# End to End Delay and Energy Consumption in a Two Tier Cluster Hierarchical Wireless Sensor Networks
## 2 Related Work  
Some previous works are partially in line with our contribution. In [9] a TDMA scheme based on an innovative TreeMAC design is proposed. Using a tree topology, TreeMAC alleviates the energy hole problem (nodes near the sink are more loaded than nodes away from the sink) but the evaluation of the end-to-end delay is not provided. In [1] a cross layer non-linear optimization model is formulated for a two tier WSN. The TDMA scheduling algorithm is based on the slot reuse concept (from cellular networks) keeping in mind three interference criteria to be satisfied. While communication from cluster members to the CH is restricted to one hop, communication between CHs and Gateways can be multiple hop. After the inter-cluster slot assignment (no intra-cluster slot assignment is considered) the nodal delay is approximated derived. The E2E delay is evaluated as the sum of the nodal delays along the path to the sink. In [10] a cluster tree topology for WSN is considered and the E2E delay--local transmission + inter-cluster transmission--is evaluated in a similar way to our proposal. However no RAP for communication between sensors and CH is assumed. Instead, only a TDMA scheduling is operative for inter CH communication in which three different sub-intervals conform a super-frame (SF), i.e., the local receiving (LR) phase, the inter cluster transmitting (IT) phase and the inter cluster receiving (IR) phase. As we do in our work, CHs forward collected data from their cluster members to the sink through other CHs hop-by-hop. However, unlike [10], in our work we combine the contention phase (FSA protocol) with the contention-free phase (TDMA scheduling) and derive an exact expression for the E2E delay. In [11] the E2E analysis of a chain of \(K\) non-preemptive nodes from sensor to the sink is investigated. Poisson arrival rate and exponential service time are assumed for high (control) and low (data) priority traffic. In order to save energy a vacation period with arbitrary distribution is introduced just to capture the concept of sleep and wake-up modes. The authors use the M/G/1 queue as an approach for the analysis of each individual node, and assume independence between the nodes, so they ignore the coupling between consecutive nodes in the chain and the concept of time slot reuse has not been taken into account. In contrast, in our approach, the data packets are of fixed size, the periods of inactivity are also deterministic, and our model captures the coupling or dependency between the neighboring nodes. In [12] a data gathering tree topology for WSN is studied. As MAC protocol they use a TDMA slot assignment where each node is only permitted to send or receive data during its assigned time slot. The difference with previous works with [12] and with our work, is that the functions of time synchronization and sleep mode are added to the time intervals with the main purpose of minimizing energy consumption and data delivery time. Also indicate that [12] considers a single-level architecture, i.e., the concept of CH with its members and associated MAC is not taken into account. On the other hand, a common feature of our work with [12] is the scheduling of consecutive data packets to be forwarded from CH to CH in consecutive data mini-slots allocated in the same time slot. In [13] a hybrid TDMA/CSMA MAC (TCH-MAC) layer protocol is proposed for a two-tier architecture. CSMA with RTS/CTS control packets is considered for communication between CH members and their CH. TDMA is the adopted MAC for inter CHs communication. Throughput and energy consumptions are the parameters evaluated by simulation. The proposal is similar to our protocol, but the contention period entails some more complexity due to the CSMA implementation. In addition, the concept of reusing time slots is not implemented nor is the end-to-end delay analyzed. In none of the proposals offered in [1,10,12,13] the energy hole problem [14] is treated. In our work this has been considered.