Adaptive Holistic Scheduling for In-Network Sensor Query Processing

Transcription

1 Adaptive Holistic Scheduling for In-Network Sensor Query Processing Hejun Wu and Qiong Luo Departent of Coputer Science and Engineering Hong Kong University of Science & Technology Clear Water Bay, Kowloon, Hong Kong {whjnn, ABSTRACT We observe two probles in the current scheduling schees for in-network sensor query processing: () A query execution plan never changes after it is injected into the network and (2) the data counication schedule rarely considers the query workload. Both probles severely hurt the perforance, because the runtie dynaics, such as the wireless connectivity and the data flows, change frequently and affect the perforance greatly. To address these two probles, we propose an adaptive, holistic scheduler, AHS, which schedules both the query operators and the data counication, and is able to adapt the schedules to the runtie dynaics. We have ipleented AHS in nesc and have tested it on real otes as well as in siulation. Our results show that AHS iproves the perforance of query processing in various dynaic settings.. INTRODUCTION In-network query processing techniques such as in-node acquisitive query processor [][24], seantic routing tree [24], and in-network aggregation [23][3] are proising for Wireless Sensor Networks (WSN), due to the counication efficiency of these techniques. For instance, using in-network processing for a SQL-style query select light fro sensors where light < 2, a node returns query results only when the predicate (light < 2) is satisfied as opposed to transitting all of its sensory data to the central server. This way, the traffic in the network can be reduced in coparison with the centralized approaches. Scheduling is indispensable for in-network query processing for two reasons. First, sleep is the ost effective eans to save energy since both idle listening and counication consue a siilar aount of energy whereas sleeping consues about / of the energy of idle listening [34][39]. Without effective sleep scheduling, nodes will keep idle listening between execution and essage receiving. Second, the ulti-hop counication in a WSN requires a careful counication schedule; otherwise, it will be overwheled with heavy collisions and long idle listening, especially when the traffic is skewed [4][2][33][36], as that generated by query processing workloads. Unfortunately, there are two probles with the current scheduling approaches for in-network query processing, which offset the potential perforance benefit resulted fro the traffic reduction of in-network processing. Firstly, the query execution schedules are usually fixed regardless of the dynaics of the data and the network. Such fixed schedules are often inefficient, as the tie in waiting for the interediate results fro other query operators on the node or fro other nodes ay be long at runtie. Secondly, existing scheduling protocols arrange fixed counication schedules, since the scheduling protocols are isolated fro the changes in query processing. With fixed counication schedules, a node ay keep idle listening in its scheduled counication periods even when the predicate on the node returns false. To address these two probles, we propose an Adaptive, Holistic Scheduler (AHS) that schedules not only the query operators but also the counication operations and that adapts both kinds of schedules to the runtie dynaics. We choose tree networks as the target for AHS, since ost current query processing systes use tree routing protocols due to their siplicity, duplicatefreeness and counication efficiency [24][27][38]. In a tree network, the sink node is the root. The parent of a node serves as the router of the node. A neighbor of a node is the one that is within the node s transission / receiving range. By this definition, a parent of a node is also a neighbor of this node. Finally, a sibling of a node is one that shares the sae parent as this node, and a neighboring sibling of the node is both a sibling and a neighbor of the node. In AHS, each node keeps a short execution log of a few epochs: () a few ost recently sapled sensory data values and (2) the nubers of packets transitted and received per epoch, so that it can estiate the query selectivities. An epoch, or a saple interval, is a fixed tie interval for a node to process a query and returns its result. With the estiated query selectivities, the node chooses a best execution order for query operators and arranges the tiing for counication. After the counication tiing and the execution order of query operators are fixed, the node turns back to schedule the start tiing of each operator for the chosen order so that the query results, if any, will be ready before the transission tiing. To efficiently and effectively schedule the query execution and counication of in-network query processing, we design AHS with the following three key features. ()Two-level dynaic selectivity estiation. AHS dynaically estiates the selectivities of queries for an epoch using a twolevel estiation fraework. The first level roughly estiates the changing trend in the selectivity for each epoch using a siple odel. If the trend estiated in the first level tells that there will be no significant change in the selectivity, the second level will be skipped for efficiency. Otherwise, the second level selectivity estiates the actual sensory data values using ore coplex odels. This two-level estiation helps reduce the estiation overhead, since the coputation overhead of the first level estiation is negligible and the second level estiation will not be activated in every epoch. (2)Selectivity based scheduling. With the estiated selectivities, AHS arranges the active tie periods for each node. As a

