- Email: [email protected]
Research on the waiting time of passengers and escalator energy consumption at the railway station
Energy and Buildings 41 (2009) 1313–1318
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Research on the waiting time of passengers and escalator energy consumption at the railway station Wei-wu Ma *, Xiao-yan Liu, Liqing Li, Xiangnan Shi, Chenn Q. Zhou School of Energy Science and Engineering, Central South University, Changsha 410083, China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 23 July 2009 Accepted 23 July 2009
Based on the Little Formula and the classical queuing model of multi-channel MjDjn, the relation of the average queue length, the maximum waiting time and the escalator service intensity were identified and the waiting time simulation model was established. With the passenger delivery data at A railway station in China and the probability distribution model of waiting time, a detailed analysis was made on the escalator allocation, power and energy consumption on holidays, ordinary working days and the largest-passengers-volume days; meanwhile, the fixed and variable energy consumption were compared and studied when the waiting time are 5, 10 and 30 s. The result shows that the waiting time settings affect the allocation and the energy consumption of the escalators and the fixed energy consumption takes 70%. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Waiting time Queuing model Little Formula Escalator allocation Fixed energy consumption Variable energy consumption
As a kind of important building transmission equipment, escalators are widely used in shopping centers, exhibition centers, railway stations, underground tunnels and other public places. Relative surveys show that escalators consume a large part of the total energy used at the railway stations [1]. Therefore, an important issue worth consideration when installing escalators is how to achieve energy-saving control and best cost performance in the provision of optimal services. The escalator allocation is a complex system project, which requires careful understanding of the building itself, performing environment, building’s use, size, height, passenger flow, etc. and the escalator transport system’s duality of randomicity, and regularity [2]. To optimize the allocations, it is of key importance to make proper analysis on the operating features and served subjects, to know the characteristics of the actual traffic flow and how it changes, to establish a reasonable mathematical model of the escalator to make a reasonable and effective analysis, which are the basis of designing high-quality escalator service system and energy conservation.
1. Calculation model for escalator waiting time 1.1. Queuing system operating features As for the queuing system of an escalator, according to its input and output flow characteristics; it can be defined as the simplest * Corresponding author. E-mail address: [email protected] (W.W. Ma). 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.07.027
flow [3], which has an important role in rule-out theory. According to the most important characteristics of the simplest flow, time intervals when passengers arrive at the escalator are subject to the negative exponential distribution; then the escalator service time should also be subject to negative exponential distribution [4]. As for parallel escalators, their operating times are independent. In addition, when the escalator is running at rated conditions, the number of passengers transmitted at every moment is the same, that is, fixed length service [5]. 1.2. Queue length theory In classical queuing theory there is a well-known formula—the Little Formula [6]. It states that under extreme equilibrium, there is a relation between the average number of passengers and their mean waiting time in this system as follows: L ¼ W l or W ¼
L
l
(1)
where the L is average queuing length, W is mean waiting time and l is system input rate. The importance of the formula Little is that in any queuing system and relevant input flow or output flow under extreme equilibrium state, the average number of passengers arrive and depart are the same within a time unit with the same flow intensity l [7]. Classic queuing model is shown using a number of symbols with a vertical bar among them and is defined as MjDjn [8]. As for the escalator system, M means the law of passengers’ arrival with negative exponential distribution; D means the probability
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1314
distribution of operating time [9], that is, fixed length service; n is the number of the escalators. According to Little Formula
r¼
l ; then l ¼ mr; L ¼ rmW; m
where r is service intensity, 0 < r < 1; m is input intensity for one escalator, persons/min; n is the number of operating escalators. Because the passengers within the system include those waiting in the queue and those being served: L ¼ L þ r ¼ rmW þ r ¼ rð1 þ mWÞ W¼
L
l
¼
rð1 þ mWÞ l
(2) (3)
Passengers’ arrival is subject to the simplest flow. When the operating time is set:
mW ¼
r 2ð1 rÞ
The queuing length for each escalator is L¼
r2 2ð1 rÞ
(4)
1.3. Escalator waiting time simulation system In this paper, the Little Formula explains the relation between the waiting time and the queue length; in addition, calculation was made for the queue length in single-channel system and multichannel system. In the simulation process, conditions that r < 1 and W is no more than the specified waiting time should be met, in order to ensure the calculated number of escalators is exactly the correct configuration [10]. Based on the configuration and formulas above, the simulation process is as follows: (1) enter the number of operating elevators, the transmission capacity of each escalator and to initialize the rate of passengers’ arrivals; (2) add 1 to l, namely, to increase the arrival rate; calculate the service intensity to make sure it is less than 1; (3) if r < 1, repeat increasing the arrival rate and to test whether the waiting time is less than t. If so, repeatedly increase the arrival rate; if not, it would take an additional escalator, and test r again, take a record of l the moment before, calculate W; (4) if r > 1, then the output l the moment before and calculate the W. When a single elevator cannot meet the delivery requirements resulting in longer queuing time, the majority of passengers will opt for the stairs instead of escalator service and at this time additional escalators are needed. Passengers will choose escalator first when they arrive. As is shown in Fig. 1, the number of passengers conveyed under different set waiting times can be calculated for the number of escalators used. Allocation of the escalators at a certain time should be considered with the most disadvantages. The largest number of passengers in a period of time is the boundary of the escalator allocation. From the data in Table 1, we can see that the longest waiting time is 14.33 s when the waiting time is 15–25 s. The actual transmission number is 43 persons/min, which is not obviously different from those when the waiting time is 10 and 30 s. Therefore, in order to make the delineation and analysis on the waiting time clear, in this paper discussions are carried when the waiting time are 5, 10 and 30 s.
