Abstract
Data-centric storage provides energy-efficient data dissemination and organization for the increasing amount of wireless data. One of the approaches in data-centric storage is that the nodes that collected data will transfer their data to other neighboring nodes that store the similar type of data. However, when the nodes are mobile, type-based data distribution alone cannot provide robust data storage and retrieval, since the nodes that store similar types may move far away and cannot be easily reachable in the future. In order to minimize the communication overhead and achieve efficient data retrieval in mobile environments, we propose a reinforcement learning-based framework called PARIS, which utilizes past node trajectory information to predict the near likely nodes in the future as the best content distributee. Our framework can adaptively improve the prediction accuracy by using the reinforcement learning technique. Our experiments demonstrate that our approach can effectively and efficiently predict the future neighborhood.
) sensors are used for animal migration tracking, and (
) wireless devices are equipped with police officers to monitor their daily patrol routes, collect crime information by areas, and record corresponding law enforcement actions. In these two scenarios, efficient data retrieval can be achieved if the data-centric storage is enabled, that is, the data is stored by the types of animals, by the activities performed by the animals, or by the tasks that are carried out by the police officers. The challenge is to design schemes that can support data-centric storage when all the nodes are moving around. In this paper, we consider a fully distributed network, in which there is no node playing the sole role as storage; each node can act as both the collector and storage node. For instance, a wireless node, playing the role of a collector node, can collect data of more than one type, but usually it only stores one type of data and transfers the rest of data of other data types to other nodes, which are the storage nodes corresponding to this collector node. Further, to reduce the communication overhead, the storage nodes are picked from the neighborhood, that is, the nodes in the transmission range, of the collector node.
-dimensional space. We note that our results can be easily extended to more than two dimensions. We denote the location of mobile node 
at time 
as 
, where 
and 
denote the 
- and 
-coordinates of 
at time point 
. Then given a time window 
that consists of 
time points, the trajectory of node 
of 
is denoted as 
. Given a set of trajectories 
of 
nodes, our goal is to use 
to predict the neighborhood of 
at a future time point 
. To achieve this goal, we define a probability model of prediction that quantifies the likelihood of the future neighborhood. Since we assume that for every node, it has a stable neighborhood within a period of time, our prediction is based on the principle that the nodes that are not only the neighbors in the past but also moving in the same direction are highly likely to be neighbors in the near future. Based on this, we define two probability parameters.
: it is used to reflect the belief from the trajectories 
that a node 
is in the same neighborhood of the node 
.
: it is used to measure the likelihood from the trajectories 
that two nodes 
and 
are moving in the same direction.
is in the neighborhood of 
in the future as 
expressed by
, a collector node 
and its neighbor nodes, if 
needs to store its data on its near likely node, then from its neighbor nodes that have available storage and store the same type of data that needs to be transferred from 
, 
picks the node that is of the maximum 
. Our model can be easily extended to choose 
nodes that are of top-
.
. We then propose two approaches, namely, trace-based and point-based, to calculate the direction probability 
. We next develop a new metric that measures the prediction accuracy.
within a time window 
, for any node 
, let 
= 
, 
and 
are neighbors at time point 
. Then the neighbor probability
is in the neighborhood of 
in the past, it will be more likely that 
remains as the neighbor of 
in the future.
- and 
-coordinates must follow the similar traces, and consequently may result in a strong correlation between their 
- and 
-coordinates, respectively, and vice versa. Figure 
and 
dimensions.
and 
coordinates versus time series for nodes 0 and 442 when they are moving together.
dimension, PCC = 0.96
dimension, PCC = 0.96
and 
, the Pearson correlation coefficient 
is defined as
(
, resp.) and 
(
, resp.) are the mean and standard deviation of 
and 
. The 
value ranges from 
1 to +1. Correlation +1/
1 means that there is a perfect positive/negative linear relationship between 
and 
. In Figure 
value 0.96 for both the 
dimension and the 
dimension shows high correlation between the coordinates of two nodes that are moving together.
