ARQ Mechanism and Retransmission Load Analysis

ARQ is a mechanism used in reliable multicast protocols to provide error control.

In this section, we briefly review this mechanism and then analyze the source re-transmission load of different rere-transmission schemes on binary trees.

5.1.1 An Overview of ARQ mechanism

ARQ is a retransmission on demand mechanism, where the sender is alerted to packet losses through feedback from receivers and lost packets are retransmitted by either the sender or other nodes [85]. An ARQ scheme can either be sender- or receiver-initiated. In a sender-initiated scheme, the sender maintains state informa-tion of receivers and detects packet losses. Receivers need to acknowledge every received packet by ACK to the sender. If the sender does not receive the ACK for a packet after time out, it will assume that the packet is lost and a retransmission or a congestion avoidance mechanism will be triggered. In a receiver-initiated scheme, receivers have the responsibility of detecting losses, e.g., by observing gaps in re-ceived packets. After a loss is detected, a NACK will be issued to report the loss and request retransmission. Usually, in multicast transmission, receiver-initiated schemes are more scalable than sender-initiated schemes [74], since the burden of maintaining reliability is distributed among receivers and NACKs are only issued when packet losses occur.

Since ARQ consists of feedback and retransmission, researchers discuss the efficiency of an ARQ reliable multicasting protocol from these two dimensions:

the scalability of ACK or NACK message in both network view and individual router view and the retransmission load. Feedback is generated by receivers and sent to the sender. It increases with the number of receivers and multicast packets.

To reduce bandwidth consumption, feedback is aggregated to present the reception of a set of packets at receivers and downstream nodes at the router. As for the retransmission load which is a function of the size and geographic spread of the multicast group, the receiver-assisted and router-assisted retransmission schemes are proposed. In a receiver-assisted retransmission scheme, when a router receives a feedback it forwards this feedback to some other receiver in its sub-network in-stead of forwarding the feedback directly to the sender. If the receiver has the required packets, it retransmits the packets. In order to reduce further bandwidth consumption and reduce recovery latency,a router-assisted retransmission scheme requires the routers store the multicast packets they forward for future retransmis-sion.

5.1.2 Mathematic analysis of ARQ’s Retransmission Load

Now we examine the source retransmission load of three retransmission schemes:

sender-originated, receiver-assisted and router-assist protocols. We suppose that a source-based multicast tree delivers packets to destinations, which are all located

at leaves. After one (re)transmission, a sub tree is constructed based on the orignal tree for the next retransmission. This sub multicast tree contains only those des-tinations which have not received the packet. All links have the same packet loss probability which is denoted as to facilitate the analysis.

S

D D

S

D D D

S

A B C

Figure 5.1: One-level binary tree and its sub trees

First, we consider a one-level binary tree as shown in Figure 5.1 where one source delivers multicast packets to two destinations which are located in the source’s coverage range. The right part of this figure lists all possible retranmission trees.

Tree is the result of transmission failure to both destinations, while tree is the case where one destination does not receive the packet and tree is empty which represnts the successful delivery to two destinations. The probability dis-tribution function of retransmission tree (number of retransmissions) can be deter-mined based on a homogeneous discrete-time Markov chain (DTMC) as shown in Figure 5.2.

B C

A

Figure 5.2: DTMC for one level binary trees

The corresponding transition probabilities can be written as the matrix

The initial state distribution of the DTMC is given by =( , , )=

(

), since the original transmission is already finished before retransmissions begin, i.e. we just have to consider the transition probabilities orig-inating from state A. The probability of being in a certain state of the DTMC after

n steps can be determined simply by calculation of the nth power of P. We are only interested in being in state C, the case of empty tree, which indicates that all receivers have obtained the packet. Hence, we get

that exactly n retransmissions are required is given by

for and

for n = 0. The expected source retransmission load can be written as

Figure 5.3: Two-level binary tree and its sub trees

Now, we analyze the source retransmission load in a two-level binary tree as shown in Figure 5.3 under a sender-originated scheme. This multicast tree has six possible retransmission sub trees. The corresponding transition probabilities can be written as the matrix

) #

The transition probabilities are given by

The expected source retransmission load can be derived from Formula 5.1.

For the receiver-assisted scheme we first have to divide the multicast group into subgroups. Let us assume that a receiver-assisted scheme would use three subgroups in our example (see Figure 5.4): consisting of S, and (the source being responsible for retransmissions), consisting of and

( being the dedicated receiver) and consisting of and ( being the dedicated receiver). As a result, from the point of view of the source, there are only three forms of sub multicast tree which corresponding to sub-tree C, E and F in the sender-originated case. The transition probabilities matrix becomes

#

#*#

The router-assisted scheme can be seen as the source reliably transmits packets to its downstream nodes and then these downstream nodes guarantee packet de-livery to their downstream nodes. Therefore, the source retransmission load is the same as the case of one-level binary tree.

Figure 5.5 illustrates how the expected retransmission load for sender-originated, receiver-assisted and router-assisted schemes varies with the loss probabilities . The diagram on the right is just an enlargement of the bottom left corner of the left one. Obviously the load of sender-originated scheme soon becomes unacceptable in two-level binary tree. Even for small loss probabilities the retransmission load is rather high. The improvement achieved by the receiver-assisted scheme is only marginal. In comparison to this, router-assisted scheme performs the best. This scheme results in acceptable load even for loss probabilities higher than 50%.

5.1.3 Discussion

When packet loss rate of wireless links is small, a two-level binary tree can be seen as a one level tree in which two leaves are a sub one-level tree. Thus, we can use the following formula to approximately calculate the retransmission load

S

Figure 5.4: Subgroups for receiver-assisted retransmission

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 5.5: Retransmission load when varying

. Consequently, as network and group size increase, the retransmission load of source in a L level tree is

. This formula demonstrates that the source retransmission load of ARQ is a function of the multicast tree size and the packet loss rate on links. In a wired network, packet loss rate is relatively small and it is network size that plays a key role in retrans-mission overhead. That is why improvements address the issue of maintaining the scalability of reliable multicasting to reduce retransmission in large scale networks [72]. Their common idea is to distribute retransmission task to nodes other than the sender through local recovery. According to the type of nodes which send recov-ery packets, the reliable protocols using local recovrecov-ery techniques can be further classified into receiver-assistance retransmission schemes and router-assistance re-transmission schemes. However, the packet loss rate in MANET is relatively high due to wireless interface and unpredictable topology changes. Consequently, even in a small network, the retransmission load might be important. As show in Figure 5.5 if the packet loss rate on each link is 0.08, the retransmission load of source (tree root) exceeds 0.5 in a two-level binary tree under sender-originated scheme.

It is necessary to employ receiver-assistance retransmission scheme and/or router-assistance retransmission scheme in reliable multicasting protocol for MANETs.