2 SELECT teperature FRO sensors WHERE teperature > 9 SAPLE INTERVAL 6s result, the assigned schedule will closely atch the tie of the counication and coputation of the node. (3)Query execution and counication pipeline. For the query execution of each node, AHS arranges the operators to be executed in a pipeline so that their inputs are ready before their execution. These operators include the sapling operators as well as the non-sapling ones, such as selection, projection and aggregation. For the wireless counication between nodes, AHS ensures the tiing of result forwarding on a parent to be later than those of the children in each epoch. This ensures sufficient but not overly long tie for the parent to forward or aggregate the results of the children. The reainder of this paper is organized as follows. Section 2 akes the proble stateent. Section 3 gives an overview of AHS. Section 4 describes the scheduler design and ipleentation. We present our experiental results in Section 5 and review related work in Section 6. Finally, we conclude this paper and outline future research directions in Section PROBLE STATEENT 2.. Proble Scenario and Assuptions AHS targets at in-network query processing applications that report data selectively and proptly [7][24][3][38], as opposed to those that collect all sensory data to a central server for processing. Figure illustrates a typical exaple. The query injected into the network requires all nodes to check their teperature readings every 6 seconds and those who have a teperature reading larger than 9 to return the query results to the sink. In this application, the proble for AHS is to schedule the query execution and the counication of the nodes with the goal of iniizing both the energy consuption and the response tie. Response tie is defined as the tie fro the start of the epoch to the tie when the sink receives all of the query result fro the nodes within the epoch. σ,π,α Scheduler Sensing & Networking Query Result nodeid: teperature: 3 Base station σ,π,α Scheduler Networking sink σ,π,α Scheduler Sensing & Networking SELECT teperature FRO sensors WHERE teperature > 9 SAPLE INTERVAL 6s nodeid: 2 teperature: 5 nodeid: 3 teperature: Danger! σ,π,α Scheduler Sensing & Networking Figure. A target WSN application Before forally defining the scheduling proble for AHS, we list our assuptions on the application environents of AHS. () Propt result reporting: We assue that there is no crossepoch buffering of packets and that a node sends out its results, if any, proptly in each epoch. This assuption allows the length of our schedule to be one epoch only. This assuption is realistic, due to the eory liitation of current generation WSNs and the data freshness requireents fro the target applications. (2) Tie synchronization: We assue that all nodes are tie synchronized so that each node knows the counication tiings of its neighbors. Currently, any schees are capable of synchronizing the nodes and the tie synchronization errors are within a few illiseconds or even icroseconds [][28]. (3) Lower-than-% selectivity on average: As the target applications are interested in a fraction of sensory data, we assue the selectivity of the queries on a node is lower than % on average. (4) Independent conjunctive query predicates: We assue that the query predicates in a conjunction AND are independent fro each other on a node except for the predicates that are on the sae attribute. We regard all conjuncts that are on the sae attribute to for one coposite predicate. This distinction of predicates on identical versus different attributes is for the scheduling of query operators as well as for the estiation of query selectivities. The general assuption of predicate independence for the selectivity estiation of conjunctive predicates is coon in traditional databases. It ay not be true for real sensory data; nevertheless, since our estiation is adaptively aintained over tie, we find this siplifying assuption sufficient for our purpose Proble Definition We first identify the ajor coponents in the energy consuption and the response tie of in-network query processing to siplify the proble. They are described in definitions The other coponents, i.e., the sleeping tie and energy, are negligible. Definition 2.: Query Execution Energy (QEE). QEE is the energy consued in executing query operators on a node. It is accuulated in ( P, where is the nuber of i Li + PI i LI i ) i= operators having been executed, Pi, L i are the power (Watt) and the execution tie of the ith operator, and PI i, LI i are the power and tie spent in idle listening during executing the ith operator, respectively. Definition 2.2: Counication Energy (CE). CE is the energy consued by a node in counication including the energy spent idle listening between counications. Definition 2.3: Query Execution Delay (QED). QED is the interval fro the start tie of an epoch to the tie the query result is ready on a node. If there is no query result, QED will be. Definition 2.4: Counication Delay (CD). CD is the interval fro the tie when a node starts the transission of a query result to the tie when the sink receives the result. It can be inferred fro the tie stap of each query result. We can use QEE + CE to denote the energy consuption of a node. QED + CD corresponds to the response tie under our assuption of propt result reporting. Note that CD is only recorded for the nodes that have query results and these results are received by the sink in an epoch. Those results that fail to be transitted are counted in the packet loss rate, a etric that describes the data quality. With definitions , we now forulate the scheduling proble for AHS in definition 2.5.

