key: cord-0646595-835m8mp0 authors: Yiting, Hu; Xiling, Luo; Dongmei, Bai title: Passenger Congestion Alleviation in Large Hub Airport Ground Access System Based on Queueing Theory date: 2021-08-26 journal: nan DOI: nan sha: 6313fc0e2738d5eb1c60c5b86b5441a3408e67d5 doc_id: 646595 cord_uid: 835m8mp0 Passenger queue congestion in the airport public transport system would cause poor travel experience and unexpected time cost. To solve this problem, we propose a hybrid congestion alleviation strategy based on transport capacity adjustment and passenger guidance in this paper. Firstly, we develop queueing models for three common ground access modes of airports, taxi, bus and subway. Then, we develop the method of successive weighted averages (MSWA) in the queueing system to optimize the passenger share rates among different airport ground access modes based on minimum queueing time. Finally, we present the complete hybrid passenger congestion alleviation strategy consists of adjusting the taxi arrival rate and bus service rate, and generating a guidance on passenger access mode choices, which can alleviate the passenger queue congestion in practical application based on obtained optimal passenger share rates. In the numerical experiments, we set two groups of parameters under the normal situation and the COVID-19 epidemic situation. The numerical results show that our strategy can alleviate the queue congestion and improve the evacuation efficiency effectively in both two backgrounds. According to data from Civil Aviation Administration of China, the total volume of passengers of Chinese civil airports in 2018 and 2019 were 1.26 billion and 1.35 billion respectively, and increased by 10.2 percent and 6.5 percent compared with the last year. Because of the widespread of COVID-19 pandemic in 2020, the volume of passengers transported by airports in China was only 0.86 billion in 2020, decreased by 36.6 percent compared with 2019. According to the latest news from CAAC, the volume of domestic passenger of Chinese civil airports in June 2021 has exceeded that of the same period in 2019, which shows a good recovery momentum. At present, with the spread of COVID-19 in global area, the airport passenger flows has significantly reduced compared with which before the epidemic. But after the epidemic being under control, the passenger flows will recover sharply. The large amount of airport passenger flows leads to a growth of travel demand on ground traffic around large airport hubs other than air traffic. As a result, in addition to the widely studied air traffic congestion (Pita, Barnhart, and Antunes 2013; Lee, Marla, and Jacquillat 2020) , the congestion on the ground transport system in the airport, consists of multiple modes of transport vehicles, appears more frequent. According to the statistical data from investigation report on composition and behavior habits of passengers in Beijing Capital International Airport in 2019, when passengers leave the airport, 33.1% took taxi, 16.3% took airport bus, 15.9% took subway and the rest took private car, online car-hailing and so on. For private vehicles, congestion usually appears in the road network around the airport. For public transports like taxi and bus, congestion not only appears in the road network but also found in the queueing process of waiting for vehicles or tickets. In the taxi stand of BCIA, according to field researches, the longest passenger queue length can be over 200 and passenger waiting time may reach 30 minutes in a workday. This can be much worse during the weekends and holidays, and results in poor travel experience and additional unexpected time cost. Queue congestion can affect passenger experience more than road congestion, so this paper focuses on queue congestion in public ground transport system to optimize it. In conclude, the queue congestion is mainly caused by two reasons. The first is that the capacity of transportation and service can not meet the needs of passengers and the second is that passengers can not grasp the real-time queueing information and choose the least queue-time mode. To solve this problem, improving the transport capacity is the first coming thought, which increase the cost at the same time, so transport capacity can not increase indefinitely. Therefore, when the transport capacity can not meet the demand after improved to its maximum, airport managers should consider guiding passengers to choose the appropriate ground access mode to make the best utility of the current transport capacity. When choosing airport ground access modes, passengers consider costs, travel time, comfort and other factors that are easy to observe or query but do not consider the queueing time that is inconvenient to know in airports, which may cause an inappropriate choice and lead to congestion. On the other hand, when a passenger arrives at the ride point of an access mode and finds it need a long time for queue, he may prefer to stay and spend time on queueing rather