Visit probability and accessibility within space–time prism of activity program

Figures & data

Table

STP:	Space–time prism	AP:	Activity program
PPA:	Potential path area	SMP:	Semi-Markov process
NTP:	Network-time prism	NAL:	Number of accessible locations
SNK:	Multi-state supernetwork	AFT:	Aggregate flexible time
TBS:	Two-stage bidirectional search	MFT:	Maximum flexible time

Figure 1. Multi-state supernetwork representation with a single mode.

Figure 2. Examples of accessibility for the four remarks.

Table 1. Highest accessibility systems in the four examples.

Example No.	NAL – Equation (14)(14) $$\mathit{\text{NAL}}\left(\tilde{s}\right)=\sum _{e}R\left(e\right),R\left(e\right)=\{\begin{array}{l}1,\text{if}\mathit{\text{e}}:s\to s^{\prime }\in \text{STP}\\ 0,\text{otherwise} \end{array}\mathrm{ }$$(14)	AFT – Equation (15)(15) $$\mathit{\text{AFT}}\left(\tilde{s}\right)=\sum _e\left(t_{{j|}_{s^{\prime }}}^{+}-t_{{i|}_s}^{-}-d_{\alpha }^{\mathrm{\text{min}}}\right)R\left(e\right),i=j$$(15)	MFT – Equation (16)(16) $$\mathit{\text{MFT}}\left(\tilde{s}\right)=\underset{e}{\mathrm{\text{max}}}\left[\left(t_{{j|}_{s^{\prime }}}^{+}-t_{{i|}_s}^{-}-d_{\alpha }^{\mathrm{\text{min}}}\right)R\left(e\right)\right],i=j$$(16)	AVP – Equation (20)(20) $$\mathit{\text{AVP}}\left(\tilde{s},t\right)=\sum _{i=1}^{\left|\zeta \left(\tilde{s},t\right)\right|}G\left(e_i,t\right)\bullet \widehat{\mathit{P}}\left({\mathit{e}}_{\mathit{i}},\mathit{t}\right)$$(20)
1	S1-1/S1-2	S1-2	S1-2	S1-2
2	S2-1/S2-2/ S2-3	S2-1/S2-2/S2-3	S2-1/S2-2/S2-3	S2-2
3	S3-2/S3-3	S3-2/S3-3	S3-1/S3-2/S3-3	S3-2
4	S4-3	S4-2/S4-3	S4-1/S4-2/S4-3	S4-2

Figure 3. Study area and a selected individual AP.

Figure 4. Histogram and the estimated distributions for travel and shopping.

Table 2. Log-likelihood, AIC, and BIC with latent classes for travel.

Number of classes	Number of parameters $P$	Log-likelihood $\mathrm{\text{ln}}\hspace{0.17em}(L)$	AIC	BIC
1	5	−6765.672654	13541.3453	13568.0072
2	10	−6765.672638	13551.3453	13604.6690
3	15	−6765.672623	13561.3453	13641.3308
4	20	−6765.672608	13571.3452	13677.9926
5	25	−6765.672593	13581.3452	13714.6544

$\mathit{\text{AIC}}=2P-2\mathrm{\text{ln}}\hspace{0.17em}\left(L\right);$ $\mathit{\text{BIC}}=P\mathrm{\text{ln}}\hspace{0.17em}(Q)-2\mathrm{\text{ln}}\hspace{0.17em}\left(L\right).$ For the LR test, the null hypothesis: ${\lambda }_k=\frac{Q}{{\sum }_{q=1}^Q{\tau }_q},$ ${\mathit{\beta }}_k=0.$

Table 3. Log-likelihood, AIC, and BIC with latent classes for shopping.

Number of classes	Number of parameters $P$	Log-likelihood $\mathrm{\text{ln}}\hspace{0.17em}(L)$	AIC	BIC
1	6	−1522.065936	3056.1319	3079.0345
2	12	−1447.648105	2919.2962	2965.1015
3	18	−1433.337018	2902.6740	2971.3820
4	24	−1420.237746	2888.4755	2980.0862
5	30	−1412.163766	2884.3275	2998.8409

For the LR test, the null hypothesis: ${\mu }_k=\frac{1}{Q}{\sum }_{q=1}^Q\mathrm{\text{ln}}\hspace{0.17em}{\tau }_q,$ ${\sigma }_k^2=\frac{1}{Q}{\sum }_{q=1}^Q{\left(\mathrm{\text{ln}}\hspace{0.17em}{\tau }_q-\frac{1}{Q}{\sum }_{q=1}^Q\mathrm{\text{ln}}\hspace{0.17em}{\tau }_q\right)}^2,$ ${\mathit{\beta }}_k=0.$

Table 4. Parameter estimates: shopping.

Class	Latent class size	${\mathit{\beta }}_k$ (p-Value)		${\mu }_k,{\sigma }_k$ (p-Value)
1	0.69	Constant	0.2631 (0.2015)	${\mu }_1$	3.5100 (<0.001)
		Gender	0.4437 (0.0342)
		Age $\le$50	−0.1044 (0.7026)	${\sigma }_1$	0.8032 (<0.001)
		50 < Age $\le$65	0.5751 (0.0113)
		Age >65 (base level)	0
2	0.31	Constant	0	${\mu }_2$	0.1027 (0.5762)
		Gender	0
		Age $\le$50	0	${\sigma }_2$	1.4470 (<0.001)
		50 < Age $\le$65	0
		Age >65 (base level)	0

Figure 5. Percentage of accessible travel links within the STP.

Figure 6. Planar STP interior of travel links at activity state 0 (none is conducted).

Figure 7. Planar STP interior of travel links at activity state 1 (only work is conducted).

Figure 8. Planar STP interior of flexible activity locations before work ($\tilde{s}:$ $0\to 2$).

Figure 9. Planar STP interior of flexible activity locations after work ($\tilde{s}:$ $1\to 3$).

Figure 10. Comparisons of $\mathit{\text{AVP}}\left(\tilde{s},t\right),$ $\mathit{\text{NAL}}\left(\tilde{s},t\right),$ $\mathit{\text{AFT}}\left(\tilde{s},t\right),$ and $\mathit{\text{MFT}}\left(\tilde{s},t\right).$

Figure 11. Flexible activity locations within STPs with maximum accessibilities.