A generic data model for moving objects

Abstract

Moving objects databases should be able to manage trips that pass through several real world environments, e.g., road network, indoor. However, the current data models only deal with the movement in one situation and cannot represent comprehensive trips for humans who can move inside a building, walk on the pavement, drive on the road, take the public vehicles (bus or train), etc. As a result, existing queries are solely limited to one environment. In this paper, we design a data model that is able to represent moving objects in multiple environments in order to support novel queries on trips in different surroundings and various transportation modes (e.g., Car, Walk, Bus). A generic and precise location representation is proposed that can apply in all environments. The idea is to let the space for moving objects be covered by a set of so-called infrastructures each of which corresponds to an environment and defines the available places for moving objects. Then, the location is represented by referencing to the infrastructure. We formulate the concept of space and infrastructure and propose the methodology to represent moving objects in different environments with the integration of precise transportation modes. Due to different infrastructure characteristics, a set of novel data types is defined to represent infrastructure components. To efficiently support new queries, we design a group of operators to access the data. We present how such a data model is implemented in a database system and report the experimental results. The new model is designed with attention to the data models of previous work for free space and road networks to have a consistent type system and framework of operators. In this way, a powerful set of generic query operations is available for querying, together with those dealing with infrastructures and transportation modes. We demonstrate these capabilities by formulating a set of sophisticated queries across all infrastructures.

Appendices

Appendix A: Operator semantics

We extend the definition of operator geodata and give domains and ranges in Table 12. geodata which plays a crucial rule for defining semantics, maps locations in different infrastructures into free space. The first three signatures are for PTN. Given a line and the relative position on the line, geodata returns a point for that position. Given a point (line) inside a region, we obtain its global position. The last one maps an indoor location to free space. This is done by ignoring the height above the ground level, i.e., projecting a room to the ground floor of a building. To have the symbol set denoting data types supported by geodata, we define IOSymbol’ = {LINE, REGION, BUSROUTE, GROOM} (⊂ IOSymbol).

Table 12 Extension for geodata

Definition A.1

=: ${\underline{\textit{genloc}}} \times {\underline{\textit{genloc}}} \rightarrow {\underline{\textit{bool}}}$

Let u,v be the two locations and the result is TRUE iff

• (i) $u.oid = \bot \wedge v.oid =\bot \wedge u.i_{loc} = v.i_{loc}$; or

• (ii) u.oid = v.oid ∧ u.i _loc  = v.i _loc ; or

• (iii) $u.oid=\bot \wedge (\exists w \in Space: w.oid = v.oid \wedge w.s\in$ IOSymbol’ ∧ $u.i_{loc} = \textbf{geodata} (w.\beta,v.i_{loc}))$; or

• (iv) $v.oid=\bot \wedge (\exists w \in Space: w.oid = u.oid \wedge w.s\in$ IOSymbol’ ∧ $v.i_{loc} = \textbf{geodata}(w.\beta,u.i_{loc}))$

Cases (i) and (ii) are straightforward as both locations are in free space or in the same IFOB. In case (iii) and (iv), if one location is in free space and the other belongs to another infrastructure, the latter maps to free space by loading the referenced IFOB.

Definition A.2

inside: ${\underline{\textit{genloc}}} \times {\underline{\textit{genrange}}} \rightarrow {\underline{\textit{bool}}}$

Let u be a single location and V be a set of locations. The result is TRUE iff $\exists v \in V$ such that

• (i) $u.oid = \bot \wedge v.oid = \bot \wedge u.i_{loc} \in v.l$; or

• (ii) u.oid = v.oid ∧ (u.i _loc  ∈ v.l ∨ $(\exists w \in Space: v.oid = w.oid \ \wedge$ $\textbf{geodata}(w.\beta, u.i_{loc}) \in \textbf{geodata}( w.\beta,v.l)))$; or

• (iii) $u.oid = \bot \wedge (\exists w \in Space:$ v.oid = w.oid ∧ w.s ∈ IOSymbol’ ∧ $u.i_{loc} \in \textbf{geodata}(w.\beta,v.l))$; or

• (iv) $v.oid = \bot \wedge (\exists w \in Space:$ u.oid = w.oid ∧ w.s ∈ IOSymbol ∧ $\textbf{geodata} (w.\beta,u.i_{loc}) \in v.l)$

Case (i) shows a single location and a set of locations in free space. If u,v reference to the same object w (case (ii)), one can directly compare the location inside w or load the referenced object to transform from relative location to global. Similarly, if one parameter corresponds to free space and the other does not, we need to perform location mapping by the referenced object. These are cases (iii) and (iv).

