Advanced Sustainable Logistics with HSR for the Development in Great Montreal Area

Abstract

Currently, the new transportation tool High-Speed Railway (HSR) pushes economic and social development to a great level in some countries. Because of its high speed (actual speed 430 km/h, experiment speed 600–1200 km/h) and high efficiency, it makes good transportation in a surprisingly quick increment and then supports supply chain logistics running at a greatly higher level than that before. Especially, a stimulation of trade volume will happen due to the increased speed of transportation within the HSR network. The success of HSR in the Asia area implies its future application may produce an economic engine in East Canada or the Great Montreal Area with extended regions, which will stimulate the local economic and social development in an excellent model. Especially for the goods flow or trade volume, the implementation of the HSR network centred in the Great Montreal Area can bring to the community. This chapter will make a mathematical model deviated from the Gravity Model to investigate the relationship between the goods flow and the HSR speed. The research on their relationship demonstrated that the HSR would be able to substitute the low-speed vehicle style and increase economic development.

1. Introduction

It can list a series of problems coming from current city logistics, which are those conflicts between poor transportation and sustainable city logistics that people pursue. Low-speed transportation always happens because heavy circulation pushes into the same narrow road in a short time for circulation, which produces problems such as the gas assumption that pollutes the air and noise damaging the environment, as a result of low efficiency in GDP development for the reason of low speed of goods and trade among cities. Sustainable advanced city logistics with HSR could solve some city circulation problems of the above. In the past, some problems existed in the limited science and techniques that could not be applied to sustainable city logistics. Currently, sustainable advanced city logistics not only improves facilities and fine policies of the authority but also is impelled by new HSR tools.

This chapter will apply a mathematical model to the simulation of the city trade logistics with HSR to look for its logical-mathematical model and apply for AI to simulate the city logistics that state the application with the HSR relative to the trade, which points out that the HSR improves the city logistics by its high speed with high efficiency for business activities. Traditionally, the plane is the quickest travel tool. However, an electrical high-speed railway (EHSR) is quicker than a plane in a short distance if the travel time is limited to 4 hours then the plane needs at least 2 hours for its boarding process, though the speed of HSR is 420 k/h and the plane is 700 k/h. This chapter will make a mathematical model to evaluate the influence and result of the application of the HSR for the trades in the Great Montreal Area (GMA). HSR can provide sustainable city logistics not only in the city area but anywhere that can be defined as city logistics. This chapter investigates what and how an HSR with smart algorithms improves sustainable city logistics in the field of trade circulation. By the data analysis, the mathematical model of the HSR in sustainable city logistics could predict a good advantage for the GDP increase in the GMA. And according to the load and the speed, other transportation tools cannot compete with HSR in terms of efficiency [1]. Especially, the higher the speed of HSR developed, the more advantages it has, and no other transportation will be comparable to such HSR [2].

When we are talking about interprovincial and international trade, speed is a key to an efficient supply, which leads to an increased demand and thus, an improvement of the local economy. This chapter will discuss first the implementation of the factor speed to the Gravitational Model for trade, then an analysis of the Great Montreal Area, including different factors that can be included in the general Gravitational Model to make it suitable for the Great Montreal Area. This chapter will compare the before and after of the implementation of HSR in the relationship with trade.

2. Literature

Sustainable advanced city logistics in the shortest time has been researched by many researchers. How to spend less time making the best city logistics service? Meituan company applies smart techniques in its delivery service in an average of 28 minutes from the provider to the customer, in which AI is used for the service among the components including the managers, delivers, providers, and customers, which benefits all shareholders among the logistics service system. However, sustainable city logistics in the suburbs are not like the urban area, which is a desolate area to make the service more difficult. To solve the problem, in 1959 in Japan, it constructed a high-speed railway (HSR) from Tokyo to Osaka, which made the city logistics better in suburban areas than before. For example, now it only takes 5 hours from Shanghai to Beijing to pass 1213.0 km. China High-speed Railway (CHSR) not only makes city logistics better at a great level in remote areas, but it also provides a sustainable solution for development in remote village areas for trades and travelers.