Fig. 1. The simulation flow of the max waiting time.
In a certain period of time, when the waiting time is 5 s, the number of passengers entering the station is less than 39 and one escalator is able to meet the transportation requirements, for more than 39 people, it would take 2 escalators. But if the waiting time is 10 s, when the number of passengers entering the station is 39–42, one escalator is enough; for more than 42 people, it would take 2 escalators. If the waiting time is 30 s, one escalator is enough for 44 people, 2 escalators are need for more than 44 people, and so on. 2. Escalator energy consumption calculation model 2.1. Escalator parameters setting To simplify the calculation, the parameters of the escalator are defined as follows in Table 2. At the same time, the escalator steps size should meet the GB16899-1997 requirements; the horizontal step is four top steps and three bottom steps; guided trip distance is at least 1.2 m [11]; in the actual escalator system, since the passengers are evenly not packed, so the actual output rate is only 40% of the theoretical transmission capacity. 2.2. Escalator energy consumption calculation The total escalator energy consumption is the sum of the energy against friction between moving parts and the energy for the Table 1 The transportation of each escalator at different waiting time. Waiting time allowed, s
Transmitted passengers persons, min
Longest waiting time, s
5 10 15 20 25 30
39 42 43 43 43 44
4.33 9.33 14.33 14.33 14.33 29.33
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1315
Table 2 Technical parameters of escalator. Rated operating velocity
Angle
Nominal width
Theoretical transmitting capacity
Output rate
0.50 m/s
358
810 mm
6750 persons/h
45 persons/min
delivery of passengers, that is, fixed and variable energy consumption. Fixed energy consumption is the energy used when the escalator is empty, while the variable energy consumption exists when the escalators carry passengers. Passengers’ going upstairs results in the increase in energy consumption while going downstairs results in decrease. Fixed energy is used to overcome the friction between steps and escalator belt and the motor and useless work in the gear box, the amount of which depends on the height and mechanical design features of escalators. Three important indices for mechanical design include: the cascade chain and type of bearings used on wheels, oriented system type, the type of gear box. The design of the modern escalator usually employs ball bearings, chain orientation and involutes gear box [12]. Fixed energy consumption for this kind of escalators is as follows: y ¼ 0:9x 0:19
(5)
X Q f ¼y ðt nÞ
(6)
where y is fixed power, kW; x is enhanced height, which is also the height between escalator steps, 4.5–6.5 m; Qf is fixed energy consumption, kW h. Variable energy consumption depends mainly on the number of passengers, enhanced height, average mass of each passenger, how passengers move on the escalator, namely moving coefficient [13]: Qv ¼
mgH k 3600 1000
(7)
where Q v is variable energy consumption, kW h; m is the mass of passengers, kg; g is acceleration of gravity, 9.81 m/s2; k is passengers’ moving coefficient; t is escalators’ operating time, h; n is the number of escalators used. The mass of a person plus his/her luggage amounts to around 60 kg; moving coefficient is 0.7–1, which describes the proportion of moving passengers and their speed; the moving coefficient is 1 when passengers do not move. 3. Case analysis
station. Fitting formula multiplied by the number of passengers sent in each train is the volume of passenger entering the waiting room to wait for the trains; you can come to the moment of number of passengers trains; by summing the number of passengers each time for all trains, will stop the train waiting the moment by moment cumulative, the passengers distribution curve at different moments can be drawn. PowerBuilder9.0 and SQL Server2005 database are used to make calculation curves as follows. 3.2. Escalator allocation With the collected data in Fig. 2, the largest number of escalators are calculated when the passenger flow reaches the peak. The waiting time is set for 5 s, because in this case there is the highest requirement of the escalators. The arrival rate (l = 274 persons/min) when the traffic flow reaches the peak is used in formula (2) for the calculation; since n is no less than 6.09, n = 7 is used for the initial calculation: when n is 7, r = l/nm = 0.870; the average queue length is: L = r2/2(1 r) =2.911 persons; average waiting time is W = L/l = 4.46 s < 5 s. Thus, when the waiting time is 5 s, 7 upstairs escalators are needed for A railway station. According to field investigation, 8 escalators were set up with one escalator is downstairs, which is almost close to actual situation. 3.3. Escalator energy consumption analysis Based on formula (9) and collected data in Fig. 3, fixed and variable energy consumption can be obtained at different moments, in which the height between escalator layers is 5 m. In order to determine the fixed energy consumption and the number of operating escalators, the relationship of variable and fixed power consumption and the passengers’ flow, power analysis is used here. From the formula (6) and (7), we can see that the fixed
