## 4 Average end-to-end delay
However, when the transition phase exceeds the optimal moment, more unrelated nodes participate in the routing and forwarding of Prelearn messages, the number of hops in a successful data transmission increases and a large amount of energy is consumed in mission calculations and information transportation. Consequently, the average end-to-end delay in the Predict and Forward algorithm begins to rise. Figure 5: The probability of the destination profile receiving Prelearn messages. Figure 6: The probability of the destination profile receiving Prelearn messages. Figure 8: Overhead. Figure 7: Delivery ratio. Figure 9: Average end-to-end delay. Figure 10 shows the comparison results between the four algorithms in terms of delivery ratio. As it can be seen, the average delivery ratio in the Predict and Forward algorithm is the highest among them. This is because the data transmission in Predict and Forward algorithm is implemented through node attributes, and Prelearn messages are transmitted to the relay nodes, which have a relatively high probability of meeting the destination profile. As the cache space continues to increase, nodes in the network can handle complex computing tasks and carry more information, so the delivery ratio is growing rapidly. In Predict and Forward scheme, the delivery ratio is over 0.9 when data cache exceeds 37.5 Mb, and it reaches the maximum value when data cache is 40 Mb. As for EIMST algorithm, it does not have an effective way to implement cache management of nodes, so the delivery ratio in this algorithm is lower than Predict and Forward. In addition, Epidemic routing algorithm and Spray and Wait algorithm produce a large number of message copies in the data transmission process, so the delivery ratio in the two algorithms is always relatively low. Overall, the delivery ratio in the Predict and Forward algorithm is 0.85 on average, which is higher than the other three algorithms. Figure 11 shows the comparison results between the four algorithms in terms of overhead on average. As it can be seen, with the increase of the cache space, the overhead on average drops dramatically. Moreover, the overhead on average in Predict and Forward scheme is the lowest among the four algorithms. When the cache space is over 20 Mb, the overhead on average in Predict and Forward algorithm always keeps the lowest, because it adopts two different phases to implement the optimal process for data transmission. When an optimal phase transition is found between Predict and Forward phases, the number of hops of a successful data transmission in Predict and Forward is less than the other algorithms, and the time spending on the routing and forwarding of Prelearn messages is also less than the other algorithms. Moreover, the increase of the cache space means there are more resources for nodes to carry information and execute computational tasks. As for the other three algorithms, the overhead on average in EIMST fluctuates between 20-150 and the overhead on average is between 80-220 in Spray and Wait or Epidemic. Figure 12 shows the comparison results between the four algorithms in terms of average end-to-end delay. As it can be seen, the average end-to-end delay in Epidemic is always the highest among them, because the node in the network may have more computation tasks in this algorithm. However, in Spray and Wait or EIMST, the multicopy model is used to implement data transmission so that the average end-to-end delay in them is superior to the Epidemic. It is clear that the average end-to-end delay in Predict and Forward algorithm is the lowest among the four algorithms, because this scheme always selects the relay nodes which have a high probability of meeting the destination profile as the next hop. When the transition phase is at the optimal moment, this scheme keeps a  
Figure 10: Delivery ratio. balanced state between exploring the network and forwarding Prelearn messages, so the average end-to-end delay in the Predict and Forward gets a minimum value of 25.