The sustainable advanced city logistics applied for an algorithm of the metaheuristics by Gogna & Tayal [3] is based on AI technology and neural networks algorithms. Holland [4] also proposed a genetic algorithm (GA) based on principles from evolution theory, which defined genetic algorithms originated from the Monte Carlo method. Murthy & Chowdhury [5] integer encoding of chromosomes used in the supply chain logistics then it developed this simulated algorithm (SA) approach for examining the equations of state and frozen states of n-body systems for the optimization of routing net. One algorithm appears to be available stochastic algorithms for global optimization from Ali & Storey [6] which could support better choice of advanced city logistics. And the advanced city logistics could applied for Ant Colony Optimization (ACO) by Marco [7] and Anirudh [8], which stated that ACO is a positive feedback and is efficient for traveling salesman problems (TSP) in the advanced city logistics. The author Zhang et al. [9] improved the logistics strategy and proposed a new Route Decomposition (RD) and a Memetic Algorithm (MA) framework for the Periodic Capacitated Arc Routing Problem (PCARP).

The advanced city logistics in cities mainly focus on the flow of trade and human beings, which is so complicated that many problems result from the heavy circulation thus causing congestion in many metropolitan areas, especially in the rush hours. Kostas [10] researched the key challenges associated with adopting, designing and managing performance-based contracts (PBC) for advanced city logistics services, in which mostly the PBC originates in upstream supply chain resources rather than downstream initiatives. The researchers Meng & Yari [11] studied the advanced city logistics for intelligent and sustainable transport by investigating the global developments in transport and city logistics and the cost-efficiency and flexibility of European transport and city logistics to show the customers’ requirements in various fields, in which it produces challenge from the relationship of sustainability issues of social, economic, and environmental parameters. Those researchers Takai Eizo [12] studied advanced city logistics through the role of operations, in which the problems in city logistics in Japan are discussed and a solution for the problem by assumptions of some cause-and-effect relationship alone is not sufficient. Advanced city logistics to improve and optimize delivery management in a smart environment process by Yassine et al. [13] was studied in which the manufacturing of products and services are sold online in various regions and transporters are principally demanded to apply the optimum types of shipping centres and shipping routines, and smart delivery city logistics should be able to meet those aspects: the delivery requirements. Masato [14] attempts to contribute to transcending the stereotypes of value systems in shipping by presenting some of the elements of current maritime. In the dynamic infrastructure, Miyashita Kunio [15] studied the structural change in international advanced city logistics, in which the type of contractual system utilizes mid to long-term contracts to shipper satisfaction because of the guarantee of long-term profit stability. Under specific conditions, selected cargo flows show the potential to be shifted to other modes of transport or at least other types of vehicles that are more suitable for operations in a dense urban environment, in which voluntary cooperation of freight operators may be considered a method of improving the effectiveness of city logistics operations from Kaszubowski [16] and different regions may take various measures and city logistics and delivery services have been optimized, in which the costs need to be optimized elsewhere. Those researches relate an important factor to the trade and human beings flow, in which the advanced logistics needs the help from HSR to solve its efficiency and help the economic development.

3. The gravitational model

The gravitational model predicts the value of trade between places i and j in relationship with these places’ GDP and distance between these two places [17]:

$$T_{\mathit{ij}}=\frac{A{Y}_i^a{Y}_j^b}{D_{\mathit{ij}}^c}$$E1

where $T_{\mathit{ij}}$ is the value of trade between places i and j.

$A$, a, b, c are constants.

$Y_i$ is the GDP of place i.

$Y_j$ is the GDP of place j.

$D_{\mathit{ij}}$ is the distance between i and j.

In general, $D_{\mathit{ij}}$ can be calculated by considering the actual distance, the cultural affinity, geographic differences, presence of multinational corporations and borders between places i and j. This chapter probes the possibility of replacing $D_{\mathit{ij}}$ with the travel time between places i and j ($t_{\mathit{ij}}$) with a change of A.

$$T_{\mathit{ij}}=\frac{A{Y}_i^a{Y}_j^b}{D_{\mathit{ij}}^c}=\frac{B{Y}_i^a{Y}_j^b}{t_{\mathit{ij}}^c}$$E2

where A/$D_{ij}^c$ = (A/$s_{ij}^c$)(1/$t_{ij}^c$) = B/$t_{ij}^{c.}$

$S_{\mathit{ij}}$ is the speed of the transportation vehicle between places i and j.

The new equation is mathematically logical as speed = distance/time, thus distance = speed*time.

