The 4G routing algorithms presented in this Chapter are evaluated in terms of their delivery success rate, level of message overhead and delay they incur. One or more scenarios are defined according to some parameters chosen mostly as fixed variables or a combination of factors (various values). The selected scenarios depict a number of situations such future networks may operate in. Not only are these metrics going to tell the reader more about the relationship between some existent and future routing approaches for 4G, but these are also expected to give some helpful and explicit insights into the understanding of routing issues and solutions in the new 4G context. As a result, the simulations are going to span a number of configurations in an attempt to identify and separate those states that offer better performance while reducing overhead and resource requirements. For instance, some specific factor value may be set to induce chemotaxy, stigmergy, diffusion or percolation, used in biological, social and physics modeling.
One objective is to show how percolation stimulus may be discovered for a given 4G scenario. The next step is then to determine the routing improvement a network engineer may obtain once this understands and knows how to handle the stimulus. Given that this is a case study, public domain software and solutions will be used whenever possible to allow the reader to repeat parts of the study. The algorithms and simulation tools may be openly obtained from the Web as well as information on the traffic and topology models used in the scenarios. With this in mind, the OMNet simulator, the PRoPHET algorithm and its set of data – mobility and traffic models have been selected to compose the network scenario. This scenario contains 50 nodes with random mobility and its simulation takes around 3995 seconds to run. The initial topology is shown in Figure 1.
To evaluate percolation in the PRoPHET scenario, both the buffer size and the number of message replication in routing information were chosen as the percolation variables that should establish a percolation threshold in the model. Next, it was necessary to check the stimulus selected and see if it was able to percolate in this scenario. In other works, this work checked if there is a buffer size limit and a message replication level that determine a stable number or a successful delivery rate of the network. In this case, messages were associated to the fluid, and both buffer and message replication to the surface when considering the analogy with the liquid percolation model used to establish when a fluid starts running through a given surface.
Firstly, the buffer size is a variable that was changed between 2 and 100, with increments that also varied between 2 to 10 with an increment of 2, while all the other variables were maintained fixed. Message replication was also set to 1. Figure 2 shows the results of this first evaluation with a stable state reached for a buffer size of 12. Hence this is the limit value of the percolation model, but the best configuration, the one with highest delivery rate, is obtained with an even smaller buffer size equal to 6.
Next, the number of the message replication was changed in the simulations from 2 to 100, with increments of 2. In turn these increments where also set to values from 2 until 10 with a step of 2. Similarly the other scenario variables were maintained constant including the buffer size set to 100. Figure 3 illustrates the results with stable state when the number of message copies is 24 or any other larger value. Hence, 24 is seen as the percolating number of copies, but the best delivery rate occurs when the number of copies is 2.
Both the variation of buffer size and message replication of only one node are also evaluated. Firstly, the buffer size of only one node is a variable that was changed from 2 to 100, incrementing this by 2 to 10 increments, while all other variables were maintained. Message replication was also maintained with a single value and buffer size of 100 for all nodes. Figure 4 presents the results of this evaluation with a stable state reached when the buffer size is 10. So this value represents the limit value of the percolation model.
Next, the effect of message replication is studied. In these simulations, a single node was selected and subjected to changes in its level of message replication. In this case, node 24 had his message replication mechanism changed to use values between 2 and 100, with increments between 2 and 10. In the scenario presented here, the buffer size was set to 100 for this special node while all variables were left unchanged. For the other nodes, message replication was fixed at 1, i.e. a single replication was used, while their buffer size had the value of 100. One can see from the results that, for example, when node 24 (the differentiated node in this scenario) sends 2 replications, it already obtained almost a 50% delivery rate. Percolation was achieved when the level of copies reached 4 (Figure 5).
In a different evaluation, the number of message replication and nodes that may replicate messages were changed. The number of nodes allowed to replicate messages was incremented until reaching 50 nodes representing the total nodes of the network scenario. The other nodes continued with their default behavior where only a single copy of any given message was injected into the network. So, initially, a unique node was making 20 copies of messages it was sending, in the next round of simulation two nodes could make 20 copies of a message and send this, then 3, 4… nodes until all the 50 nodes where doing this. Strangely, the results have shown that even when there were different numbers of nodes with the same number of replication (heterogeneous network), when the number of copies was 50,100 and 150, the delivery rate of node 24 presented the same behavior as in Figure 6 (a special and identical function). There is a stable behavior when the number of copies is 50, 100 and 150. For example, when there are 3 nodes with 50, or 100, or 150 copies, the delivery rate is 27%. When the number of copies for 7 nodes is 20, 50, 100 or 150, the delivery rate is 43%. This shows that it is necessary to run extensive simulations, for any given scenario, in order to determine the minimum number of copies as well as the minimum number of nodes making message copying that offer a good delivery level that ensures a required quality of service level to node 24 in this case. It is clear that one needs to establish the percolation pair (replication level, number of nodes that do message replication) in order to ensure that:
- All the nodes of a network are able to achieve their minimum QoS requirements in terms of message delivery in this scenario. Other QoS parameters such as bandwidth, delay and jitter may also be observed as reference levels to achieve;
- To avoid clogging the network with unnecessary message copies and possibly leading to the congestion of parts of the network, one needs to consider the traffic overhead and network occupation as new metrics for choosing the right percolation pairs that may achieve similar levels of message delivery or other QoS requirements.
Actually, by observing only node 24 delivery rate, the simulations have shown that a configuration where 8 nodes make 20 message replicas each gives the best delivery to this node.
New studies and simulations are needed to gain more insights on how to build some rules of thumb for the optimized routing configuration for this type of algorithms. Although each topology may need a different setup, but one expects to hopefully find some general rules that apply across the spectrum of 4G topologies and provide adequate routing performance.
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