3 Definition 2.5: Scheduling for In-network Query Processing in WSNs (SIQP). Given a tree network G = (V, E), rooted at the sink node r, r V, a nuber of selection, projection, and aggregation queries q, q 2, q n that have been installed on each node, find the tiing of the query operators and counications on each node v, v V, such that the tiing of the nodes results in the iniu QEE + CE for each node and the iniu QED + CD for all queries on each node for the current epoch. This proble can be divided into two sub-probles. The first one is to get the iniu QEE + CE. It is siilar to the proble of getting the least cost of ultiple queries with pipelining in traditional databases, which is proved to be NP-hard []. The second sub-proble, iniu QED + CD, is ore coplex than the NP-hard proble, which schedules only one packet transission for each node per epoch to get the inial CD, as proved in the work of Lu et. al [2]. Furtherore, there is no existing solution to solve both probles efficiently Tasks to Schedule With the proble defined in Section 2.2, the ajor tasks for a scheduler are thus scheduling the query execution and the wireless counication towards the goal of iniizing the query execution and counication energy and delay Sensor Query Execution Copared with the query execution in traditional databases, sensor query execution has unique characteristics on the following four aspects. ()Tuple fetching. In traditional databases, all fields in a base tuple are readily available no atter they are in a row-based or colun-based storage odel. In contrast, a field in a conceptual (virtual) sensor data tuple ay not have an actual value unless it is sapled by a sensor [24]. (2)Operator evaluation. As each field is independently sapled, sapling operators on different attributes in a sensor node can be done in parallel. A sapling operator can also run in parallel with a non-sapling operator, if this non-sapling operator does not need the result of the sapling operator. (3)Indexing. Indexing is generally inapplicable in query processing on each sensor node due to the resource constraint and the strea nature of sensory data. For instance, SAO [22], an efficient index for general data streas keeps about 2-5 tuples for each query, which is infeasible for the current sensor nodes due to the eory liitation. (4)Cost distribution. In a sensor node, the ajor cost of query processing not only includes the cost of active operations such as coputation, receiving and transission, but also includes the cost of idle listening to wait for query results fro other nodes [37][39] Wireless Counication The wireless counication in WSNs has a nuber of liitations, including collision, noise, no receiving in sleeping, and a short packet length. These constraints require the scheduler to avoid siultaneous transissions of neighbors, and to consider the packet loss detected by the ACK essages, the coordination of a receiver and a transitter, and the nuber of packets per epoch. 3. SCHEDULER OVERVIEW Considering the characteristics of query execution and counication in WSNs and our scheduling goal, we design the architecture of AHS to enable both the operator level and the packet counication level scheduling for ulti-query processing. Currently, the prototype of AHS schedules the acquisitional (selection and projection) as well as aggregation queries supported in TinyDB [23][24]. 3.. Ters Used in AHS This section defines the ters used in AHS. First, slot. AHS uses a tie slot as the tie unit in a schedule. The length of a slot is fixed to be the transission tie of one data packet [5][4][2][33]. Second, four types of selectivities. As entioned in previous sections, AHS bases its scheduling decisions on the selectivities. The four types of selectivities are listed in the following, in which the first three are used in AHS for scheduling and the last one is used in our experients. () The selectivity of a predicate. This is the sae as that in traditional databases [3]. (2)The selectivity of all acquisitional queries on the node and on all of its children (SAQA) SAQA is estiated as. N s /N t N s is the total nuber of acquisitional query result packets generated on the node and received fro the children per epoch; N t is the total nuber of query result packets of the acquisitional queries that will be received fro the children and generated by the node itself per epoch assuing each acquisitional query has one result on each node per epoch. N t is the sae as the nuber of the transission slots allocated by a tree-based wireless scheduling protocol such as DCS [37] and FPS [4]. It can be accuulated fro the children control packets for the slot allocation, as will be described later. (3) The selectivity of all aggregation queries on the node (SGQ). SGQ is estiated in a way siilar to (), except for that the result packets are for all aggregation queries. This selectivity is estiated as. N gs /N gt N gs is the nuber of query result packets of all aggregation queries on the node; N gt is the total nuber of aggregation query result packets assuing each aggregation query has one result on the node per epoch. Note that SGQ is not always %, because when an aggregation query with a predicate has no result on a node, the node will not report itself in the aggregation query. (4) Average selectivity in the network. This type of selectivity is used in our experients and it is widely used in real world sensor network applications to describe the nuber of nodes that have query results to the total nuber of nodes in a network Architecture As shown in Figure 2, AHS on each node consists of a buffer anager, a query plan anager, an operator executer, a slot anager and a runtie status onitor. The buffer anager keeps the interediate results fro the query operators and the query results fro the children. The interediate results fro the operators will be used by the later operators. The ones fro the children will be used as input of

4 aggregate operators for aggregation queries or will be forwarded as query results for acquisitional queries. AHS Buffer Sensors Results fro children Query Plan anager Interediate tuples Slot anager Runtie Status onitor Transceiver Figure 2. AHS architecture Operator Executer Query results Network The query plan anager constructs a query evaluation plan for each query and optiizes the operator execution order for queries to reduce the query execution energy (QEE), using the estiated selectivity and the cost including the easured energy consuption and execution tie of each operator. In a query plan, each operator operates on individual attributes instead of aterialized tuples. Specifically, the selection operator operates on a predicate involving an attribute and a constant or another attribute. Such a selection predicate is called a ter and is not necessarily an execution unit in traditional databases [3]. The Boolean operations of AND, and OR between the selection operators are called connectors. With this definition, a query plan in AHS differs fro that in traditional databases. Figure 3 shows an exaple of a query evaluation plan of query Q. Note that, the query operators still can be regarded as operating on the logical tuples of all attributes. Q: SELECT count (nodeid) FRO sensors WHERE light > 6 AND teperature > 5 SAPLE INTERVAL 6 seconds count (nodeid) σ teperature > 5 Λ saple teperature σ light > 6 saple light Light sensor Teperature sensor Figure 3. A query evaluation