Definition A.3

intersects: ${\underline{\textit{genrange}}} \times {\underline{\textit{genrange}}} \rightarrow {\underline{\textit{bool}}}$

The result is TRUE iff $\exists u \in U, \exists v \in V$ such that

• (i) $u.oid = \bot \wedge v.oid = \bot \wedge u.l ~ \textbf{intersects} ~ v.l$ ; or

• (ii) $u.oid = v.oid \wedge u.l ~ \textbf{intersects} ~ v.l$ ; or

• (iii) $u.oid = \bot \wedge (\exists w \in Space:$ v.oid = w.oid  ∧ w.s ∈ IOSymbol’ ∧ u.l intersects geodata (w.β, v.l)); or

• (iv) $v.oid = \bot \wedge (\exists w \in Space:$ u.oid = w.oid ∧ w.s ∈ IOSymbol’ ∧ v.l intersects geodata(w.β, u.l))

Definition A.4

distance: ${\underline{\textit{genloc}}} \times {\underline{\textit{genloc}}} \rightarrow \underline{\textit{real}}$

$\textbf{length}(\textbf{trajectory}(\textbf{trip}(u, v)))$

Definition A.5

trajectory: ${\underline{\textit{genmo}}} \rightarrow {\underline{\textit{genrange}}}$

The result is a set of (oid, l, m) where m = u _i .m and the values for oid and l are defined in the following.

• (i) $u_i.oid = \bot ~\Rightarrow ~oid = \bot \wedge l= \cup f(t)(t\in u_i.i)$; or

• (ii) $\exists w \in Space$: u.oid = w.oid  ∧  (w.s =  REGION ∨ w.s = GROOM), then oid = u.oid, l = ∪ f(t).i _loc (t ∈ u _i .i); or

• (iii) $\exists w \in Space$: u.oid = w.oid  ∧  (w.s = LINE ∨ w.s = BUSROUTE), then $oid = u.oid, l=\cup \textbf{geodata}(w.\beta,f(t).i_{loc})(t\in u_i.i)$; or

• (iv) $\exists w_1, w_2 \in Space: u.oid w_1.oid \wedge w_1.s \mathrm{MPPTN} \wedge \textbf{ref\_id}(w_1)w_2.oid$, then $oid = w_2.oid, l= \textbf{trajectory}(\textbf{atperiods}(w_1,u_i.i$))

The trajectory of a moving object is a set of movement projections, each of which shows the path of a unit u _i  ∈ mo. The meaning for (i) and (ii) should be clear. In case (iii), the object moves along a pre-defined path, e.g., a road or bus route. For case (iv), the location in u _i maps to a bus. Then, the trajectory is the bus movement, which goes to case (iii).

Definition A.6

at: ${\underline{\textit{genmo}}} \times {\underline{\textit{genloc}}} \rightarrow {\underline{\textit{genmo}}}$

Let mo = < u ₁, u ₂, ..., u _n  > be the moving object and v denote the location.

• (i) $v.i_{loc} \neq \bot$, the result is < u ₁′,...,u _k ′ > where u _i ′ ∈ mo ∧ ∀ t ∈ u _i ′.i: f(t) = v; or

• (ii) $v.oid \neq \bot \wedge v.i_{loc}=\bot$, then the result is < u ₁′,...,u _k ′ > where u _i ′ ∈ mo ∧

  • (a) u _i ′.oid = v.oid; or

  • (b) $u_i'.oid = \bot \wedge (\exists w \in Space$ such that w.oid = v.oid ∧ ∀ t ∈ u _i ′.i: f(t) ∈ w.β ∧ w.s ∈   IOSymbol’)

The meaning is clear if the second argument represents a precise location (case (i)). If the location only records an object id (case (ii)), then the units in the result could have the same reference id as the input, or the unit location maps to the place covered by the given IFOB.