3.1. Probability distribution model of passengers’ arrival With the assistance of checking staff in the railway station, we took a record of the tickets information and arrival time in 5 July 2008 and obtained exactly how long in advance they arrive at the waiting rooms. By the statistics over 2340 effective samples, we obtained the proportion of passengers waiting at different time. Gauss model in MATLAB is used to fit the investigated and statistical data. Fitting curve formula is obtained as follows: f ðxÞ ¼ 0:001363eðx34:45=2:03Þ þ 0:01035eðx39:94=14:12Þ
2
0:0006494eðx27:2=5:496Þ 0:004484eðx45:89=10:29Þ
2
2
þ 0:003125eðx30:46=25Þ 0:00176eðx40:89=6:652Þ
þ 0:002001eðx54:09=101:9Þ þ 0:005905eðx43:26=40:76Þ
2
(9)
where x is passengers’ waiting time, minutes; f(x) is the proportion of passengers who wait for x minutes. We chose ordinary working days, holidays and the largestpassengers-volume days to carry out the research at A railway
Fig. 2. Passenger arrival curve of three kinds of working day at A railway station.
1316
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
Fig. 3. The fixed and variable power of three kinds of working days at waiting time of 5 s.
power is only related to the number of operating escalators, while variable power is up to the passengers flow, as is shown in Fig. 3. In this figure, the grades of fixed power indicate the number of used escalators. When the variable power increases, the fixed power and the number of used escalators increase; when variable power decreases, the fixed power and the number of used escalators then decrease. The most escalators are used when the variable power is at peak. We can find that the changes of fixed power are closely related to variable power. Among the figures, Fig. 3(a) has frequent changes of fixed and variable power as a result of large passengers flow, while Fig. 3(c) is relatively more stable. From Fig. 3, we find that the fixed escalator power is only related to the number of escalators used and has cascade change accordingly; variable power is related to the number of passengers on the escalators at a certain moment and changes almost the same as how the population changes. Fixed energy consumption is generated when the load is free and has dominant position in total energy consumption. Variable power accounts for about 30% of total energy consumption. Thus, appropriate reduction in the number of escalators used can make a great contribution to energy conservation. Since the passengers’ flow is very small at the early morning, there is little difference for the escalator power and number of escalators used when the waiting time is set as 5, 10 or 30 s. To highlight the impact of waiting time on power and the number of
escalators used, the time period of 6:50–22:10 is taken for analysis, as is shown in Fig. 4. In the period of 10:45–13:17, when the waiting time is 5 and 30 s, the number of escalators used is 7; as for 10 s, the number of escalators used changes for four times and at this time there is an obvious energy-saving effect. In the period of 13:50–14:25, when waiting time is 5 and 30 s, four escalators are needed; 3 are needed for 10 s. In the period of 15:56–16:18 as shown in Fig. 2, the number of passengers reaches the peak of the day and seven escalators are needed for whatever waiting time. In the period of 17:54–18:25, when the waiting time is 5 s and 10 s, to reopen 7 escalators is needed; when the waiting time is 30 s, to open 6 escalators can meet the requirement. The shorter the passengers’ waiting time is, the higher demand for good service is. To reduce the waiting time to 0 leads to too many used escalators and too big power. Long waiting time results in passengers’ discomfort. However, if the waiting time is too long, then the majority of passengers will give up the escalator service and choose the stairs to go to the upper waiting rooms. In this case, the escalators fail to work and lead to waste of energy. Therefore, an appropriate set waiting time and number of escalators will ensure high-quality services and energy conservation. As is shown in Fig. 4, the number of escalators is regulated by the passengers. Then the fixed escalator energy consumption changes linearly with the number of escalators while the variable energy consumption changes with the number of passengers. The
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1317
of the loss of self-work and the loss of resistance work; variable energy consumption changes with the amount of passengers on the escalators. From the chart it is known: (1) Among all the energy consumption parts, the resistance accounts for the largest proportion. Different energy consumption parts are shown in Table 3.
