A Mixed-Integer Cost Estimation Model for Scheduling the Mobile Element in Wireless Sensor Networks

In Wireless Sensor Networks, recent studies reveal mobility as a solution for collecting the data from the sensor nodes in a wireless sensor network. The mobile element acts as mechanical carriers for collecting the data from the sensor nodes. Each sensor node is assigned a buffer for accumulating the sensed data and data loss occurs if the buffer overflows. Therefore scheduling of the mobile element such that none of the buffer overflows is a major issue involved in collecting the data from the sensor nodes. The proposed problem incorporates the partition of the sensor nodes into clusters according to their geographical regions. Within each cluster, a hierarchical tree structure is formed such that the baselevel nodes are the nodes visited by the mobile element. The remaining nodes within this region form a tree structure so that these nodes relay the data to the next hop nodes. The data is segregated to the next level nodes depending upon the number of nodes in that level. The grouping of data is dynamic since it is based upon the number of nodes in the next level. This occurs as a recursive relay process until it reaches the boundary nodes (i. e. nodes near the mobile element). Data collection of all the nodes from these boundary nodes by the mobile element implies the following: i) the visit of the mobile element is minimized ii) the lifetime of the mobile element is increased iii) occurrence of the loss of data will be reduced because at least a part of the data can be recovered due to the splitting up of the data between the next level nodes iv) the deadline for the collection of data from the sensor nodes will not be missed since there is a periodic relay of the collected data from the high-level to the boundary nodes. Further, this paper presents the mobile element scheduling problem (MES) as a mixed-integer programming (MIP) model and optimizes the cost by scheduling with earliness-tardiness penalties. The objective is to optimize the cost of the earliness-tardiness penalties and also to reduce the buffer overflow so that the capacity constraints are also taken into consideration. Also the MES-MIP modeling structure can be exploited to analyze the penalty cost involved in the scheduling of the ME which can be further employed for larger set of sensor nodes.