and 
at each time point 
within a time window 
to determine whether two nodes are moving together. The key idea is that the collector node computes the moving directions of the neighbor nodes at all time points in the time window 
and measures the Pearson correlation coefficients of the moving directions.
and its trajectory 
, where 
and 
are the 
and 
coordinates of the node at each time point 
respectively, we define the gradient
to measure the moving direction at the time point 
to 
. Figure 
may not be accurate when the trajectory between the time points 
and 
is not linear, we argue that we can always reduce the error by adding more time points on the nonlinear trajectories, so that the subtrajectories are close to linear format. For example, as shown in Figure 
and 
into smaller units by adding a time point 
between 
and 
, as a result the trajectories between 
and 
as well as between 
and 
are close to linear.
and 
, let 
and 
be the trajectories of 
and 
of the time window 
. For both 
and 
, the collector node 
computes 
at each time point 
and put them into two vectors 
and 
, with 
from trajectory 
in 
and from 
in 
. It is straightforward that with 
time points in 
, there are 
s in 
and 
. Finally, we measure the Pearson correlation coefficient of 
and 
. If the coefficient is positive, we take it as the direction probability 
of node 
and 
. Otherwise, we value 
as 
.
and 
of two nodes 
and 
, first, the collector node 
computes the Pearson correlation coefficient between the 
-coordinates of 
and that of 
and collects the positive coefficients 
. Similarly, it calculates the Pearson correlation coefficient of the 
-coordinates of 
and that of 
. Let the set of positive coefficients be 
and 
dimensions. Since the correlation coefficients on 
and 
dimensions are independent, we multiply 
and 
as the direction probability
is normalized as needed.
and future 
. The window of past 
is used as the "training set" to predict the near likely nodes, whereas the window of future 
, is used as the "test set" to verify the accuracy of the prediction. We choose 
nodes, denoted as 
, as the "test participants". Our accuracy measurement consists of two steps.
in 
, we find its near likely node 
that is of the maximum 
in the time window 
. For 
nodes, we collect 
such neighbor nodes and put their 
into a vector 
. Thus 
consists of 
probability values.
from Step 1, we calculate its 
of the window 
and store 
in a vector 
, which is also a set of 
probability values. Our measurement of accuracy is based on the distance of 
and 
. The smaller the distance is, the more accurate the prediction result will be.
and 
, our metric of Prediction Accuracy is based on KL-divergence. KL-divergence is a noncommutative measure of the difference between two probability distributions in probability theory and information theory [
and 
, the KL-divergence of 
from 
is defined as
is, the more 
is similar to 
, which consequently indicates that our prediction of future near likely node is more accurate.
from the past window and 
from the future window, we compute the positive and negative probability difference vectors 
and 
:
(
, resp.) are the ones whose probabilities are increasing (decreasing, resp.). We measure CDF of both 
and 
. Intuitively, the closer the distributions of 
and 
to the value 0 are, the more accurate the prediction is.
needs to transfer its data to other nodes, and the communication between nodes is only performed at the specific time point. Thus, the on-demand scheme reduces the communication overhead and energy consumption incurred from frequent information exchange. There are two requirements when choosing the nodes that the data will be transferred to
.
sends a request to all the nodes in its neighborhood. The request consists of the inquiry of the allowed data type, the size of the available storage, and the trajectory of the next 
time points in the time window 
. The neighbor nodes reply the request of 
with proper information.
collects the answers and picks the node that satisfies the above two requirements as the near likely node 
.
sends its data to its near likely node 
, and updates its data track table. The data track table consists of entries in the format of 
, with each entry used for tracking which node the data is stored on, so that when there is a user query for the data, node 
can efficiently redirect the query. The 
is the node identity of the near likely node that stores data with index 
in the data track table.
runs step 1 and 2 from the on-demand data transfer procedure for the corresponding type of data with 
and identifies a new near likely node 
.
then sends a request to the previous near likely node 
and asks 
to transfer the data with 
to node 
.
receives the confirmation from 
that the data transfer is successful, it updates its data track table by replacing 
with 
.
keeps an observation of the change of KL-divergence incurred by expansion/shrinkage of the time window. We say the prediction accuracy falls if the KL-divergence increases. Otherwise, we say the prediction accuracy improves. Based on this, we developed an algorithm based on reinforcement learning, called WINTER (WINdow adjusTment with Expanding and shRinking), which adaptively adjusts the time window size by the following:
to 
, then for time window 
, we "reverse" the operation, that is, if the operation on 
is expansion/shrinkage, we shrink/expand for 
.
to 
. Then we repeat the same operation on 
for 
.
