### Reliable mac layer multicast in ieee 802.11 wireless networks

As decreases with , we can obtain the following inequality from 14 , setting :. Solving the quadratic inequality , we prove that it holds with , where is determined by Thus, 22 holds with.

## Reliable MAC layer multicast in IEEE 802.11 wireless networks

Now let. As follows from 10 , increases with and hence. Since 22 holds with , it also holds with. Now, we consider throughput QoS requirement. Since PLR sequences and are nonincreasing, then using 17 , we can derive the following inequality:. According to 10 and 16 , and increases with , that is,. Hence the inequality holds. At the same time, we have. This allows us to rewrite the previous inequality in the following form:.

Thus, in the optimization we need to consider and only, where is the minimal recipient number which PER is less than defined by The selection is performed from the whole set of recipients, according to their weights. Let us partition all recipients into sets. In set , there are recipients, which PER is nearly the same and approximately equal to. Obviously, we assign the same weights to all recipients of set that makes optimization of the weight distribution easier. This partition makes numerical analysis and optimization of the weighted ELBP much easier in the case of a large number of recipients.

Of course, the partition is not reasonable with a small number of recipients. In this case, we just set and. As ACK-leaders are to be selected, the selection procedure is carried out in steps. At step , an ACK-leader from set is selected with probability. That is, , , is a selection vector indicating which recipients have been selected after steps. Obviously, and vector indicates all current ACK-leaders responsible for acknowledging the current data burst transmission. The multicast sender stops transmitting a packet when all current ACK-leaders acknowledge the packet and thus, receive the packet successfully.

Taking 26 into account, the probability distribution of can be found recursively. Here and further, for any and , if for all and. To find , we consider a process of a given packet transmission.

CSE 574-14-05: Introduction to IEEE 802.11 Wireless LANs

Let us introduce a success vector , where is the number of recipients in set , which successfully receive the packet after transmission attempts. Obviously, and. The probability of the success vector change from to after the th attempt, given that the th attempt failed for at least one of recipients which were current ACK-leaders, is. Let be the probability that after attempts the packet transmission process does not complete successfully and the success vector is.

Hence, the probability that not all recipients serving as current ACK-leaders have received the data packet after attempts, is. To find PLR for a fixed recipient from set , we introduce the probability that the success vector changes from to so that the given recipient does not receive the packet by the end of th attempt:. Thus, the probability that after the th attempt, the packet transmission process does not stop, the given recipient from set does not receive the packet and the success vector is , is obtained recursively for all such that :.

Now, we can find expressions for probabilities that attempts have been carried out to transmit the packet and the given recipient from set has not received the packet in any of these attempts. Thus, the PLR for a recipient from set is:. Throughput for any recipient from set is given by 17 , where we substitute for. In this section, we use our analytical models to investigate and to optimize ELBP multicast schemes with different wireless technologies and in different use cases.

As we don't apply any simplifications and assumptions about original ELBP multicast schemes, our mathematical models are accurate and there is no need to validate them via simulation. Although we use some simulation to obtain the input data the dependence of recipient's PER on distance for our analytical models. As the first usecase, let us consider an All model parameters correspond to the IEEE Let fixed ELBP be used. Based on Theorem 1, we conclude that recipients from sets 1—4 only can be selected as ACK-leaders, that is,.

Further, for any tuple , , we estimate PLR and throughput for every recipient by 12 , 14 and 17 and check if QoS requirements 1 and 2 are met. In this way we form an admitted region of and. In Figure 5 , we show values of consumed bandwidth fraction defined by 3 with. We see that the following 2 tuples are close to optimum: , , and ,. An IEEE To increase the network capacity and QoS provisioning, a BS is equipped with sector antenna.

Each sector of this antenna covers a separate area with a part of all SSs in it, achieving spatial diversity. In fact, we can consider each sector as an individual IEEE So, further results will concern one of such sectors. Let us assume that the BS is a multicast sender and the only multicast data burst is transmitted in every frame, that is,. The So, the maximal number of retransmissions is , according to 8. First, we consider more general case shown in Figure 6. To start numerical analysis we need to derive the dependence of recipient's PER on distance for the investigated network.

We divide the process in two steps. First, we obtain the dependence of signal-to-noise ratio SNR on distance according to the path loss model in [ 24 ] with a critical parameter. In Figure 7 , we show the simulation data for various packet lengths. We also include the analytical approximation of the dependencies obtained by simulation.

We approximate the simulation data using the formula. As it is shown in Figure 7 , the proposed analytical approximation fits perfectly the simulation data. Using 38 with , we find PER for every recipient. Thus, for a given number of stations and PER distribution, we can find the optimal number of ACK-leaders minimizing the bandwidth allocated for a given multicast connection per frame see 7 , while meeting a certain QoS requirement on PLR for all recipients.

The figure shows two of ELBP main advantages. The first advantage is the scalability. We can see also that the optimal number of ACK-leaders is nearly proportional to the number of recipients. The second advantage is the supremacy over the pure LBP in reliability. Let us consider the case, when there are multiple sets of recipients and recipients of the same set have the same PERs. For certainty, let us assume 3 sets in this usecase, which correspond to 3 small settlements covered by a single sector of an IEEE The total number of recipients is. Let us define QoS requirements.

The PLR characteristics of these multicast schemes are shown in Figure In contrast, the other schemes need much more ACK-leaders. The next step of our investigation is to find the optimal burst size. For that, we find how throughput depends on with optimal numbers of ACK-leaders found at the previous step.

## Figure 10 from Reliable MAC layer multicast in IEEE wireless networks - Semantic Scholar

The throughput characteristics are given in Figure This figure shows that the optimal burst size which minimizes in 7 is equal to 7 in case of weighted ELBP, while it is equal to 8 for full random selection scheme and 9 for fixed ELBP. At last, let us show the allocated bandwidth with these selection schemes.

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Existing standards of high rate wireless networks consider multicast as unreliable service, which is inappropriate for many multimedia applications making strict QoS demands. In this paper, we study a promising enhanced leader based protocol ELBP for reliable multicasting in wireless networks. In ELBP, multicast packets are transmitted in bursts and several multicast recipients called the ACK-leaders are appointed to be responsible for multicast data packets acknowledging. Specific QoS requirements maximal packets loss ratio, maximal latency, minimal reserved rate can be met by varying such ELBP parameters as the number of ACK-leaders as well as the data burst size and periodicity.

We develop accurate analytical models to estimate reliability and performance indices with these schemes and to find their optimal parameters. Reliable multicast in multi-access wireless LANs. Wireless Networks , , 7 3 : — Tang K, Gerla M. MAC reliable broadcast in ad hoc networks. Bertsekas D, Gallagher R G. Data Networks. Second Edtion. Prentice-Hall, Tobagi F A, Kleinrock L.

## RMAC: A Reliable MAC Protocol Supporting Multicast for Wireless Ad Hoc Networks

Packet switching in radio channels: Part II—-The hidden terminal problem in carrier sense multiple-access and the busy-tone solution. IEEE Trans.

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