The new equation also makes sense, for $Y_i$, $Y_j$,$D_{\mathit{ij}}$ large, as the more time it takes to travel from places i to j, the more reluctant people tend to trade from places i to j as the relative monetary and time cost increase. With the same logic, in contrast, the less time it takes to travel from places i to j, the value of trade increases as trade demand and supply are more efficient.

4. Montreal trade data

In order to construct a Gravity Model suitable for the Great Montreal Area—finding B, a, b and c—we need to consider several data in order to achieve the goal using simulation and AI analysis.

As the most recent data available for our purpose is in 2014, all data will be in 2014. Note that as the Great Montreal Area does not have HSR yet, the choice of year does not matter as long as it is prior the date of this chapter’s publication, as the HSR influence over data does not exist. However, more recent data can lead to more precise final results in terms of simulated trade volume as they are the results of other factors that improve the trade.

First, the volume of trade between the Great Montreal Area with its trade partners is main trade in Quebec. Note that as the public information contains only the information about the Great Montreal Area’s province, Quebec, consider Quebec’s first. Table 1 contains the data of Quebec trade partners—10 Canadian provinces, 3 Canadian territories and top 10 US state trade partners. As the above trade data is not available for the Great Montreal Area, we can estimate instead the Great Montreal Area’s in proportion of its GDP ratio over Quebec’s.

Trade Partners	Export from Trade Partners (in millions of $CAD)	Import from Trade Partners(in millions of $CAD)	Total Trade with Trade Partners(in millions of $CAD)	GDP of Trade Partners(in millions of $CAD) [19, 20, 21]1
Newfoundland and Labrador	1897	2014	3911	32136.7
Prince Edward Island	380	260	640	5332
Nova Scotia	2581	1511	4092	36258.3
New Brunswick	3254	3565	6819	29,650
Ontario	38,644	42,087	80,731	676838.4
Manitoba	2172	2030	4202	59499.7
Saskatchewan	1942	944	2886	78506.4
Alberta	9737	6350	16,087	365191.1
British Columbia	6215	4157	10,372	225863.3
Yukon	71	18	89	2650.3
Northwest Territories	221	87	308	4656.5
Nunavut	297	38	335	2350.9
Texas	3575.147956	7709.004393	11284.15235	1781770.194
New York	6036.504659	2038.388785	8074.893444	1535564.161
Vermont	3412.103269	1383.52492	4795.628189	32409.32894
Pennsylvania	3362.580985	1215.489027	4578.070012	755902.3393
Ohio	3449.320952	754.691009	4204.011961	652916.6188
New Jersey	2304.565172	1086.196318	3390.76149	598898.127
Connecticut	2467.022152	615.315773	3082.337925	270207.2607
Massachusetts	1708.700031	1242.214485	2950.914516	506801.9852
Tennessee	2525.264476	289.61916	2814.883636	329905.1122
California	1566.896317	1190.712692	2757.609009	2593340.192

Table 1.

Data of Quebec’s trade partners in 2014 [18].

¹

GDP: For Canadian provinces: https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610048701; For US provinces: https://hub.arcgis.com/datasets/a2a8826c4ba44f89a684000fe7c05b8c_0?geometry=-126.256%2C20.471%2C1.185%2C63.314&selectedAttribute=GDP_by_State___97_to_16__dol_39; adjusted for 1 $CAD = 0.905912 $US in 2014 for exchange based on https://www.ofx.com/en-ca/forex-news/historical-exchange-rates/yearly-average-rates/

$${\text{Trade}}_{\text{Great Montreal Area},\text{Quebec}’\mathrm{s}\text{Trade Partner}}/{\text{Trade}}_{\text{Quebec},\text{Qubec}’\mathrm{s}\text{Trade Partner}}={\mathrm{GDP}}_{\text{Great Montreal Area}}/{\mathrm{GDP}}_{\text{Quebec}}$$

Thus, Trade_{Great Montreal Area, Quebec’s Trade Partner}

$$\begin{array}{l}=({\text{Trade}}_{\text{Quebec},\text{Qubec}’\mathrm{s}\text{Trade Partner}}\ast {\mathrm{GDP}}_{\text{Great Montreal Area}}/{\mathrm{GDP}}_{\text{Quebec}}\\ {=}_{}{\text{Trade}}_{\text{Quebec},\text{Qubec}’\mathrm{s}\text{Trade Partner}}\ast \left(\mathrm{190,227,000,000}\text{\$}\mathrm{CAD}\left[23\right]/338319000000\text{\$}\mathrm{CAD}\left[24\right]\right)\\ ={\text{Trade}}_{\text{Quebec},\text{Qubec}’\mathrm{s}\text{Trade Partner}}\ast 0.56227111\end{array}$$

