# A minimum cost heterogeneous sensor network with a lifetime constraint

## Summary (3 min read)

### 1 INTRODUCTION

- SENSOR networks are dense networks of low cost,wireless nodes that sense certain phenomena in the area of interest and report their observations to a central base station for further analysis.
- Type 0 nodes do the basic sensing as well as the relaying of packets since multihop communication is used within each cluster.
- Each visit of the aircraft triggers a sensing and data gathering cycle on the ground during which every node sends a packet to its cluster head.
- {mhatre, cath, mazum, shroff}@ecn.purdue.edu., also known as E-mail.

### 3 PROBLEM FORMULATION AND MODELS USED

- There are two types of nodes; nodes of energy level E0 deployed Authorized licensed use limited to: University of Waterloo.
- Thus, the aircraft serves as the remote base station.
- For the sake of simplicity, in the rest of this paper, the authors assume that all the clusters send information to the base station during every data gathering cycle.
- In the second scenario, nodes are deterministically placed along grid points.

### 3.1 Cost Model

- Let C0 and C1 be the cost per node for each type of node.
- Then, a simple model for a cost function is,.

### Ci ¼ i þ Ei;

- Where i and are some constants that depend on the manufacturing process.
- The constant i is the cost of the hardware of a type i node (excluding the battery cost), while is the proportionality constant for the battery cost.

### 3.2 Connectivity and Coverage Model

- For the sensor network to provide sensing coverage of the region and for the nodes to successfully use multihop communication, it is necessary to ensure that the conditions for node connectivity and area coverage be met.
- Using a similar approach, the authors can study the case in which nodes are deployed over a unit area with a two-dimensional homogeneous Poisson point process.
- The authors restrict ourselves to omni- directional sensing in order to keep the model generic.
- For simplicity, the authors assume that r is also the critical distance between any two nodes for successful transmission.

### 3.3 Lifetime Constraint Model

- This is because the critical nodes are the last hop nodes for all the paths (see Fig. 1).
- Hence, among all the type 0 nodes in a cluster, the critical nodes have the highest burden of relaying data.
- In order to have a sharp cutoff effect, the authors also require that almost all the nodes in the network expire at about the same time.
- This ensures that very little residual energy is left behind when the system becomes unusable, i.e., when coverage and/or connectivity are lost.
- Let P0 be the average energy spent by a typical critical node during each cycle, and let P1 be the average energy spent by a typical cluster head during each cycle.

### 3.4 Energy Model

- This consists of energy spent on relaying packets of other nodes that are in the same cell (Pr0 ), and transmitting one’s own data (Et0 per packet).
- The authors also assume that during each data gathering cycle a type 0 node sends one packet of its own to its cluster head.
- This consists of energy spent on receiving data from other nodes in the cell (Er0 per packet), processing and compressing the received data (Ef per packet), and transmitting the compressed data to the aircraft (Et1 per packet).
- The authors also assume that the cluster heads coordinate MAC and routing in their respective clusters so that no energy is wasted on packet collisions or idle listening (ideal MAC assumption).

### 4.1 Random Deployment

- For that, the authors need some results from stochastic geometry [14].
- Since type 0 nodes as well as type 1 nodes are deployed using a homogeneous Poisson point process, the authors can shift the origin to one of the type 1 points and use Campbell’s theorem and Slivnyak’s theorem [16] to compute the expected number of type 0 nodes in a typical Voronoi cell.
- The authors have introduced the constants c0, c1, c2, and c3 for ease of notation.
- The authors assume a propagation loss model of 1x 2 for communication between a node and its cluster head, and 2x 4 for communication between the cluster heads and the base station.

### 4.2 Grid Deployment

- Now, the authors consider a simple grid of nodes in which nodes are placed along grid points with distance r between them.
- The authors would like to compare the results that they get for the random node deployment scenario with those for the grid deployment scenario.
- The proof is along similar lines as before and is therefore skipped.
- As the energy spent in countering the propagation loss to communicate with the aircraft ( Hk) is much larger than the other energy terms ( rk, l, Ef ), c2 dominates over other ci (see (14) and (15)).
- If the nodes are unreliable and the authors use the random deployment model, all their results are still valid with minor modifications because even in this case, the coverage-connectivity constraint retains the same log = form .

### 5 NUMERICAL RESULTS

- The authors provide justifications for the approximations that they made in obtaining (23) by using some typical transceiver radio parameters.
- Hence, for the above settings, all the distances should be divided by 10km.
- These are typical values for practical surveillance networks.
- From Fig. 2, it is clear that the approximation works quite well for the settings of practical interest since the curves corresponding to the exact and the approximate solutions overlap.
- As H decreases, the communication between the cluster heads and the aircraft becomes less expensive.

### 6 CONCLUSIONS

- The authors consider two types of hierarchical sensor networks: one that uses random uniform deployment and the other that uses grid deployment.
- Type 0 nodes have energy level E0 and are deployed with intensity 0, while type 1 nodes have energy level E1 and are deployed with intensity 1.
- The authors provide results that guarantee a minimum lifetime (i.e., at least T successful data gathering trips) of the sensor network.
- For this, the authors note that the cluster heads as well as the nodes within one hop of the cluster heads, i.e., the critical nodes have the maximum relaying burden and, therefore, these nodes are likely to run out of battery before other nodes.
- The authors compare the results for the random deployment with those of the grid deployment.

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##### Citations

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### Cites background from "A minimum cost heterogeneous sensor..."

...Mhatre et al. [11] evaluated a hierarchical network with two types of nodes: sensors deployed with intensity λ0, and nodes with higher energy and communication capacity deployed with intensity λ1....

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...[17] considered a heterogeneous sensor network in which the nodes are to be deployed over a unit area for the purpose of surveillance....

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...The use of mobile sinks with predictable mobility has been more recently presented in [ 32 , 45, 46] and [9]....

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##### References

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...In [11], cluster head rotation requires that all the nodes be capable of performing data aggregation as well as long range transmissions to the remote base station....

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...RELATED WORK In [11], Heinzelman et al consider a homogeneous clustered network in which each cluster head collects data from its one hop neighbors, aggregates the gathered data, and transmits it directly to the remote 3...

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...We assume the radio model used in [11] wherein the energy required to transmit a packet over distance x is l+ μx....

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### "A minimum cost heterogeneous sensor..." refers background in this paper

...In [11], Bandyopadhyay and Coyle consider a homogeneous sensor network in which nodes are uniformly deployed using a two-dimensional Poisson point process over a unit area....

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