Fig. 4. The fixed power on the largest passenger volume day of different waiting time.
fixed and variable escalator energy consumption (when the waiting time is 5 s) are demonstrated in Fig. 5. Escalator energy consumption consists of the fixed and variable energy consumption: fixed escalator energy consumption consists
The main impact on the escalators’ energy consumption comes from fixed energy consumption; during operation, the influencing factor of variable energy consumption is the number of passengers to take the escalators; variable energy consumption accounts for about 30% of total energy consumption while 70% for variable energy consumption. Change of fixed energy exerts a very heavy impact on the changes of total energy consumption. In order to achieve the energy-saving effect, fixed energy consumption should be controlled, that is, to control the number of used escalators. (2) The adjustment of escalator numbers in different working days are as follows: 17 in ordinary working days, 21 in holidays, 35 in largest-passengers-volume days. The greater the passengers’ flow, the more frequent changes of the escalator. The main task of this paper is to examine the relationship between the waiting time and the escalator energy consumption. Figs. 3–5 show detailed analysis on the escalator allocation, the
Fig. 5. The result of subentry energy consumption of the waiting time of 5 s.
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1318
Table 3 The proportion of subentry energy consumption of the waiting time of 5 s.
Ordinary working days Holidays Largest-passengersvolume days
Fixed energy consumption, kW h
Variable energy consumption, kW h
73.0% 73.4% 72.2%
27.0% 26.6% 27.8%
As it shown in Table 4, energy consumption can be saved by 5.18% and 6.23% when the waiting time is 10 and 30 s compared with 5 s. The shorter the waiting time is, the more comfortable the passengers feel. It can be ensured that passengers take the escalator at their arrival, yet at the same time the energy consumption is greater. Longer waiting time is relatively more energy-saving. 4. Conclusions
Fig. 6. The energy consumption of escalator at different waiting time.
(a) If the waiting time is set as 5 s, the maximum waiting time is 4.33 s, and a single escalator transmission capacity is 39 persons/min; if the waiting time is set as 10 and 30 s, the maximum waiting time is 9.33 and 29.33 s, and a single escalator transmission capacity is 42 and 44 persons/min. (b) Variable power accounts for about 30% of total energy consumption and fixed power accounts for about 70% with dominant position. (c) Energy consumption can be saved by 5.18% and 6.23% when the waiting time is 10 and 30 s compared with 5 s. The shorter the waiting time is, the higher demand for service quality is, which yet leads to too many escalators and great energy consumption; the more passengers are, the bigger the energy-saving potential is. (d) The highest energy consumption is 562.6 kW h in the largestpassengers-volume days when the waiting time is 5 s; the lowest energy consumption is 311.2 kW h in ordinary working days when the waiting time is 30 s. References
Table 4 The energy-saving percentage at waiting time of 10 and 30 s compared to 5 s.
10 s 30 s
Ordinary working days
Holidays
Largest-passengersvolume days
2.61% 5.06%
5.18% 6.23%
3.15% 6.51%
power and different energy consumption parts. The escalator energy consumptions with different waiting times in three kinds of working days are shown as in Fig. 6. As for the same waiting time in different working days: the more passengers are, the greater the energy consumption is; as for different waiting times on the same day: the shorter the waiting time is, the greater the energy consumption is. Among working days throughout the year, the highest energy consumption is 562.6 kW h, when the waiting time is 5 in largest-passengersvolume days. The lowest energy consumption is 311.2 kW h when the waiting time is 30 s in ordinary working days.
[1] J.Y. Song, The Study of Elevator Optimizing Configuration Method Based on Markov Network Queuing Theory, Electrical Engineering & Automation, Tianjin, 2003, pp. 36–58. [2] C.L. Lu, The Queuing, Beijing University of Posts and Telecommunications Press, Beijing, 1994, pp. 43–83. [3] G.H. Xu, Random Service System, Science Press, Beijing, 1980, pp. 7–18. [4] Z.Q. Yu, X.L. Ma, Random process Theory and the Application, Tianjin Science and Technology Press, Tianjin, 1996, pp. 400–404. [5] W.X. Yang, A Traffic Model Based on Markov Process in Circuit-switched Networks, Journal of Yunnan University 20 (1) (1998) 27–30. [6] G.C. Barney, Up-peak, down-peak and interfloor performance, Elevator World 44 (4) (1999) 100–103. [7] A.T.P. So, H.S. Kuok, S.K. Liu, W.S. Chan, New developments in elevator traffic analysis. Elevator technology 5, IAEE (1993) 212–221. [8] F.S. Lu, The Queuing Theory and the Application, Hunan Science and Technology Press, Hunan, 1983, pp. 240–259. [9] R.H. Sun, J.P. Li, The Queuing Bases, Science press, 2002, pp. 44–59. [10] Y.F. Li, Verification, validation and accreditation on digital simulation model, Journal of Central South University: Science and Technology 35 (2) (2004) 273–276. [11] W. Wang, J.X. Lu, Calculation on braking ability of escalator and automatic footway, Journal of Machine Design 23 (5) (2006) 18–19. [12] L. Al-Sharif, General theory of escalator energy consumption with calculations and examples, Elevator World 46 (5) (1998) 74–79. [13] W.Q. Xing, The general theory of escalators consumption calculation and example analysis, China Elevator 11 (9) (2000) 40–44.