With the estimated ratio (Table 2)

Trade Partners	Estimation of Total Trade with Trade Partners (in millions of $CAD)	GDP of Trade Partners (in millions of $CAD)	Distance from the Great Montreal Area to the Trade Partners (in km) [22]
Newfoundland and Labrador	2199.042315	32136.7	1426
Prince Edward Island	359.853511	5332	1136.1
Nova Scotia	2300.813386	36258.3	1242.9
New Brunswick	3834.126706	29,650	748.7
Ontario	45392.70906	676838.4	1076
Manitoba	2362.663208	59499.7	2014.75
Saskatchewan	1622.714426	78506.4	3168.9
Alberta	9045.255363	365191.1	3838.6
British Columbia	5831.875963	225863.3	3899
Yukon	50.04212888	2650.3	4222
Northwest Territories	173.1795022	4656.5	3744
Nunavut	188.3608222	2350.9	2805
Texas	6344.752878	1781770.194	3083.6
New York	4540.279308	1535564.161	599.6
Vermont	2696.44319	32409.32894	172.6
Pennsylvania	2574.116512	755902.3393	701.6
Ohio	2363.794476	652916.6188	1108.5
New Jersey	1906.52723	598898.127	703.4
Connecticut	1733.10957	270207.2607	517.9
Massachusetts	1659.213983	506801.9852	503.5
Tennessee	1582.727749	329905.1122	1863.1
California	1550.523881	2593340.192	4790.8

Table 2.

Data of great Montreal Area’s trade partners in 2014.

Now, consider the average time it takes for trade to arrive from the starting point to the destination [23, 24].

The most recent data about the repartition of transportation modes in Canadian trade is 2011s (Table 3).

Transportation Modes	Repartition (%) [25]	Average Speed (km/h)
Trucking	57.0558956	96.5605 [26]
Air	20.7237506	925.373 [27]
Rail	18.8841057	35.4056 [28]
Marine	3.3362481	4.97097 [29]

Table 3.

Repartition of transportation modes in Canadian trade in 2011.

Thus, we can obtain an average speed for trade transportation:

$$\begin{array}{l}57.0558956\%\ast 96.5605+20.7237506\%\ast 925.373+18.8841057\%\ast 35.4056+3.3362481\ast 497097\\ =2537173254\mathrm{km}/\mathrm{h}\end{array}$$

Remark that this speed is less than the current average HSR speed—325 km/h [30], much less than 660 km/h and 1000–1400 km/h HSR may exist in the future (Table 4).

Trade Partners	Estimation of Total Trade with Trade Partners(in millions of $CAD): $T_{\mathit{ij}}$	GDP of Trade Partners(in millions of $CAD): Yj	Time taken from the Great Montreal Area to the Trade Partners with an average speed of 253.7173254 km/h(in h): tij
Newfoundland and Labrador	2199.042315	32136.7	5.620428
Prince Edward Island	359.853511	5332	4.477818
Nova Scotia	2300.813386	36258.3	4.898759
New Brunswick	3834.126706	29,650	2.950922
Ontario	45392.70906	676838.4	4.24094
Manitoba	2362.663208	59499.7	7.940924
Saskatchewan	1622.714426	78506.4	12.48988
Alberta	9045.255363	365191.1	15.12944
British Columbia	5831.875963	225863.3	15.3675
Yukon	50.04212888	2650.3	16.64057
Northwest Territories	173.1795022	4656.5	14.75658
Nunavut	188.3608222	2350.9	11.05561
Texas	6344.752878	1781770.194	12.15368
New York	4540.279308	1535564.161	2.36326
Vermont	2696.44319	32409.32894	0.680285
Pennsylvania	2574.116512	755902.3393	2.765282
Ohio	2363.794476	652916.6188	4.369035
New Jersey	1906.52723	598898.127	2.772377
Connecticut	1733.10957	270207.2607	2.041248
Massachusetts	1659.213983	506801.9852	1.984492
Tennessee	1582.727749	329905.1122	7.343212
California	1550.523881	2593340.192	18.88243

Table 4.

Data for simulation.