than walk a long distance to change another access mode, which may also form the congestion. Consequently, a guidance on passenger ground access mode choices is needed. To obtain the best ground access mode choice, we consider the multinomial logit (MNL) model. In queueing system, the access mode queueing time highly related to the passenger arrival rate is continually changing, while the costs, comfort and other transport utilities passengers may consider are relatively fixed. Therefore, it is necessary to balance the static transport utility and the dynamic queueing time in MNL for a proper choice. The balancing process is similar to the balance between minimum travel path and travel time in the problem of road traffic flow assignment, which are usually solved by Method of Successive Average (MSA) (Bar-Gera and Boyce 2006; Pineda et al. 2016; Delle Site 2018) and method of successive weighted average (MSWA) (Liu, He, and He 2009; Wang et al. 2020) . MSWA has higher efficiency and better convergence than MSA due to the development on the predetermined sequence of step sizes. Therefore, we extend MSWA to solve the passenger flow assignment here for the appropriate passenger choice guidance. In order to implement the transport capacity adjustment and passenger guidance method to deal with airport ground public transport queue congestion, this paper proposes a hybrid congestion alleviation algorithm combining transport capacity adjustment and passenger choice guidance. Firstly, we develop three queueing models of common ground access modes based on queueing theory in which the process of taking taxi is modeled by double-ended queueing model, the process of taking bus is modeled by a series of classical M/M/c/K queueing model and Min(N,T) renewal process and the process of taking subway is modeled by series connection of two M/M/c/K queueing models. The corresponding transition queueing time is obtained and taken as improvement target. Secondly, in the proposed hybrid methods, we change the service rate in ground access system to adjust the transport capacity, and optimize the passenger share rate by extended MSWA to implement the passenger guidance. Finally, in order to reflect the importance of the airport in the epidemic prevention and control, and the applicability of our proposed hybrid methods in different situations, based on the background of COVID-19, we consider some control measures taken for epidemic and set two groups of parameters according to epidemic background and normality in the numerical simulation. The results show that our proposed methods can effectively reduce the average passenger queueing time of the ground access system in these two situations. The main contributions of this paper can be summarized as follows: • We propose a hybrid method for solve the passenger queue congestion problem, which can perform transport capacity adjustment and passenger guidance simultaneously to realize the coordinated operation of passengers and transport, and evacuate the queue congestion in the ground public transport system. The method can accord with the small passenger flow situation under epidemic background and the large passenger flow situation under normality, which fit the daily management. • Taking taxi, bus and subway as examples, we propose basic queueing models of different airport ground access modes. In this model, transport capacity adjustment can be implemented by adjusting the ticket counters for bus ticket and taxi arrival rate, and passenger guidance can be realized by adjusting the passenger share rate among different airport access modes. • A method of successive weighted average is developed in queueing system to calculate the optimal passenger share rate for accurate passenger guidance. The MSWA has a fast computation speed, can converge quickly, and can consider dynamic part and static part of transport utilities simultaneously for a rational and appropriate passenger share rate to alleviate the passenger queue congestion. The rest of this paper is organized as follows. In Section 2, we present an overview of related research. In Section 3, we develop mathematical models of service and queueing process of taxi, bus and subway. Section 4 calculates the instantaneous expected queue length and time, sets the passenger waiting area size. Section 5 presents detailed algorithms of transport capacity adjustment strategy, the optimization of passenger share rates and the complete congestion alleviation strategy combining them. Several numerical examples are presented in Section 6 to demonstrate the performance on solving queuing system congestion problem and some differences between epidemic background and normality. Finally, some conclusions are drawn in Section 7. Scholars have made some attempts to alleviate the congestion in the queueing process of airport hub ground transport system. For the taxi queue congestion, Shi and Lian (2016) use a double-ended queueing model to simulate the taxi taking process in