plan The query plan anager also decides on the tiing of the execution of each operator, given the arranged slots for acquisitional queries and aggregation queries fro the slot anager. It uses an operator queue, in which each operator bears a query id and an operator id, to indicate which operator is to be executed next. It pushes the operators into the queue according to the optiized operator execution order. During query execution, it pops an operator and calls the operator executor to run the operator with a logical tuple fro the buffer as input. The slot anager allocates the tie slots for counication based on two types of estiated selectivities on each node, SAQA, and SGQ. Additionally, the slot anager runs a schedule aintenance routine on each node periodically at runtie. The interval between two consecutive aintenance routines is called a aintenance cycle. The aintenance cycle is fixed in the network so that all nodes are active and can counicate during a aintenance routine. In a aintenance routine, each node perfors the following tasks: () it broadcasts the inforation of its transission slots if they changed, (2) it updates the inforation of the transission slots of the neighbors so that later it will not use these slots for transission to avoid collisions with its neighbors, (3) it reallocates or releases transission slots activated by changes of the selectivities, and (4) it re-estiates SAQA if there are route changes on the node or on the children. We will show the purpose of these tasks in the later sections. Finally, the runtie status onitor logs the runtie statistics of the following factors: the historical sensory data of a few past epochs, the estiated selectivity of each selection operator, the length of idle listening tie of the past epoch, and the average nuber of retransission ties of the past epochs. With the updated statistics of the selectivity, the query plan anager will rearrange the order of the operators or the slot anager will reallocate slots when there are significant selectivity changes Workflow Overview We use an exaple WSN in Figure 4 to illustrate the overall runtie logic of AHS. Suppose in the WSN there are two running queries, an acquisitional query Q-x and an aggregation query Q-y, whose epoch lengths are the sae. The query plans of these two queries on node are shown in the figure, where the query plan of Q-y illustrates that the aggregate operator c needs to aggregate the result of the children of node. We assue that the sensory data sapling operators, p, r, and s are on different attributes but have the sae cost in this exaple. Suppose that at soe point during execution on node, the selectivity of operator b becoes uch lower than that of operator a and that the selectivity of Q-x becoes lower than a syste defined selectivity threshold. We will describe the selectivity threshold in later sections. WSN: 3 2 Query plan of Q-x on node : Λ a P Sensor p b r Sensor r Figure 4. Two query plans c Query plan of Q-y on s node : Sensor s Transceiver We now deonstrate in Figure 5 two schedules for node produced by AHS and our previous scheduler DCS [37] on TinyDB [25], respectively. Other existing scheduling protocols that use a slot as the unit would arrange siilar slots to DCS for this WSN. The baseline schedule, (i), generated by DCS, is shown in the lower left of Figure 5. The execution order of the query operators is fixed in this schedule. In this schedule, slot is for forwarding node 2 s result for Q-x, slots 2 and 3 are for transitting the result of Q-x and Q-y on node, respectively. Since the sapling operators are on different attributes and thus can be executed in parallel aong theselves or with another non-sapling operator, we use three parallel tie lines to illustrate that the operators are executed concurrently. As the CPU needs to send a coand to start p, r, and s sequentially, their start ties are slightly different. In contrast, the optiized schedule (ii), generated by AHS is shown in the lower right of Figure 5. The dynaic scheduling process of AHS is as follows. Initially, the query execution order in AHS is the sae as that of the baseline schedule (i). During query execution, the node finds that the selectivity of operator b is uch lower than that of operator a and it will reoptiize the

5 execution order. Also, it finds the selectivity of Q-x on node becoes lower than the selectivity threshold and infors the slot anager to adjust the transission slots. Execution and receiving (i) Query result transission Baseline schedule Sensory data sapling Sleeping Optiized schedule s Receiving r 2 3 Receiving s p 3 result fro result fro p node 2 a b c node 2 r b c a t Epoch Epoch (ii) Figure 5. Alternative query schedules Idle listening or receiving Under this circustance, the node rearranges the order of the query operators as follows. Sapling operator r is set to run first so that operator b can use the sapled data of r. The next sapling operator to run is s, but not p. The reason is as follows. If the Boolean result of operator b is false, operators p and a will no longer need to run since a is connected with b by AND. During this waiting, operator c is executed to reduce idle listening. The slot anager reallocates the slots, when the selectivity becoes lower the threshold. Since the selectivity of Q-x is now lower than the syste defined threshold, the slot anager does not allocate a slot for Q-x on node (the slot 2 in schedule (i) is saved in (ii)). In coparison with the baseline schedule, the query execution tie, the counication tie and the delay are reduced. 4. SCHEULER DESIGN We design AHS to schedule the operations on individual nodes dynaically and heuristically due to the NP-hard property of the target proble and the liited resources such as the CPU and the eory of sensor nodes. Since the query execution slots are deterined after the counication slots such that the query results will be ready before the counication slots, the query execution delay will not affect the response tie in AHS. If the query execution is finished before the end of the assigned query execution slots, the node will be put to sleep until it is tie for the counication on the node. Hence, we oit the query execution tie when designing the heuristics for AHS. Before looking at the scheduling strategies and algoriths in AHS, we first present the estiation of the selectivities, since the ost of the strategies in AHS are based on the. 4.. Selectivity Estiation This section describes the estiation of the first three types of selectivity in Section Selectivity of a Predicate In AHS, the predicate selectivity is estiated as the probability of the next sensory data value satisfying the query predicate. AHS uses a two-level fraework for this selectivity estiation. The first level roughly estiates the trend of change of the sensory data on the node per epoch. If the trend of change suggests that the difference between the next estiated selectivity and the current one will be less than a predefined selectivity threshold, the second level selectivity estiation will be skipped. Otherwise, the node will start the second level estiation. In our experients, t we set the selectivity threshold to be.3 for our test dataset. In the second level of estiation, the node uses ore coplex but ore accurate odels to estiate the selectivity. This two-level fraework helps to reduce the invocation of the second level estiation, which is ore