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Research on the waiting time of passengers and escalator energy consumption at the railway station Wei-wu Ma *, Xiao-yan Liu, Liqing Li, Xiangnan Shi, Chenn Q. Zhou School of Energy Science and Engineering, Central South University, Changsha 410083, China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 23 July 2009 Accepted 23 July 2009
Based on the Little Formula and the classical queuing model of multi-channel MjDjn, the relation of the average queue length, the maximum waiting time and the escalator service intensity were identified and the waiting time simulation model was established. With the passenger delivery data at A railway station in China and the probability distribution model of waiting time, a detailed analysis was made on the escalator allocation, power and energy consumption on holidays, ordinary working days and the largest-passengers-volume days; meanwhile, the fixed and variable energy consumption were compared and studied when the waiting time are 5, 10 and 30 s. The result shows that the waiting time settings affect the allocation and the energy consumption of the escalators and the fixed energy consumption takes 70%. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Waiting time Queuing model Little Formula Escalator allocation Fixed energy consumption Variable energy consumption
As a kind of important building transmission equipment, escalators are widely used in shopping centers, exhibition centers, railway stations, underground tunnels and other public places. Relative surveys show that escalators consume a large part of the total energy used at the railway stations [1]. Therefore, an important issue worth consideration when installing escalators is how to achieve energy-saving control and best cost performance in the provision of optimal services. The escalator allocation is a complex system project, which requires careful understanding of the building itself, performing environment, building’s use, size, height, passenger flow, etc. and the escalator transport system’s duality of randomicity, and regularity [2]. To optimize the allocations, it is of key importance to make proper analysis on the operating features and served subjects, to know the characteristics of the actual traffic flow and how it changes, to establish a reasonable mathematical model of the escalator to make a reasonable and effective analysis, which are the basis of designing high-quality escalator service system and energy conservation.
1. Calculation model for escalator waiting time 1.1. Queuing system operating features As for the queuing system of an escalator, according to its input and output flow characteristics; it can be defined as the simplest * Corresponding author. E-mail address: [email protected] (W.W. Ma). 0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2009.07.027
flow [3], which has an important role in rule-out theory. According to the most important characteristics of the simplest flow, time intervals when passengers arrive at the escalator are subject to the negative exponential distribution; then the escalator service time should also be subject to negative exponential distribution [4]. As for parallel escalators, their operating times are independent. In addition, when the escalator is running at rated conditions, the number of passengers transmitted at every moment is the same, that is, fixed length service [5]. 1.2. Queue length theory In classical queuing theory there is a well-known formula—the Little Formula [6]. It states that under extreme equilibrium, there is a relation between the average number of passengers and their mean waiting time in this system as follows: L ¼ W l or W ¼
L
l
(1)
where the L is average queuing length, W is mean waiting time and l is system input rate. The importance of the formula Little is that in any queuing system and relevant input flow or output flow under extreme equilibrium state, the average number of passengers arrive and depart are the same within a time unit with the same flow intensity l [7]. Classic queuing model is shown using a number of symbols with a vertical bar among them and is defined as MjDjn [8]. As for the escalator system, M means the law of passengers’ arrival with negative exponential distribution; D means the probability
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1314
distribution of operating time [9], that is, fixed length service; n is the number of the escalators. According to Little Formula
r¼
l ; then l ¼ mr; L ¼ rmW; m
where r is service intensity, 0 < r < 1; m is input intensity for one escalator, persons/min; n is the number of operating escalators. Because the passengers within the system include those waiting in the queue and those being served: L ¼ L þ r ¼ rmW þ r ¼ rð1 þ mWÞ W¼
L
l
¼
rð1 þ mWÞ l
(2) (3)
Passengers’ arrival is subject to the simplest flow. When the operating time is set:
mW ¼
r 2ð1 rÞ
The queuing length for each escalator is L¼
r2 2ð1 rÞ
(4)
1.3. Escalator waiting time simulation system In this paper, the Little Formula explains the relation between the waiting time and the queue length; in addition, calculation was made for the queue length in single-channel system and multichannel system. In the simulation process, conditions that r < 1 and W is no more than the specified waiting time should be met, in order to ensure the calculated number of escalators is exactly the correct configuration [10]. Based on the configuration and formulas above, the simulation process is as follows: (1) enter the number of operating elevators, the transmission capacity of each escalator and to initialize the rate of passengers’ arrivals; (2) add 1 to l, namely, to increase the arrival rate; calculate the service intensity to make sure it is less than 1; (3) if r < 1, repeat increasing the arrival rate and to test whether the waiting time is less than t. If so, repeatedly increase the arrival rate; if not, it would take an additional escalator, and test r again, take a record of l the moment before, calculate W; (4) if r > 1, then the output l the moment before and calculate the W. When a single elevator cannot meet the delivery requirements resulting in longer queuing time, the majority of passengers will opt for the stairs instead of escalator service and at this time additional escalators are needed. Passengers will choose escalator first when they arrive. As is shown in Fig. 1, the number of passengers conveyed under different set waiting times can be calculated for the number of escalators used. Allocation of the escalators at a certain time should be considered with the most disadvantages. The largest number of passengers in a period of time is the boundary of the escalator allocation. From the data in Table 1, we can see that the longest waiting time is 14.33 s when the waiting time is 15–25 s. The actual transmission number is 43 persons/min, which is not obviously different from those when the waiting time is 10 and 30 s. Therefore, in order to make the delineation and analysis on the waiting time clear, in this paper discussions are carried when the waiting time are 5, 10 and 30 s.