Definition A.7

intersection: ${\underline{\textit{genrange}}} \times {\underline{\textit{genrange}}} \rightarrow {\underline{\textit{genrange}}}$

Let U and V be the two arguments, and the result is denoted by L. The value for L is defined in the following: ∀ $l_i \in D_{\underline{\emph{genloc}}}$: l _i inside L $\Rightarrow$ l _i inside U ∧ l _i inside V.

Definition A.8

at: ${\underline{\textit{genmo}}} \times {\underline{\textit{genrange}}} \rightarrow {\underline{\textit{genmo}}}$

Let mo = < u ₁, u ₂, ..., u _n  > be the moving object and V be a set of locations. We use L ($\in D_{{\underline{\textit{genrange}}}}$) to denote the intersection locations between trajectory(mo) and V. The result is mo′ = < u ₁′, u ₂′, ... , u _k ′ > fulfilling the condition: ∀ u _j ′ ∈ mo′, $\forall t \in u_j'.i: f(t) (\in D_{\underline{\emph{genloc}}})$ inside L.

Appendix B: Example relations and query signatures

The following relations are used in the queries throughout the paper. Infrastructure relations are accessed by the get_infra operator.

$$ \texttt{MOGendon(Mo\_id: int, Traj: genmo, Name: string)} $$

rel_busstop :

(BusStopId: int, Stop: busstop, Name: string)

rel_busroute :

(BusRouteId: int, Route; busroute, Name: string, Up: bool)

rel_bus :

(BusId: int, BusTrip: mpptn, Name: string)

rel_room :

(RoomId: int, Room: groom, Name: string)

rel_door :

(DoorId: int, Door: door)

rel_roompath :

(RoomPathId: int, Door1: int, Door2: int, Weight: real, Room: groom, Name: string, Path: line)

rel_rbo :

(RegId: int, Reg: region, Name: string)

rel_rn :

(RoadId: int, Road: line, Name: string)

In the following tables we show the signatures of operations used in the queries. Operator get_infra is omitted as it occurs in almost every query. We define subtype to mean that the operator performs a conversion from a specific type to a generic type.

No.	Operator	Signature		Definition
Q1
Q2	geodata	busroute × busstop	→ point	Section 4.1.2
Q3	atinstant	genmo × instant	→ intime(genloc)	Table 6
	val	intime(genloc)	→ genloc	Table 6
Q4	atperiods	genmo × periods	→ genmo	Table 6
	val	intime(genloc)	→ genloc	Table 6
	=	genloc × genloc	→ bool	Table 7
Q5	get_mode	genmo	→ set(tm)	Table 9
	contains	set(tm) × tm	→ bool	Section 6.3
Q6	at	genmo × tm	→ genmo	Table 9
	deftime	genmo	→ periods	Table 6
	duration	periods	→ real	Table 6
Q7	ref_id	mpptn	→ int	Table 9
	at	genmo × tm	→ genmo	Table 9
	get_ref	genmo	→ set(ioref )	Table 9
	contains	set(ioref ) × int	→ bool	Section 6.3
Q8	subtype	busstop	< genloc	Table 10
	at	genmo × tm	→ genmo	Table 9
	at	genmo × genloc	→ genmo	Table 8
	deftime	genmo	→ periods	Table 6
	duration	periods	→ real	Table 6
Q9	contains	set(region) × region	→ bool	Section 6.3
	freespace	groom	→ region	Table 11
	contains	set(string) × string	→ bool	Section 6.3
Q10	freespace	mpptn	→ mpoint	Table 11
	passes	mpoint × region	→ bool	[18]
Q11	ref_id	mpptn	→ int	Table 9
	distance	mpoint × mpoint	→ mreal	[18]
	freespace	mpptn	→ mpoint	Table 11
	freespace	genmo	→ mpoint	Table 11
	at	genmo × tm	→ genmo	Table 9
Q12	subtype	busroute	< genrange	Table 10
	subtype	line	< genrange	Table 10
	intersects	genrange × genrange	→ bool	Table 7
Q13	atperiods	genmo × periods	→ genmo	Table 6
	at	genmo × tm	→ genmo	Table 9
	get_ref	genmo	→ set(ioref )	Table 9
	contains	set(ioref ) × int	→ bool	Section 6.3
Q14	at	genmo × tm	→ genmo	Table 9
	trajectory	genmo	→ genrange	Table 8
Q15	subtype	groom	< genrange	Table 10
	at	genmo × genrange	→ genmo	Table 8
	deftime	genmo	→ periods	Table 6
	components	periods	→ set(periods)	Section 6.3
	duration	periods	→ real	Table 6
Q16	ref_id	mpptn	→ int	Table 9
	subtype	busstop	< genloc	Table 10
	genloc	int × real × real	→ genloc	Table 11
	at	genmo × genloc	→ genmo	Table 8
	initial	genmo	→ intime(genloc)	Table 6
	val	intime(genloc)	→ genloc	Table 6
	=	genloc × genloc	→ bool	Table 7
Q17	subtype	groom	< genrange	Table 10
	passes	genmo × genrange	→ bool	Table 8
	subtype	busstop	< genloc	Table 10
	atperiods	genmo × periods	→ genmo	Table 6
	at	genmo × tm	→ genmo	Table 9
	initial	genmo	→ intime(genloc)	Table 6
	final	genmo	→ intime(genloc)	Table 6
	val	intime(genloc)	→ genloc	Table 6
	=	genloc × genloc	→ bool	Table 7
Q18	subtype	gline	< genrange	Table 10
	atperiods	genmo × periods	→ genmo	Table 8
	components	periods	→ set(periods)	Section 6.3
	final	genmo	→ intime(genloc)	Table 6
	val	intime(genloc)	→ genloc	Table 6
	at	genmo × tm	→ genmo	Table 9
	inside	genloc × genrange	→ bool	Table 7