expensive than the first one. Additionally, with the fraework, a user can apply different odels and thresholds that atch the sensory data distribution. In each level, we estiate the selectivity to be the probability that the sensory data range falls within the predicate range. If the query predicate is an open range, we use the value range in the hardware for the open end. In AHS, we used a linear regression odel in the first level due to its siplicity and its capability of predicting the trend of data changes [26]. We used Equation () for the first level estiation, given a range (P, P ) specified in the query predicate, and the estiated sensory data value range [ Y, Y ]. The function ap([ Y,Y ],( P,P )) coputes the length of the fraction of [ Y, Y ] that falls within (P, P ), as shown in Figure 6. Y is the estiated iniu sensory data value and Y is the estiated axiu sensory data value in the next epoch. They are coputed fro Y = Y + E and, where Y = Y + E Y is the estiated sensory data value of the next, epoch and E and E are the iniu and axiu estiation errors in the training dataset in the execution log on each node under the linear regression odel. The training dataset is stored in a queue and is updated using pairs of sapled data values and estiated data values in every epoch. Since soeties a sapling operator is skipped and thus a dataset ay have outdated sensory data values. To avoid the outdated values to be used, AHS sets a tieout to each sensory dataset and the data ites of a dataset will be updated in the later epochs when tieout occurs on the dataset. The size of the training dataset is deterined by the eory size on each node. In AHS for TelosB [34] otes, we set the training dataset size for each sensor to contain 4 attribute values. S E Y ap = Estiated range of the sensory data values P ([ Y,Y ],( P,P )) () Y Y Y Predicate of the query P ap([y,y ],( P,P )) Sensory data value Figure 6. Selectivity coputation in the first level We used Equation (2) for the second level selectivity estiation. It coputes the average selectivity of the next n epochs, given the predicate (P, P ), Y (t ) and Y (t ), where Y (t ) and Y (t ) give the iniu and axiu estiated sensory data values at tie t, t [t, t n ]. There are k intersection points between the four curves Y (t ), Y (t ), P, and P. The tie value of each intersection point is x i, i [, k].

6 Figure 7 illustrates the coputation of Equation (2). The selectivity is the ratio of the shaded area to the area between Y (t ) and Y (t ) ( t [ t s, t n ] ). The coputation of the integral on a node is as follows. First, it finds the intersection points. In this figure, the nuber of intersection points, k, is 3. In each tie segent between two intersection points, we use the antiderivative of the function in(p, Y (t ) ) and the function ax(p, Y (t ) ), to copute the shaded area. Since the functions are known in advance, a sensor node can use their antiderivatives directly without coputing the antiderivatives due to the CPU capacity liitation. For instance, the function ax(p, Y (t ) ) between (x, x 2 ) is Y (t ) and that between (x2, x 3 ) is P. S EI Sensory data value = P P k i= x i+ xi ap([y tn t (Y ( t ) Y( t )],( P,P ( t ) Y( t ))dt Y (t) Y (t) x x 2 x 3 t t n tie Figure 7. Selectivity coputation in the second level In AHS, we propose a gradient exponential oving average (GEA) odel for the second level since it is able to estiate the n sensory data values whereas the coonly used exponential oving average (EA) odels can only predict one next value [4]. AHS would have to regard all the n next sensory data values as the sae if using these EA odels. In AHS, n is set as the average nuber of consecutive sensory data values that have the sae sign in the gradients in the training dataset. We neglect the gradients that are within the hardware errors. n is thus not fixed and is able to adapt to the data changes in our GEA odel: when the sensory data values fluctuate frequently, the estiation interval will be short, i.e., the odel will estiate fewer values. As will be shown in our tests on EA odels and GEA, GEA outperfors the in estiation accuracy. We do not use Support Vector Regression (SVR) or the Dual Kalan Filter (DKF) [6] odels, due to the resource liitation of sensor nodes on storage and CPU capability. K=3 The GEA function is shown in Equation (3), where is the estiation of the sensory data value at tie t; Y is the newly sapled sensory data value; and G is the estiated gradient fro the training dataset. For efficiency, we average the last n gradients in the training dataset as the estiated gradient G. In the equation, the weight α is set as.7, when the estiation accuracy on our test dataset is the highest t t ))dt Y t (2) Y = ( α ) Y + α( Y + t* G) (3) Finally, AHS coputes Y t ) = Y + E with these n estiated sensory data values ( t and Y ( t ) = Yt + E Y t (<t n). We now use a test to show the accuracy of GEA in AHS. The source dataset was sapled fro a garden of our capus using ICA2 otes [9]. The predicate is light ( 8, 9). Figure 8 shows the selectivity estiation error of AHS using three odels. SEA is the basic EA odel, LEA the low pass EA odel [4], and GEA the odel we used. Selectivity Estiation Error SEA LEA GEA 5 5 #Selectivity Estiation Figure 8. Coparison of selectivity estiation ethods Estiation of SAQA and SGQ A naive approach to estiate the selectivity of all queries of a node is to add up the selectivity of each query on the node and the children. However, this ay cause the su to be larger than. For instance, if a node runs two queries and the selectivity of one query on the node is.5 while that on the other query is.6, the selectivity of the node is then. by this approach. Therefore, instead of suing up across queries and nodes, AHS still uses the sae fraework as that for the selectivity estiation of predicates. However, as described next, it uses a different dataset fro that in the selectivity estiation of predicate. In estiating the selectivity of all acquisitional queries of the node and its children (SAQA), each ite of the dataset is N s ; and the values for the range of (P, P ) is then (, Nt), where N s and N t are described in Section 3.. Siilarly, the dataset for estiating the selectivity of all aggregation queries of the node (SGQ) is N gs and the range of (P, P ) is then (, N gt ) Scheduling of Query Operator The goal of query operator scheduling is that the query execution tie is iniized. Our strategies are then called the in Query Execution Energy (in QEE) ones. We design a cost function to estiate the query execution energy to direct the decision on the query execution order Cost Function The cost function is given in Equation (4), which estiates the query execution energy per epoch. In this equation, f is the nuber of sensory data sapling operators whose execution has no overlap in tie with the other non-sapling operators. Norally, f is as there ust be at least one sapling operator to be executed first to start the query execution. Cs j, and Ls j are the execution power and tie of the jth sapling operator respectively. is the nuber of the non-sapling operators to be executed. P i is the probability of the execution of the ith nonsapling operator, estiated in Equation (5). C cj, and Lc i are the execution power and execution tie of the ith query operator, respectively. Cs j, Ls j, C cj, and Lc i can be easured in a sensor node and stored in the catalog in each node.

