### A Simulation Model for the Life-Time of Wireless Sensor Networks

Abdelrahman Elleithy
2011 International Journal of Ad Hoc, Sensor and Ubiquitous Computing
In this paper we present a model for the lifetime of wireless sensor networks. The model takes into consideration several parameters such as the total number of sensors, network size, percentage of sink nodes, location of sensors, the mobility of sensors, and power consumption. A definition of the life time of the network based on three different criteria is introduced; percentage of available power to total power, percentage of alive sensors to total sensors, and percentage of alive sink
more » ... of alive sink sensors to total sink sensors. A Matlab based simulator is developed for the introduced model. A number of wireless sensor networks scenarios are presented and discussed. Wireless sensors have received increased attention in the past years due to their popularity and cost effectiveness when they are used in harsh environments. They have been used in many applications including military applications, environmental applications, health applications, and home applications. Although they are very cost effective and easily deployed in harsh environments, they are limited by the power available through their life cycle. Sensors are usually deployed with limited power which is depleted over their lifecycle. Once their power is depleted, the sensors become dead and they are no more useful. An evaluation of the life cycle of a wireless sensor network is very essential to estimate how long a network can live and when the network and its sensors might be replaced or recharged if possible. In this section we present a model for the lifetime of Wireless sensor networks based on a paper by [1]. The model takes different parameters that used in literature. The following parameters are considered: 1. The time until the first sensor is drained of its energy [2]; 2. The time until the first cluster head is drained of its energy [3] ; 2 3. The time there is at least a certain fraction β of surviving nodes in the network [4]; 4. The time until all nodes have been drained of their energy [5]; 5. K-coverage: the time the area of interest is covered by at least k nodes [6] ; 6. 100% coverage a. The time each target is covered by at least one node [7] ; b. The time the whole area is covered by at least one node [8] ; 7. α-coverage a. The accumulated time during which at least α portion of the region is covered by at least one node [9]; b. The time until the coverage drops below a predefined threshold α (until last drop below threshold) [10] ; c. The continuous operational time of the system before either the coverage or delivery ratio first drops below a predefined threshold [11]; 8. The number of successful data-gathering trips [12] ; 9. The number of total transmitted messages [13]; 10. The percentage of nodes that have a path to the base station [11]; 11. Expectation of the entire interval during which the probability of guaranteeing connectivity and k-coverage simultaneously is at least α [6]; 12. The time until connectivity or coverage are lost [14]; 13. The time until the network no longer provides an acceptable event detection ratio [5]; 14. The time period during which the network continuously satisfies the application requirement [15]; 15. min(t1, t2, t3) with t1: time for cardinality of largest connected component of communication graph to drop below c1 × n(t), t2: time for n(t) to drop below c2 ×n, t3: time for the covered volume to drop below c3 ×l d [16]. PARAMETERS USED IN THE MODEL In this section we address parameters that were introduced in literature that can be used in a complete model for a wireless sensors networks life time. The following parameters are introduced: 1. The total number of available sensors 2. The set of all nodes those that are alive at a certain time t 3. The set of nodes those that are active at a time t