Fig. 1. The simulation flow of the max waiting time.
In a certain period of time, when the waiting time is 5 s, the number of passengers entering the station is less than 39 and one escalator is able to meet the transportation requirements, for more than 39 people, it would take 2 escalators. But if the waiting time is 10 s, when the number of passengers entering the station is 39–42, one escalator is enough; for more than 42 people, it would take 2 escalators. If the waiting time is 30 s, one escalator is enough for 44 people, 2 escalators are need for more than 44 people, and so on. 2. Escalator energy consumption calculation model 2.1. Escalator parameters setting To simplify the calculation, the parameters of the escalator are defined as follows in Table 2. At the same time, the escalator steps size should meet the GB16899-1997 requirements; the horizontal step is four top steps and three bottom steps; guided trip distance is at least 1.2 m [11]; in the actual escalator system, since the passengers are evenly not packed, so the actual output rate is only 40% of the theoretical transmission capacity. 2.2. Escalator energy consumption calculation The total escalator energy consumption is the sum of the energy against friction between moving parts and the energy for the Table 1 The transportation of each escalator at different waiting time. Waiting time allowed, s
Transmitted passengers persons, min
Longest waiting time, s
5 10 15 20 25 30
39 42 43 43 43 44
4.33 9.33 14.33 14.33 14.33 29.33
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1315
Table 2 Technical parameters of escalator. Rated operating velocity
Angle
Nominal width
Theoretical transmitting capacity
Output rate
0.50 m/s
358
810 mm
6750 persons/h
45 persons/min
delivery of passengers, that is, fixed and variable energy consumption. Fixed energy consumption is the energy used when the escalator is empty, while the variable energy consumption exists when the escalators carry passengers. Passengers’ going upstairs results in the increase in energy consumption while going downstairs results in decrease. Fixed energy is used to overcome the friction between steps and escalator belt and the motor and useless work in the gear box, the amount of which depends on the height and mechanical design features of escalators. Three important indices for mechanical design include: the cascade chain and type of bearings used on wheels, oriented system type, the type of gear box. The design of the modern escalator usually employs ball bearings, chain orientation and involutes gear box [12]. Fixed energy consumption for this kind of escalators is as follows: y ¼ 0:9x 0:19
(5)
X Q f ¼y ðt nÞ
(6)
where y is fixed power, kW; x is enhanced height, which is also the height between escalator steps, 4.5–6.5 m; Qf is fixed energy consumption, kW h. Variable energy consumption depends mainly on the number of passengers, enhanced height, average mass of each passenger, how passengers move on the escalator, namely moving coefficient [13]: Qv ¼
mgH k 3600 1000
(7)
where Q v is variable energy consumption, kW h; m is the mass of passengers, kg; g is acceleration of gravity, 9.81 m/s2; k is passengers’ moving coefficient; t is escalators’ operating time, h; n is the number of escalators used. The mass of a person plus his/her luggage amounts to around 60 kg; moving coefficient is 0.7–1, which describes the proportion of moving passengers and their speed; the moving coefficient is 1 when passengers do not move. 3. Case analysis
station. Fitting formula multiplied by the number of passengers sent in each train is the volume of passenger entering the waiting room to wait for the trains; you can come to the moment of number of passengers trains; by summing the number of passengers each time for all trains, will stop the train waiting the moment by moment cumulative, the passengers distribution curve at different moments can be drawn. PowerBuilder9.0 and SQL Server2005 database are used to make calculation curves as follows. 3.2. Escalator allocation With the collected data in Fig. 2, the largest number of escalators are calculated when the passenger flow reaches the peak. The waiting time is set for 5 s, because in this case there is the highest requirement of the escalators. The arrival rate (l = 274 persons/min) when the traffic flow reaches the peak is used in formula (2) for the calculation; since n is no less than 6.09, n = 7 is used for the initial calculation: when n is 7, r = l/nm = 0.870; the average queue length is: L = r2/2(1 r) =2.911 persons; average waiting time is W = L/l = 4.46 s < 5 s. Thus, when the waiting time is 5 s, 7 upstairs escalators are needed for A railway station. According to field investigation, 8 escalators were set up with one escalator is downstairs, which is almost close to actual situation. 3.3. Escalator energy consumption analysis Based on formula (9) and collected data in Fig. 3, fixed and variable energy consumption can be obtained at different moments, in which the height between escalator layers is 5 m. In order to determine the fixed energy consumption and the number of operating escalators, the relationship of variable and fixed power consumption and the passengers’ flow, power analysis is used here. From the formula (6) and (7), we can see that the fixed