7 f j= E = CsjLs + PCc Lc (4) j i i= The probability P i of the ith non-sapling operator is defined in Equation (5), where S i is the selectivity of the ith operator. P i (i > ) = S i * P i 2, if connected with the previous i- operators by AND. in (, P i ), if connected with previous i- operators by OR. P i = : not connected with previous operators (i = ) Different orders of query operators ay significantly affect the cost, due to the different probabilities of a query operator to be executed. Next, we show our heuristics rules to decide an order of query operators based on this cost function Search Space The fundaental issue for query execution ordering is the size of the search space. Since it is cost-inefficient to traverse all perutations of the query operators is and ore so in resourceconstrained WSNs, we propose a siple rule to liit the search space as follows. Rule 4.: If the nuber of possible orders is saller than a threshold h n, the scheduler should use the cost function to decide an optial order aong all orders; otherwise, the scheduler should use soe predefined strategies to liit the nuber of operator order. Each of the possible operator orders in Rule 4. guarantees that an operator, o, whose output will be used as input of another operator, o 2, will precede o 2. The threshold h n is deterined by the available eory space. If the nuber of all possible orders is within the threshold, the Series-Parallel algorith by ona and Sidney [29] and the cost function in Equation (4) can be used together to obtain an optial ordering of the operators. The predefined strategies in AHS currently include the selectivitybased strategy and the query execution pipelining strategy, which will be described in the following sections Strategy for Query Operator Ordering It can be seen fro the cost function that the lowest selectivity operator first (LSF) strategy ay reduce the execution of the later query operators, because it increases the probability of skipping the other operators that are connected with the lowest selectivity operator by AND. Specifically, AHS defines an LSF rule as shown in Rule 4.2. Rule 4.2: In an execution order of operators, if () an operator, o, of a lower selectivity succeeds another operator, o 2, (2) o 2 is connected with o by AND, and (3) swapping the order of o and o2 results in a lower cost, the scheduler will swap the order of o and o 2. Proposition 4.: Rule 4.2 guarantees that the nuber of nonsapling operators to execute is inial if all of the operators consue the sae aount of energy. Proof. We prove by contradiction. Assue there is an operator execution order in which the nuber of non-sapling operators executed is inial and there is an operator, o, with a higher selectivity, S h, be executed before an operator o 2, of a lower selectivity, S l ; o and o 2 are connected by AND. Then the i i (5) expected nuber of the execution of the two operators will be (+ S h ). In contrast, if o 2 is executed first, the expected nuber of execution is (+ S l ). There exists an execution order with a saller nuber of executions of operators. As the costs of the operators are the sae, this new order will have a lower cost than the original one and Rule 2 will choose this new execution order Query Execution Pipelining We use heuristics to direct the dynaic operator execution in a pipeline at runtie. The objective is to enable each operator to be executed without waiting for its input while allowing the resource sharing and selectivity based schedule optiization. As the resource sharing issues in WSNs are siilar to those in traditional databases [] and they have been well addressed recently [27], we skip the issues of how to deterine resource sharing in query execution. We use Procedure for pipelining the query execution. The procedure decides on which sapling operator should be executed. The input of the procedure is all the operators of queries, and the order of the non-sapling operators that is given by the query plan anager using the two rules described in the previous sections. The procedure executes the operators for one epoch. It is activated whenever an operator is executed. The variable current_round is initialized to at the start of the epoch. In the start of each epoch, the procedure starts executing the current sapling operator (Lines and 2). Lines 4-5 are to preprocess the operators to exclude the operator fro execution if the following two conditions hold: () the operator is connected with the previous operator by AND ; and (2) the previous operator outputs no tuples. If a non-sapling operator is skipped in this preprocessing, the sapling operators that feed it are skipped too. The procedure executes the current round operator if the operator passes the preprocessing (Lines 8 and 9). Procedure Input: Operators & the execution order of non-sapling operators : if current_round = = 2 : sapling_op(operators[order[]].field) 3 : else 4: if has_and( operators[order[ current_round +]]) &&!pre_result 5 : current_round ++ 6 : else 7 : sapling_op(operators[order[ current_round +]].field) 8 : execute_op(operators[order[ current_round]) 9 : current_round++ To show the benefit of this query execution pipelining and the previous LSF strategy in AHS, we calculated the nuber of operators in Q (Section 3.2), Q2, and Q3 by AHS and those of other two scheduling schees. The first schee is called Serial, in which queries are executed one by one. The second one is called Batch, in which the sapling operators of the query are executed in a batch and then the non-sapling operators start processing the sapled data. Batch is adopted in ost of the current query processing systes [24][38]. Table shows the execution tie in ters of the nuber of operators executed. The table shows that query execution pipelining and LSF are efficient in reducing the execution tie, which in turn, reduces the energy. Q2: SELECT nodeid, teperature, light, FRO sensors WHERE teperature > 5 AND light < 8