) Let 
and 
be the collector node and its predicted near likely neighbor;
) 
;
)repeat
) Let 
and 
be the KL-divergence measured from time window 
and 
;
) Let 
be the operation (expansion or shrinkage) on time window 
;
) if (
) then
) //KL-divergence improves;
) if
== "expansion" then
) The size of the next time window 
; 
) else
) The size of the next time window 
; 
1; 
) end if
) else
) //KL-divergence falls;
) if
== "expansion" then
) The size of the next time window 
;
) 
"shrinkage"; 
) else
) The size of the next time window 
;
) 
"expansion"; 
) end if
) end if
) 
;
) until The time points are exhausted;
25000 m. We created two simulation scenarios, one is in walking speed of 4 ft/s, and the other is in vehicular driving speed of 50 ft/s. For the walking scenario, two data sets, we call 
and 
, are obtained using this simulation environment with 1000 and 5000 nodes generated, respectively, and placed randomly inside the city.
to the past probability 
of the near likely node on top of the KL-divergence. We split our study time to a past time window for prediction and a future time window to evaluate our prediction. In the following discussion, we use the percentage of study time as the measurement of window size.
to the past probability 
of the near likely node. Figure 
and the negative difference 
, the CDF curve of the trace-based scheme lies to the left side of the point-based scheme.
to the past probability 
of the near likely node under the case of the average number of neighbors is 15 in walking scenario. Positive difference (0.2, 0.2)Positive difference (0.4, 0.2)Negative difference (0.2, 0.2)Negative difference (0.4, 0.2)
for both of our schemes. We observed that for each scheme, the curves of different average number of neighbors are close to each other, suggesting that the prediction accuracy is not sensitive to different average number of neighbors. These results are very encouraging as it indicates that given a prediction scheme the prediction accuracy only relies on the window size.
to the past probability 
of the near likely node under different average number of neighbors in walking scenario: 5, 15, and 45. Point-based scheme (0.4, 0.4)Trace-based scheme (0.4, 0.4)
and 
dimensions, whereas the point-based scheme only calculates the correlation coefficient for gradient. Further, the time measurements of the large data set are also in the order of milliseconds as shown in Figure 
) coordinates and a timestamp, each of float type. In other words, each trajectory record consists of 12 bytes. Therefore, one transmission packet can contain at most 42 trajectories. If one node records its trajectory every 
seconds, then the trajectory information of 
seconds can be stored in 
packets.
seconds, to apply the neighborhood prediction mechanism, the collector node needs to collect the trajectory of 
seconds from its 
neighbors. Therefore, there are 
packets transmitted to the collector node from its neighbors. Assume the collector node needs to transfer its data of size 
to the storage node within these 
seconds. Then the size of the transmission packets needed for collecting trajectory information is 
of the data sent to the identified near likely node by the collector node. We assume that 
is less than 1.
and the percentage of transmission packets 
are not affected by the moving speed of the mobile nodes. Thus, the communication overhead incurred from the trajectory information exchange in our approach is not sensitive to the mobility model.
= 5, the trajectories of 
of seconds to be collected, the data size 
varying from 1 MB to 5 MB, and each node recording its trajectories every 
seconds. We observed that small overhead fraction values in percentage that are always less than 0.7%. Specifically, it is as small as 0.05% for the data size of 5 MB and trajectory of 60 seconds. Furthermore, we noticed that the larger the data size is, the smaller the fraction will be. The same trend is also observed in Figure 