5. Simulation and AI analysis

Now, using the data, we will run simulations in order to find the constant terms B, a, b and c in the formula

$$T_{\mathit{ij}}=\frac{B{Y}_i^a{Y}_j^b}{t_{ij}^c}.$$E3

Yi = Great Montreal GDP = 190,227 M $CA

The attempt to find constants for formula (3) consists of linear regression [31]. Thus, first, we make the predicted formula (3) linear.

$$T_{\mathit{ij}}=\frac{B{Y}_i^a{Y}_j^b}{t_{\mathit{ij}}^c}$$E4

$$ln{T}_{\mathit{ij}}=ln\mathrm{B}+\mathit{a}\ast ln{\mathrm{Y}}_{\mathrm{i}}+\mathit{b}\ast ln{\mathrm{Y}}_{\mathrm{j}}-\mathit{c}\ast ln{\mathrm{t}}_{\mathrm{ij}}$$E5

As we use (5) to estimate the gravity function for the Great Montreal Area i in relationship to another area j, we can set

ln T_ij = pred_j

ln B = a₀

$a\ast \mathit{ln}{Y}_i=a_{\mathit{1}}\ast x_{\mathit{1}}=a_{\mathit{1}}\ast \mathit{ln}\left(\mathit{190227}\right)$

$\mathit{b}\ast \ln {\mathrm{Y}}_{\mathrm{j}}={\mathit{a}}_{\mathrm{2}}\ast {\mathit{x}}_{\mathrm{\text{2j}}}$

$\mathit{c}\ast \ln {\mathrm{t}}_{\mathrm{ij}}={\mathit{a}}_{\mathrm{3}}\ast {\mathit{x}}_{\mathit{\text{3j}}}$

Thus, (5) becomes pred_j = a₀ + a₁$\ast$x_1j + a₂$\ast$x_2j - a₃$\ast$x_3j

To obtain the best-fit constants for the equation using regression, we need to consider the cost function before simulation. The cost function consists of mean square error (MSE) —an average difference square between the estimated total trade volumes and the true ones. As we have 22 trading partners to consider, our cost function is

$$C=\frac{1}{22}\sum _{j=1}^{22}{\left(\mathit{pre}{d}_j-y_j\right)}^2$$E6

Where y_j is the actual total trade with trade partners (in millions of $CAD) in the table for Data for simulation.

Thus, our goal is to minimize the cost function using simulation

$$minC=min\frac{1}{22}\sum _{j=1}^{22}{\left(a_0+a_1\ast x_1+a_2\ast x_{2j}-a_3\ast x_{3j}-y_j\right)}^2$$E7

Based on directional derivatives, $\nabla C=\left[\begin{array}{c}\frac{\partial C}{\partial a_0}\\ \frac{\partial C}{\partial a_1}\\ \begin{array}{c}\frac{\partial C}{\partial a_2}\\ \frac{\partial C}{\partial a_3}\end{array}\end{array}\right]$ always points in the direction of the steepest ascent [32]. Hence, the negative$\nabla C$ will lead to the most descent. Thus, it suffices to use derivatives to update the constants $a_0,a_1,a_2\mathit{\text{and}}{a}_3$ through gradient descent.

Thus, for $n=22;\mathit{\text{learning rate}}\alpha \mathit{\text{small}}$

$$\frac{\partial C}{\partial a_0}=\frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right);a_0=a_0-\alpha \frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)$$E8

$$\frac{\partial C}{\partial a_1}=\frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)x_1;a_1=a_1-\alpha \frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)x_1$$E9

$$\frac{\partial C}{\partial a_2}=\frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)x_{2j};a_2=a_2-\alpha \frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)x_{2j}$$E10

$$\frac{\partial C}{\partial a_3}=\frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)\left(-x_{3j}\right);a_3=a_3+\alpha \frac{2}{n}\sum _{j=1}^n\left(\mathit{pre}{d}_j-y_j\right)x_{3j}$$E11

Through simulations, we can update $a_0,a_1,a_2\mathit{\text{and}}{a}_3$ m times to approximate the min C.

Using the AI in python to simulate,

Trying with several numbers of simulation and $\alpha$, we obtain (Table 5)

Table 5.

Simulation results.