8 SAPLE INTERVAL 6 seconds Q3: SELECT noise, nodeid FRO sensors WHERE noise > 5 SAPLE INTERVAL 6 seconds Table. Nuber of operators executed Serial Batch AHS Scheduling of Wireless Counication The optial counication schedule for in-network query processing in a WSN is that the counication delay (CD) of each node is iniized. Since the proble of finding such one in a WSN was proved to be NP-hard [2], we seek to get the inial counication tie (in-ct) instead. Our consideration is that, with the counication tie on each node reduced, the counication delay will be reduced accordingly as AHS tries to ake the slots of neighbor nodes consecutive. eanwhile, the energy in counication will also be reduced, since the counication tie is reduced. Specifically, AHS works towards the goal with three techniques. The first one is the selectivity-based counication slot allocation, the second is the counication pipelining, and the last one is the dynaic slot adjustent. We present their details in the following Selectivity-Based Slot Allocation To avoid the collisions aong neighbor nodes, AHS follows the rules defined n our previous work, DCS [37]. oreover, AHS dynaically allocates the slots of a node in accordance with the flowing two selectivities, () the selectivity of all acquisitional queries of the node and its children (SAQA), and (2) the selectivity of all aggregation queries of the node (SGQ). AHS attepts to allocate each node with a iniu nuber of counication slots as required by the current workloads, specifically the nuber of packets the node needs to send per epoch on average. This way, AHS reduces unused counication slots and correspondingly the counication delay and idle listening. With the estiated query workload, AHS uses a heuristic scheduling algorith to arrange the Transission Slots (TS) for acquisitional and aggregation queries, respectively. The receiving slots of a node can be fixed correspondingly with the transission slots of its children. The heuristic algorith includes two procedures: Request for Transission (RT) and Assignent of Transission (AT). The forer is for a node to send its request for transission slots to the parent and the latter is for a parent to assign a child with the suitable TSs upon receiving the request. A transission request includes () N r and N rg : the required nubers of TSs for acquisitional and aggregation queries; (2) N t (in Section 3.) and (3) {T i }: the set of receiving slots on the node and the slots that have been taken up by its neighbors.. The required nubers of TSs for acquisitional and aggregation queries N r and N rg are coputed as N r = SAQA * Nt and N rg = SGQ*N gt, where N gt is defined in Section 3.. Given the request fro a child, Procedure AT decides the TSs for the child. The operation is siilar to that of eory allocation - finding satisfying slots that are not used by other children or neighbors to avoid the transission conflicts with its neighbors and children. The difference is that the allocated TSs should also follow the counication pipelining rule, as presented next Counication Pipelining To reduce the counication delay, in procedure AT, the allocated slots should be chosen following the constraints for counication pipelining. We define the counication pipelining rule (Rule 4.3): Rule 4.3: The TSs allocated to each node should follow: () each receiving slot for an acquisitional query result packet fro the child has a later TS for forwarding the result; and (2) the TSs for an aggregation query are later than all of the receiving slots for the aggregation query. In processing acquisitional queries, if there is a TS before all of the receiving slots for the children, this TS will be wasted. Siilarly, if there is a TS for an aggregation query before a receiving slot to receive the result for the aggregation query fro a child, the node has to use another slot to transit the aggregated result fro the child. The condition () in Rule 4.3 is described in Inequality (6). Suppose the allocated TSs are Ts, Ts 2, Ts, and the TSs of the children are Tsc,Tsc 2, Tsc N, the allocated slots should satisfy Inequality (6). This inequality specifies that the nuber of TSs for the node should be greater than or equal to the nuber of the children s TSs, which precede the TSs of the node. i= Tsi Ts (for any, n such that, n N, > n) (6) n k= ck 4.4. Dynaic Slot Adjustent During query processing in a WSN, the assigned TSs ay be too few or too any to transit the data of a node. There are two reasons. First, since the selectivity estiation errors are inevitable, the TSs of a node ay be either too few or be too any for its transission in a single epoch. Second, noise ay corrupt the counication of a node and cause retransission, which in turn, akes the TSs fewer than required. AHS addresses this proble using slot sharing, patch RP (Receiving Period) and dynaic transission allocation / release echaniss Slot Sharing When a node finds that the nuber of its TSs is too few for its transission, the node will first use a slot sharing echanis to attept to transit its packets. In this echanis, the node onitors the counication of its neighboring siblings in the current epoch. Recall fro the Introduction section that a neighboring sibling is both a sibling and a neighbor of the node. If a node finds that one of its neighboring siblings has finished transission and has unused TSs, it will try to transit its data during these unused TSs. However, if the node cannot find any unused slots of its neighboring siblings or it has no neighboring siblings, it will use the patch RP echanis next Patch RP The patch RP echanis reserves an RP (receiving period) that includes a nuber of receiving slots, Rs, on each parent node. The children can transit their query results within this patch RP. Equation (7) is used to deterine the length of the reserved period in each parent node. In Equation (7), Ea is the average error of the selectivity estiation of the SAQA and SGQ. N t and N gt are described in Section 3.. R is the average nuber of