3.1. Probability distribution model of passengers’ arrival With the assistance of checking staff in the railway station, we took a record of the tickets information and arrival time in 5 July 2008 and obtained exactly how long in advance they arrive at the waiting rooms. By the statistics over 2340 effective samples, we obtained the proportion of passengers waiting at different time. Gauss model in MATLAB is used to fit the investigated and statistical data. Fitting curve formula is obtained as follows: f ðxÞ ¼ 0:001363eðx34:45=2:03Þ þ 0:01035eðx39:94=14:12Þ
2
0:0006494eðx27:2=5:496Þ 0:004484eðx45:89=10:29Þ
2
2
þ 0:003125eðx30:46=25Þ 0:00176eðx40:89=6:652Þ
þ 0:002001eðx54:09=101:9Þ þ 0:005905eðx43:26=40:76Þ
2
(9)
where x is passengers’ waiting time, minutes; f(x) is the proportion of passengers who wait for x minutes. We chose ordinary working days, holidays and the largestpassengers-volume days to carry out the research at A railway
Fig. 2. Passenger arrival curve of three kinds of working day at A railway station.
1316
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
Fig. 3. The fixed and variable power of three kinds of working days at waiting time of 5 s.
power is only related to the number of operating escalators, while variable power is up to the passengers flow, as is shown in Fig. 3. In this figure, the grades of fixed power indicate the number of used escalators. When the variable power increases, the fixed power and the number of used escalators increase; when variable power decreases, the fixed power and the number of used escalators then decrease. The most escalators are used when the variable power is at peak. We can find that the changes of fixed power are closely related to variable power. Among the figures, Fig. 3(a) has frequent changes of fixed and variable power as a result of large passengers flow, while Fig. 3(c) is relatively more stable. From Fig. 3, we find that the fixed escalator power is only related to the number of escalators used and has cascade change accordingly; variable power is related to the number of passengers on the escalators at a certain moment and changes almost the same as how the population changes. Fixed energy consumption is generated when the load is free and has dominant position in total energy consumption. Variable power accounts for about 30% of total energy consumption. Thus, appropriate reduction in the number of escalators used can make a great contribution to energy conservation. Since the passengers’ flow is very small at the early morning, there is little difference for the escalator power and number of escalators used when the waiting time is set as 5, 10 or 30 s. To highlight the impact of waiting time on power and the number of
escalators used, the time period of 6:50–22:10 is taken for analysis, as is shown in Fig. 4. In the period of 10:45–13:17, when the waiting time is 5 and 30 s, the number of escalators used is 7; as for 10 s, the number of escalators used changes for four times and at this time there is an obvious energy-saving effect. In the period of 13:50–14:25, when waiting time is 5 and 30 s, four escalators are needed; 3 are needed for 10 s. In the period of 15:56–16:18 as shown in Fig. 2, the number of passengers reaches the peak of the day and seven escalators are needed for whatever waiting time. In the period of 17:54–18:25, when the waiting time is 5 s and 10 s, to reopen 7 escalators is needed; when the waiting time is 30 s, to open 6 escalators can meet the requirement. The shorter the passengers’ waiting time is, the higher demand for good service is. To reduce the waiting time to 0 leads to too many used escalators and too big power. Long waiting time results in passengers’ discomfort. However, if the waiting time is too long, then the majority of passengers will give up the escalator service and choose the stairs to go to the upper waiting rooms. In this case, the escalators fail to work and lead to waste of energy. Therefore, an appropriate set waiting time and number of escalators will ensure high-quality services and energy conservation. As is shown in Fig. 4, the number of escalators is regulated by the passengers. Then the fixed escalator energy consumption changes linearly with the number of escalators while the variable energy consumption changes with the number of passengers. The
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1317
of the loss of self-work and the loss of resistance work; variable energy consumption changes with the amount of passengers on the escalators. From the chart it is known: (1) Among all the energy consumption parts, the resistance accounts for the largest proportion. Different energy consumption parts are shown in Table 3.