large airport hub, the queueing interests in the double-ended queueing model were discussed under observable and unobservable cases with two types of customer behaviors (selfishly optimal and socially optimal). Wang, Wang, and Zhang (2017) considered the customer behaviors in double-ended queueing model with the gate policy to balance the queueing time costs and operating costs. Wang and Yan (2019) developed a taxi dispatching algorithm based on the double ended M/M/1 taxi-passenger queueing model. These papers are all based on the double-ended queueing model for the typical scenario of taxi waiting process at the taxi stand that on the one side of the queue are passengers while on the other side are taxis. The passenger queueing model in taxi stand of this paper is based on these researches, but makes some changes according to actual situation. Airport bus and subway have a similar characteristic that their operation is depending on the timetable with the certain number of transport and certain headway, so controllable strategies such as timetable rescheduling and transport rescheduling can enhance the stability of bus and subway system under disruptions. The timetable rescheduling method for the sudden large-scale disruptions and daily operation is studied in Cadarso, Marín, and Maróti (2013) ; Veelenturf et al. (2016) ; Zhu and Goverde (2020) ; Xu and Ng (2020) and Yang et al. (2018) ; Yin et al. (2019) ; Long, Luan, and Corman (2021) . Transport rescheduling method for the potential disruptions is investigated in Cadarso, Marín, and Maróti (2013) ; Kroon, Maróti, and Nielsen (2015) . Liebchen (2008) ; Lu et al. (2016) ; Chen et al. (2017) focus on timetable and route design for long-term decision-making. The above-mentioned researches all focus on the process after the transport leaves the platform, and we consider the passenger queueing process before the leave, which is a new point of view. Large airport hubs play an important role in the prevention, control and spread of epidemic. Wells et al. (2020) used daily COVID-19 incidence data and global airport network connectivity from mainland China to estimate countrylevel exportation risks of the outbreak and found a significant correlation between the timing of global exportation events and airline connectivity with mainland China. Entry screening in international airport is an intuitive barrier for the prevention of infected people entering a country or region (Quilty et al. 2020) , however, under some situation of dense crowd especially in the queueing system, the chances of virus disseminating will increase greatly. Therefore, taking strict control measures in airport to evacuate passengers and alleviate the congestion, such as increasing the queueing interval between passengers, is of vital importance. We add the epidemic prevention measure in the experiment of this paper to show the importance of it, which also reflects the applicability of our hybrid congestion alleviation algorithm. The airport ground transport system consists of different airport ground access modes. This paper considers three access modes of them including taxi, airport bus and subway to model the process of taking ground transport to leave. The process of passengers leaving the airport arrival exit can be regarded as a Poisson process with rate λ, and each passenger has to choose a certain mode and join the corresponding queueing system to leave. Each access mode subjects to the first-come, first-serve discipline, and the number of vehicles is unlimited. The percentages of passengers choosing taxi, airport bus and subway are α, β and γ respectively, so passenger arrival rates in their queueing systems are λ X = αλ, λ B = βλ and λ S = γλ respectively. The passenger waiting area sizes of taxi and airport bus are set as K X and K B respectively, but the passenger waiting area size of subway is unlimited, that is because subway is the most stable and has the largest capacity, while taxi and airport bus are easily affected by weather and traffic congestion. This means, the newcome passenger choosing taxi or airport bus join the corresponding queue if the number of queueing passengers is less than the waiting area size, but will switch to subway immediately once the waiting area is full. Under this condition, α, β and γ should satisfy the following equation: where p X,KX and p B,KB are the probabilities that numbers of passengers in taxi and airport bus queueing systems reach corresponding waiting area sizes. For passengers who feel really tired after long journey, taxi is always the first choice for them in which they can arrive the destination directly, quickly and comfortable. The service process of taxi can be described as follows. Taxis queue up in the taxi queueing pool for passengers and passengers queue up in queueing channels of the waiting area to get in a taxi, which forms a typical doubleended queueing system. Since we mainly focus on the passenger congestion problem in this paper, we assuming that there