By intuition, the gradient leads to the min C with larger m steps with the smallest learning rate

$\alpha$, which leads the movement and the direction for each step. However, considering the tables, we can clearly see that it is not the case. For example, the result of 10³ simulations with $\alpha$ = 10⁻⁷ is worse than smaller m and bigger $\alpha$. Thus, we can conclude that C is not convex. Consider the best-predicted $a_0,a_1,a_2\mathit{\text{and}}{a}_3$ with the biggest R², the one with 10⁶ simulations and $\alpha$ = 0.0001 (Figure 1).

Figure 1.

Simulation result with m = 106 and α = 0.0001.

By Z-score $\frac{x-\mu }{\sigma }$, all differences obtained from ln(trade volume) – ln(simulated trade volume) are within 2$\sigma$ except the one at ln(distance) = 1.44478 (Table 6).

Standard deviation $\sigma$ = 0.958541006
Difference X	Z score	Difference X	Z score	Difference X	Z score
0.784075	0.817988	1.115281	1.16352	−0.60912	−0.63546
−0.25032	−0.26115	−1.55597	−1.62327	−0.90255	−0.94159
0.737396	0.76929	−0.6078	−0.63409	−0.70779	−0.7384
1.209447	1.261758	−0.28137	−0.29354	−1.05105	−1.09651
2.321481	2.421891	0.178352	0.186066	−0.55755	−0.58167
0.659641	0.688172	−0.51413	−0.53636	−1.29027	−1.34608
0.27318	0.284996	0.433499	0.452249
1.326773	1.384158	−0.71121	−0.74198

Table 6.

Difference of non-simulated and simulated trade volume.

Thus, by excluding the outlier, we obtain (Figure 2)

Figure 2.

Simulation result with m = 106 and α = 0.0001 without outlier.

Thus, consider the estimated $a_0,a_1,a_2\mathit{\text{and}}{a}_3$ and previous settings for $T_{\mathit{ij}}=\frac{B{Y}_i^a{Y}_j^b}{t_{\mathit{ij}}^c}$, In addition, to consider the influence of noise to the predicted value, we can also add a residual in the formula to the estimated value.

Thus,

$$T_{\mathit{ij}}=exp\left(\mathit{ln}B+a\ast \mathit{ln}{Y}_i+b\ast \mathit{ln}{Y}_j-c\ast \mathit{ln}{t}_i\right)+\in ;$$E12

where $\in =$Actual Total trade – Simulated trade value

$$\mathrm{B}=e^{a_0}={\mathrm{e}}^{0.01933223206441371}$$

$$a=a_1=0.235002098251484$$

$$b=a_2=0.4218958455297647$$

$$c=a_3=0.23241753184881292$$

R² = 0.5678982124691647 (Tables 7–9)

Trade Partners	ln(Total Trade with Trade Partners)(in ln(millions) of $CAD)	ln(Simulated Total Trade with Trade Partners)(in ln(millions) of $CAD)	(Estimated) Total Trade with Trade Partners(in millions of $CAD)	Simulated Total Trade with Trade Partners(in millions of $CAD)	Adjustment ∈(in millions of $CAD)
Newfoundland and Labrador	7.695777233	6.853095312	2199.042315	946.8070388	1252.235276
Prince Edward Island	5.885697035	6.148077493	359.853511	467.8171399	−107.9636289
Nova Scotia	7.741017985	6.935945535	2300.813386	1028.591362	1272.222024
New Brunswick	8.251696971	6.96886162	3834.126706	1063.01195	2771.114756
Ontario	10.72310678	8.204249089	45392.70906	3656.453945	41736.25512
Manitoba	7.76754474	7.032643024	2362.663208	1133.021259	1229.641949
Saskatchewan	7.391855598	7.044336861	1622.714426	1146.348395	476.3660306
Alberta	9.10999563	7.648332464	9045.255363	2097.145607	6948.109756
British Columbia	8.671094005	7.441986786	5831.875963	1706.136584	4125.739379
Yukon	3.912865228	5.548053438	50.04212888	256.7373141	−206.6951852
Northwest Territories	5.154328642	5.813756233	173.1795022	334.8746333	−161.6951311
Nunavut	5.23835939	5.592515625	188.3608222	268.4099901	−80.0491679
Texas	8.755383432	8.367914608	6344.752878	4306.645648	2038.10723
New York	8.420743811	8.685779367	4540.279308	5918.151114	−1377.871806
Vermont	7.899688847	7.347444238	2696.44319	1552.224338	1144.218852
Pennsylvania	7.853261652	8.350251559	2574.116512	4231.245018	−1657.128506
Ohio	7.768023436	8.182151848	2363.794476	3576.542562	−1212.748086
New Jersey	7.553038662	8.251429965	1906.52723	3833.103108	−1926.575878
Connecticut	7.457672513	7.986795255	1733.10957	2941.853943	−1208.744373
Massachusetts	7.414099265	8.258692476	1659.213983	3861.042395	−2201.828412
Tennessee	7.366905061	7.773467941	1582.727749	2376.699266	−793.9715167
California	7.346348141	8.423865627	1550.523881	4554.475371	−3003.95149
Total	165.3785041	162.8596464	100312.1252	51257.338	49054.78719