9 retransission ties of its children per epoch, which can be got fro the packet headers fro its children. Rs = E a ( SAQA * N t + SGQ*N gt ) + R (7) If the patch RP still cannot satisfy the transission requireents of the node, the node will further to the third echanis, dynaic transission allocation Dynaic Slot Allocation / Release In this echanis, if the TSs of a node are too few for its transission, the node estiates the nuber of additional TSs required for the packets that fail to be transitted. With this estiated nuber of additional TSs, the node starts the heuristic scheduling algorith to send a new request for the additional TSs. Upon receiving this request, the parent will assign ore TSs to the node. On the other hand, if the nuber of TSs of a node is too any for its transission, it will send a request to its parent for releasing its TSs. The released slots will be reallocated by the parent to the other children or by the neighbors of the node. Since slot releasing ay cause frequent slot changes in the TSs of the nodes, AHS defines a threshold to liit the shortest interval between two ties of slot releases on each node. 5. EVALUATION 5.. Experient Setup We ipleented AHS using the nesc language [2]. It runs on top of the tree routing protocol as in TinyDB [25]. The code size is about 4.4KB and it needs 5.8KB RA to run. We used both TOSSI [8][9] and TelosB otes [34] to evaluate AHS. TOSSI is a siulator that is able to run the nesc progras of sensor otes [9][34], but it does not siulate the interrupts of hardware, which akes TOSSI fail to provide accurate energy consuption inforation. The reason for choosing a TelosB ote is that a TelosB ote is equipped with ore eory than otes such as a ICA2 ote [9], which has a RA size of 4KB. Since we got no eulator that can realistically eulate TelosB otes to study the constructed schedule on each node, we eployed TOSSI to study the response tie of each node and easured the energy consuption using TelosB otes. The networks deployed in the siulator and the TelosB otes are listed in Table 2. We assue the transission range of all of the nodes is eters, as siilar to that of a TelosB ote we used. The length of each slot is set to be 6 s, since we easured that the packet transission tie of a TelosB ote was about 57s. Table 2. Network description Nae Topology Description, and Network Type 6 Single-hop, in TOSSI 4-hop, 8*8 rectangular area, in TOSSI 3 6-hop, 2*2 rectangular area, in TOSSI 5 8-hop, 6*6 rectangular area, in TOSSI 6 Single-hop, TelosB otes, CPU: 8 Hz SP43 RA: KB, Flash eory: 48 KB Sensor: Teperature In siulation, the source sensory data for the input of the 6-node siulated network are collected fro a garden in our capus. Sensory Data Value The source data for the -node siulated network data are synthesized fro the Intel Lab dataset [5] using the linear regression odel to interpolate the sensory data to the locations that are not covered in the Intel Lab dataset, since the nuber of nodes in the original dataset is only 54. Both datasets are for the input of the siulated light and the teperature sensor. The queries used are Q4 and Q5. Due to the different environents of our capus and Intel Lab, the average light values of the were different. Therefore, the predicates in the queries were different for the 6-node network and other networks in TOSSI for the sae network selectivity. Q4: SELECT light, nodeid fro sensors WHERE light < PTH and light > PTL SAPLE INTERVAL 6 seconds Q5: SELECT count(nodeid) fro sensors WHERE tep < PT SAPLE INTERVAL 6 seconds Due to the hardware liitation of our TelosB otes, which are only equipped with a teperature sensor, we ran Q6 to easure the energy consuption of each node in the TelosB network. Since a TelosB ote uses a different sensor fro that of ICA2, the predicate was uch different fro the previous two queries. The value is set as the highest sensory data value sapled in our lab so that we could use a hair drier to change the selectivity of this query on each node to easure the energy consuption under different selectivities. Q6: SELECT teperature, nodeid fro sensors WHERE tep > 285 SAPLE INTERVAL 6 seconds In the following, we present siulation and easureent results on the five networks. We copare AHS with DCS, our previous scheduling schee that also works for in-network query processing, but produces fixed schedules Experiental Results We first tested the 6-node network with Q4, in which the predicate is set to be light > 8 and light < 9, so that the selectivity of the query on each node changes with our source dataset, as shown on the left of Figure 9. This dynaic setting allowed us to observe the changes in the network response tie resulted fro the schedule optiization in AHS. On the right of the figure shows that AHS got a uch lower response tie than DCS when the selectivity of the query decreased on ost nodes. node node2 node3 node4 node #Epochs Figure 9. Sensory data and response tie Siilarly, we logged the transission slots on a node in the - node siulated network running query Q4, as shown in Figure. The predicate is light > 425 and light <. The figure shows that the nuber of transission slots changed in accordance with 5 Average Response Tie (slots) DCS AHS #Epochs