###### Abstract
Then, in the improvement phase, the retransmission time slots are added to link groups as long as they satisfy the delay constraint. In the shared time slot scheduling method, retransmission time slots are shared among multiple packets to reduce the number of slots while satisfying the required reliability. [PERSON] et al. [11] proposed a method called SchdEx to extend a scheduling algorithm to guarantee the end-to-end reliability, which determines the number of time slots to each link based on packet loss rates of the entire network. The SchedEx method decomposes the end-to-end reliability into node-to-node reliability to make the calculation easy. [PERSON] et al. [12] proposed a flow-based assignment method to reduce the required number of time-slots by prioritizing the flows sharing links and assigning shared time-slots efficiently among the flows. The above methods in [10; 11; 12] focused on the reliability of the sensor data transmission of flows and reducing the number of time-slots to be assigned to guarantee the required end-to-end reliability. These approaches transmit a packet multiple times in successive time slots to provide the required reliability. These approaches, however, can increase the average end-to-end delay of packets and the number of packets buffered in the queue of the node where multiple flows are multiplexed. This paper proposes a new scheme to estimate the probabilistic amount of packets, called queue level (QL), in the buffer of each node based on the packet reception rates (PRRs) of the wireless links. A node with higher QL means that it can have more packets probabilistically in the queue than the node with lower QL. This paper also proposes a QL-based centralized scheduling algorithm to assign time slots efficiently in TDMA-based IWSNs. The proposed algorithm first calculates the number of time slots that need to be assigned to each node based on the target end-to-end reliability and PRR values of the wireless links. To determine (time-slot, channel) for the time slots assigned to the nodes, the proposed scheduling algorithm uses a prioritization scheme, which gives higher priority to the node with higher QL. By assigning time slots first to the node with the highest QL, we can reduce the average end-to-end delay of packets and reduce the number of packets buffered in the queue while satisfying the required end-to-end reliability. We evaluated the performance of the proposed scheduling algorithm through a simulation using a Cooja simulator in Contiki [13] and compared it with the flow-based prioritization approach in [12]. In the simulation on an example network in [12] with the target end-to-end reliability of 99%, each node transmitted one packet for each slot frame during 5000 slot frames following the schedules of the proposed algorithm and the flow-based approach, respectively. The simulation results showed that all of the flows guaranteed the target reliability in both of the algorithms: on average, 99.76% in the proposed algorithm and 99.85% in the existing approach. On the other hand, the proposed algorithm showed much better performance than the existing approach in terms of the average end-to-end delay and the number of buffered packets in the queue. The average end-to-end delay of packets of the flow-based approach was 184.4 ms and that of the proposed algorithm was 87.8 ms, which was more than 50 less than the flow-based approach. In the case of packet buffering, the average of maximally buffered packets of the proposed algorithm was lower than or equal to that of the flow-based approach in all nodes. In the case of the flow-based approach, the buffering requirement increases linearly, depending on the number of flows sharing a link. On the other hand, the number of buffered packets in all nodes were maintained at a fixed value (about 2 in the simulation). The rest of this paper is organized as follows. In Section 2, we describe the network model and the notation used in the paper.