Fig. 4. The fixed power on the largest passenger volume day of different waiting time.
fixed and variable escalator energy consumption (when the waiting time is 5 s) are demonstrated in Fig. 5. Escalator energy consumption consists of the fixed and variable energy consumption: fixed escalator energy consumption consists
The main impact on the escalators’ energy consumption comes from fixed energy consumption; during operation, the influencing factor of variable energy consumption is the number of passengers to take the escalators; variable energy consumption accounts for about 30% of total energy consumption while 70% for variable energy consumption. Change of fixed energy exerts a very heavy impact on the changes of total energy consumption. In order to achieve the energy-saving effect, fixed energy consumption should be controlled, that is, to control the number of used escalators. (2) The adjustment of escalator numbers in different working days are as follows: 17 in ordinary working days, 21 in holidays, 35 in largest-passengers-volume days. The greater the passengers’ flow, the more frequent changes of the escalator. The main task of this paper is to examine the relationship between the waiting time and the escalator energy consumption. Figs. 3–5 show detailed analysis on the escalator allocation, the
Fig. 5. The result of subentry energy consumption of the waiting time of 5 s.
W.-w. Ma et al. / Energy and Buildings 41 (2009) 1313–1318
1318
Table 3 The proportion of subentry energy consumption of the waiting time of 5 s.
Ordinary working days Holidays Largest-passengersvolume days
Fixed energy consumption, kW h
Variable energy consumption, kW h
73.0% 73.4% 72.2%
27.0% 26.6% 27.8%
As it shown in Table 4, energy consumption can be saved by 5.18% and 6.23% when the waiting time is 10 and 30 s compared with 5 s. The shorter the waiting time is, the more comfortable the passengers feel. It can be ensured that passengers take the escalator at their arrival, yet at the same time the energy consumption is greater. Longer waiting time is relatively more energy-saving. 4. Conclusions
Fig. 6. The energy consumption of escalator at different waiting time.
(a) If the waiting time is set as 5 s, the maximum waiting time is 4.33 s, and a single escalator transmission capacity is 39 persons/min; if the waiting time is set as 10 and 30 s, the maximum waiting time is 9.33 and 29.33 s, and a single escalator transmission capacity is 42 and 44 persons/min. (b) Variable power accounts for about 30% of total energy consumption and fixed power accounts for about 70% with dominant position. (c) Energy consumption can be saved by 5.18% and 6.23% when the waiting time is 10 and 30 s compared with 5 s. The shorter the waiting time is, the higher demand for service quality is, which yet leads to too many escalators and great energy consumption; the more passengers are, the bigger the energy-saving potential is. (d) The highest energy consumption is 562.6 kW h in the largestpassengers-volume days when the waiting time is 5 s; the lowest energy consumption is 311.2 kW h in ordinary working days when the waiting time is 30 s. References
Table 4 The energy-saving percentage at waiting time of 10 and 30 s compared to 5 s.
10 s 30 s
Ordinary working days
Holidays
Largest-passengersvolume days
2.61% 5.06%
5.18% 6.23%
3.15% 6.51%
power and different energy consumption parts. The escalator energy consumptions with different waiting times in three kinds of working days are shown as in Fig. 6. As for the same waiting time in different working days: the more passengers are, the greater the energy consumption is; as for different waiting times on the same day: the shorter the waiting time is, the greater the energy consumption is. Among working days throughout the year, the highest energy consumption is 562.6 kW h, when the waiting time is 5 in largest-passengersvolume days. The lowest energy consumption is 311.2 kW h when the waiting time is 30 s in ordinary working days.
[1] J.Y. Song, The Study of Elevator Optimizing Configuration Method Based on Markov Network Queuing Theory, Electrical Engineering & Automation, Tianjin, 2003, pp. 36–58. [2] C.L. Lu, The Queuing, Beijing University of Posts and Telecommunications Press, Beijing, 1994, pp. 43–83. [3] G.H. Xu, Random Service System, Science Press, Beijing, 1980, pp. 7–18. [4] Z.Q. Yu, X.L. Ma, Random process Theory and the Application, Tianjin Science and Technology Press, Tianjin, 1996, pp. 400–404. [5] W.X. Yang, A Traffic Model Based on Markov Process in Circuit-switched Networks, Journal of Yunnan University 20 (1) (1998) 27–30. [6] G.C. Barney, Up-peak, down-peak and interfloor performance, Elevator World 44 (4) (1999) 100–103. [7] A.T.P. So, H.S. Kuok, S.K. Liu, W.S. Chan, New developments in elevator traffic analysis. Elevator technology 5, IAEE (1993) 212–221. [8] F.S. Lu, The Queuing Theory and the Application, Hunan Science and Technology Press, Hunan, 1983, pp. 240–259. [9] R.H. Sun, J.P. Li, The Queuing Bases, Science press, 2002, pp. 44–59. [10] Y.F. Li, Verification, validation and accreditation on digital simulation model, Journal of Central South University: Science and Technology 35 (2) (2004) 273–276. [11] W. Wang, J.X. Lu, Calculation on braking ability of escalator and automatic footway, Journal of Machine Design 23 (5) (2006) 18–19. [12] L. Al-Sharif, General theory of escalator energy consumption with calculations and examples, Elevator World 46 (5) (1998) 74–79. [13] W.Q. Xing, The general theory of escalators consumption calculation and example analysis, China Elevator 11 (9) (2000) 40–44.