Table 7.

Data adjustment with residual $\in$.

Trade Partners	GDP of Trade Partners(in millions of $CAD): Yj	Distance from the Great Montreal Area to the Trade Partners (in km)	Time taken from the Great Montreal Area to the Trade Partners with HSR speed of (in h): tij
			325 km/h	660 km/h	1000 km/h	1400 km/h
Newfoundland and Labrador	32136.7	1426	4.387692308	2.160606061	1.426	1.018571429
Prince Edward Island	5332	1136.1	3.495692308	1.721363636	1.1361	0.8115
Nova Scotia	36258.3	1242.9	3.824307692	1.883181818	1.2429	0.887785714
New Brunswick	29,650	748.7	2.303692308	1.134393939	0.7487	0.534785714
Ontario	676838.4	1076	3.310769231	1.63030303	1.076	0.768571429
Manitoba	59499.7	2014.75	6.199230769	3.052651515	2.01475	1.439107143
Saskatchewan	78506.4	3168.9	9.750461538	4.801363636	3.1689	2.2635
Alberta	365191.1	3838.6	11.81107692	5.816060606	3.8386	2.741857143
British Columbia	225863.3	3899	11.99692308	5.907575758	3.899	2.785
Yukon	2650.3	4222	12.99076923	6.396969697	4.222	3.015714286
Northwest Territories	4656.5	3744	11.52	5.672727273	3.744	2.674285714
Nunavut	2350.9	2805	8.630769231	4.25	2.805	2.003571429
Texas	1781770.194	3083.6	9.488	4.672121212	3.0836	2.202571429
New York	1535564.161	599.6	1.844923077	0.908484848	0.5996	0.428285714
Vermont	32409.32894	172.6	0.531076923	0.261515152	0.1726	0.123285714
Pennsylvania	755902.3393	701.6	2.158769231	1.063030303	0.7016	0.501142857
Ohio	652916.6188	1108.5	3.410769231	1.679545455	1.1085	0.791785714
New Jersey	598898.127	703.4	2.164307692	1.065757576	0.7034	0.502428571
Connecticut	270207.2607	517.9	1.593538462	0.78469697	0.5179	0.369928571
Massachusetts	506801.9852	503.5	1.549230769	0.762878788	0.5035	0.359642857
Tennessee	329905.1122	1863.1	5.732615385	2.822878788	1.8631	1.330785714
California	2593340.192	4790.8	14.74092308	7.258787879	4.7908	3.422

Table 8.

Data (in 2014) with the integration of HSR.