Appendix C: Type system in free space and road network

Table 13 Data types in [14, 18, 20]

Definition C.1

$$ \begin{array}{rll} \mathit{UBool} &=& \{(i,b)|i \in D_{\underline{\emph{interval}}}, b\in D_{{\underline{\textit{bool}}}}\}\\ D_{{\underline{\textit{mbool}}}}& =& \{<u_1,u_2,...,u_n>|n \geq 0,n \in D_{\underline{\emph{int}}}, ~\mathit{and}~ \forall i \in [1,n], u_i \in \mathit{UBool} \} \end{array} $$

Definition C.2

$$ \begin{array}{rll} \mathit{UPoint} &=& \{(i,p_1,p_2)|i \in D_{\underline{\emph{interval}}}, p_1,p_2 \in D_{{\underline{\textit{point}}}}\}\\ D_{{\underline{\textit{mpoint}}}} &=& \{<u_1,u_2,...,u_n>|n \geq 0,n \in D_{\underline{\emph{int}}}, ~\mathit{and} ~\forall i \in [1,n], u_i \in \mathit{UPoint}\} \end{array} $$

Definition C.3

$$ \begin{array}{rll} \mathit{NLoc} &=& \{(rid,pos,side)| rid \in D_{\underline{\emph{int}}}, pos \in D_{\underline{\emph{real}}}, side \in D_{{\underline{\textit{bool}}}}\}\\ D_{{\underline{\textit{gpoint}}}} &=& \{(n\_id,gp)| n\_id \in D_{\underline{\emph{int}}}, gp \in \mathit{NLoc} \} \end{array} $$

Definition C.4

$$ \begin{array}{rll} \mathit{NReg} &=& \{(rid,pos_1,pos_2)|rid \in D_{\underline{\emph{int}}}, pos_1, pos_2 \in D_{\underline{\emph{real}}} \}\\ D_{{\underline{\textit{gline}}}} &=& \{(n\_id,gl)| n\_id \in D_{\underline{\emph{int}}}, gl \in \mathit{NReg} \} \end{array} $$

Definition C.5

$$ \begin{array}{rll} \mathit{UGPoint} &=& \{(i,gp_1,gp_2)|i \in D_{\underline{\emph{interval}}}, gp_1,gp_2 \in \mathit{NLoc}~ \mathit{and}\\ && (i)~ gp_1.rid = gp_2.rid;\\ && (ii)~gp_1.side = gp_2.side \}\\ D_{{\underline{\textit{mgpoint}}}} &=& \{<u_1,u_2,...,u_n>|n \geq 0,n \in D_{\underline{\emph{int}}},~ \mathit{and}\ \forall i \in [1,n], u_i \in \mathit{UGPoint}\} \end{array} $$