## 1 Introduction
To reflect a static distance instead of the immediate distance, EAR2 considers the expected area where a mobile sink will be located by using its movement speed. To deliver real-time data within the desired time deadline, EAR2 guarantees that the total summation of the unicasting time to the expected area and the flooding time within the expected area is smaller than the deadline. To do this, EAR2 calculates a delivery speed using the static distance to the expected area and the unicasting time and observes the flooding time from various network environments. In EAR2, the source transmits data to the expected area with the delivery speed, and the first sensor node in the area then floods the area to deliver the data to the mobile sink that is dynamically located in the area. However, since EAR2 uses a single flooding point, it has a high flooding time and data loss problems [14; 15]. Therefore, to solve the problems of EAR2, we propose a protocol called EAR2M that extends EAR2 by exploiting multiple flooding points. By using multiple flooding points, EAR2M reduces the flooding time and enhances the reliability of data transmission. Because EAR2M provides lower flooding times than EAR2, it demands less data delivery speeds and thus achieves lower deadline miss ratios compared with EAR2. The efficiency of the transmission delay and energy consumption are two important challenging issues in wireless sensor networks [16; 17] Thus, we also propose two extensions of EAR2M, called EAR2M_R and EAR2M_E for efficient data transmission from a source to multiple flooding points. EAR2M_R and EAR2M_E aim to reduce the transmission delay and the energy consumption for data transmission among multiple flooding points, respectively. Although both EAR2M_R and EAR2M_E have better performance than EAR2M, they have a trade-offbetween the transmission delay and the energy consumption. We conducted simulations in various network environments through the network simulator NS2 to evaluate the network performance of the proposed protocols. Simulation results conducted in various environments verified that EAR2 significantly improves the network performance when compared with the existing protocols SPEED [4] and THVR [6] in terms of deadline miss ratio and energy consumption. Simulation results showed that EAR2 enhances the deadline miss ratio and the energy efficiency by 57.94% and 39.80% over SPEED, respectively, and by 36.40% and 20.18% over THVR, respectively. Additionally, the simulation results showed that EAR2M has a better performance than EAR2, and EAR2M with four flooding points improves the deadline miss ratio and the energy consumption by average values of 12.69% and 131.86% over EAR2. We have also demonstrated that EAR2M_R and EAR2M_E have a trade-off between the deadline miss ratio and energy consumption through simulation results. The remainder of this paper is organized as follows. First, we provide the literature review on real-time routing in Section 2. The network model and the overview of our expected area-based real-time routing (EAR2) protocol are presented in Section 3. Details of EAR2 and EAR2M are described in Sections 4 and 5, respectively. The extensions, EAR2M_R and EAR2M_E of EAR2M are described in Section 6. The simulation results are provided in Section 7 to evaluate the performance of EAR2, EAR2M, EAR2M_R, and EAR2M_E. The paper is concluded in Section 8.