Trade Partners	(Estimated) Total Trade with Trade Partners(in millions of $)	Time taken from the Great Montreal Area to the Trade Partners with HSR speed of (in h): tij
		325 km/h		660 km/h
		Adjusted Estimated Total Trade (in millions of $)	Difference compared to the one without HSR	Adjusted Estimated Total Trade (in millions of $)	Difference compared to the one without HSR
Newfoundland and Labrador	2199.042315	2255.127092	56.08477718	2434.622691	235.5803765
Prince Edward Island	359.853511	387.5649865	27.71147548	476.2537208	116.4002098
Nova Scotia	2300.813386	2361.742715	60.9293288	2556.742979	255.9295933
New Brunswick	3834.126706	3897.094962	62.9682563	4098.620679	264.4939731
Ontario	45392.70906	45609.30167	216.5926069	46302.4919	909.7828407
Manitoba	2362.663208	2429.778515	67.11530679	2644.57659	281.9133825
Saskatchewan	1622.714426	1690.619175	67.90474895	1907.943808	285.229382
Alberta	9045.255363	9169.48125	124.2258869	9567.057939	521.8025758
British Columbia	5831.875963	5932.940157	101.0641937	6256.389388	424.5134249
Yukon	50.04212888	65.25014327	15.20801439	113.9223818	63.88025296
Northwest Territories	173.1795022	193.0160353	19.83653313	256.5015403	83.32203814
Nunavut	188.3608222	204.2602757	15.89945352	255.1454192	66.78459703
Texas	6344.752878	6599.860046	255.1071675	7416.313568	1071.56069
New York	4540.279308	4890.845128	350.5658205	6012.807723	1472.528415
Vermont	2696.44319	2788.390284	91.94709419	3082.660844	386.2176536
Pennsylvania	2574.116512	2824.75727	250.6407582	3626.916348	1052.799836
Ohio	2363.794476	2575.653476	211.8590003	3253.694116	889.8996403
New Jersey	1906.52723	2133.583774	227.0565437	2860.26314	953.7359105
Connecticut	1733.10957	1907.372346	174.262776	2465.088771	731.9792008
Massachusetts	1659.213983	1887.92553	228.7115471	2619.901625	960.6876415
Tennessee	1582.727749	1723.513192	140.7854433	2174.087641	591.3598917
California	1550.523881	1820.311415	269.7875341	2683.748476	1133.224595
Total	100312.1252	103348.3894	3036.264267	113065.7513	12753.62612
Change in %		3.02681681		12.71394271

Table 9.

Data of great Montreal Area’s trade (in 2014) with the integration of HSR.

Thus, integrating in the formula, we obtain

Through simulation, we can see an integration of HSR of 325 km/h will bring $CAN 3036.264267 million of trade in addition (+3.02681681%); 660 km/h for $CAN 12753.62612 million of trade in addition (+12.71394271%).

6. Discussion

City sustainable logistics relates to many infrastructures as well as software like authority policy, IT applications, and incorporations of both hardware and software. When HSR transportation is put into daily running, it needs to research what will happen to help city sustainable logistics and what will make bad efforts to the circulation. Normally, because of the high speed of HSR, it will advance economic or GDP development in society. However, other transportation methods may decrease their activities or even fail to the new strong challenge coming from HSR, which could beat down those professional fields, for example, the short airlines, by which people would take several hours to board, travel, and leave the airport; if by HSR, 1 hour enough to pass 400 or 600 km. Then, we need to research more what is the reality of economic multi-process by the application of both HSR and traditional vehicles, and how much the degree of their effectiveness by the process. However, when we apply more data to make AI simulation, which also verifies the correctness of the previous logical process, one of the best solutions is:

$$\mathrm{B}=e^{a_0}={\mathrm{e}}^{0.01528038323988512}$$

$$a=a_1=0.19633948638164284$$

$$b=a_2=0.46481636346029886$$

$$c=a_3=0.2607251197660339$$

$${\mathrm{R}}^2=0.5407492632618118$$

7. Conclusion

Through the simulation and AI analysis with multivariable linear regression with MSE and gradient descent, based on the gravitational model for trade, we can conclude an integration of a high-speed transportation vehicle such as HSR will improve the volume of trade, thus positively influencing the economy of the Great Montreal Area.

Further improvements for a better estimated total volume after the integration of HSR can be considered.

1. Although this chapter considers the most recent public data as inputs that Statistics Canada can offer, these data are the ones from 7 to 10 years ago. Because of the economic changes that happened in the Great Montreal Area, more recent data can improve the results. In addition, if one can obtain of the repartition of trade of the Great Montreal Area and its trade partners (instead of the province of Quebec and the Great Montreal Area), more precise results can be obtained. Plus, while most data are based on 2014s, data used for the repartition of transportation modes to estimate the HSR speed is 2011s which is the newest data that can be found. Thus, data used in different year may also not depict completely the economic picture.

2. Inclusion of data of additional trade partners as inputs can improve the results and give insights for the differences between the estimated and actual trade volume, leading to elements as additional inputs that one can consider including in the linear regression.

3. Because of the complexity of the multivariable linear regression, further estimation techniques can be used such as interpolation or maximum likelihood estimation to double check the simulated results.

Appendix

See Tables A1–A4

Table A1.

Simulation results.

Table A2.

Simulation results.

Table A3.

Simulation results.

Table A4.

Simulation results.