deal with the arrival rate increment, i.e., $\Delta P_{B}\left( g_{1}\right) \le \Delta P_{B}\left( g_{2}\right)$ will hold for most situations. Then

$$\begin{aligned}&\frac{P_{B}\left( g_{1}+\Delta g\right) -P_{B}\left( g_{1}\right) }{\Delta g}\le \frac{P_{B}\left( g_{2}+\Delta g\right) -P_{B}\left( g_{2}\right) }{\Delta g}\nonumber \\&\Rightarrow P_{B}'\left( g_{1}\right) \le P_{B}'\left( g_{2}\right) \Rightarrow P_{B}''\left( g\right) \ge 0 \end{aligned}$$

(26)

The (26) indicates that the blocking probability $P_{B}$ is a convex function with the arrival rate $G$.

We refer to some simple queuing processes which have analytic solutions to check whether they are convex. For example, for an M/M/1/K queue and an M/M/m/m queue, the blocking probability is

$$\begin{aligned} P_{B}\left( g\right) =\frac{(1-g/\mu )\cdot (g/\mu )^{K}}{1-(g/\mu )^{K+1}} \end{aligned}$$

and

$$\begin{aligned} P_{B}\left( g\right) =\frac{(g/\mu )^{m}/m!}{\sum _{n=0}^{m}(g/\mu )/n!} \end{aligned}$$

respectively, they are both convex. The blocking curve of $\text {GI}^\text {X}$/M/1/K queue has been studied in [33], the result is convex. Different settings of M/G/c/K queuing models have been presented in [27]. When the buffer size is larger than the number of servers to a considerable range, the blocking probability $P_{B}$ is convex with the arrival rate. Note that in our model, there is only one server, and we can set $K>3$ to fall into the convex region.