are enough taxis in the taxi queueing pool, and the process from the taxi queueing pool to the passenger waiting area is controlled by the fixed release rate of taxi queueing pool and the number (the same as passenger queueing channels) of open lanes. The maximum number of passengers allowed queueing in a queue channel is K X . There are c X1 queue channels for passengers in the passenger waiting area and c X2 parking spots for taxis in every queue channel. A dispatcher is assigned to each open queue channel and in charge of the passing process of taxis and passengers. Based on the above assumption, the taxi transport capacity depends on the taxi arrival rate which can be adjusted by modifying the number of opening queue channels. The adjustment rule is according to the current passengers arrival rate and the queue length, and will be introduced in Section 4. The taxi service process is shown in Fig. 1 . Taxis arrive at the taxi stand according to a Poison process with rate µ X . Set the passenger sojourn time in taxi transportation system as W X . The system utilization of the queueing model in each taxi queue channel is ρ X = λX cX2µX . The airport bus service system can be divided into two processes, buying tickets and waiting for departure. The bus can transport multiple passengers at one time and has a nice riding comfort, but it does not go directly to the destination of passengers, and usually spend passengers a certain waiting time. In the airport bus service system, passengers should first buy tickets before getting on the bus. Some passengers may buy tickets at the ticket office with the probability q B and others buy e-tickets online in advance with the probability 1 − q B . There are c B ticket counters at the ticket office opening for ticket sales at the same time. The transport capacity adjustment in bus service system is implemented by adjusting the number of ticket counters, which is actually the adjustment of ticketing rate. Ticket check is treated as part of the waiting process, so passengers turn into the waiting process for bus departure immediately after getting tickets. These two steps will be modeled respectively. Based on the above discussion, the queueing process in the buying tickets step can be treated as a M/M/c/K model where the passenger arrival rate is λ B1 = q B λ B = q B βλ. The passenger input is a Poisson process of parameter λ B1 and the time of passengers buying tickets subject to a negative exponential distribution with parameter µ B which is the ticket sale rate. Passengers are only allowed to get on the current bus unless it becomes full. The queueing model utilization of this service process is ρ B = λB1 cBµB . The input of the second step, all passengers buying tickets on site and online, can be treated as a Poisson distribution of parameter λ B2 which is the passenger arrival rate in this step. Bus departure follows the Min(N, T )-policy, that is, the bus starts when it is full of passengers or time T has passed after the last bus departs. According to the analysis above, the bus departure process can be regarded as a renewal process, and the update interval is a distribution of Min(N, T ), where N is the bus capacity and T is a fixed time. The whole sojourn time of a passenger in the airport Ticketing after security check Ticketing before security check Figure 2 .: The subway service process. bus service system can be written W B . The cost of taking subway is the lowest among the three access modes discussed in this paper, but its accessibility and comfort are relatively the worst. The subway service system is composed of four steps: passing the security check, buying tickets, walking to the subway platform and waiting for the train departure. The order of passing the security check and buying tickets may be reversed in different subway stations, as shown in Fig. 2 . Define the passenger arrival rate of the security check as λ S1 and the one of buying tickets as λ S2 . Some passengers queue up to buy tickets with the probability q S , and the others holding subway cards or QR codes can go directly to the next step with the probability 1 − q S . The service time of passing the security check and buying tickets are negative exponential distributions of parameter µ S1 and µ S2 respectively, and the number of security check servers and ticket counters are n 1 and n 2 respectively which are both fixed. The passenger waiting area size in the subway service system is not limited as mentioned before. The security check queueing model and the ticket queueing model constitutes a M/M/c-M/M/c series service system, and the queueing model utilizations of passing security check and buying tickets are ρ S1 = λS1 n1µS1 and ρ S2 = λS2 n2µS2 respectively. We define the walking time to the subway platform as t 3 , the train headway as fixed time M , the stop time of a train at the platform as a fixed value B and the passenger sojourn time in the whole subway service system as W S . Passenger sojourn time W X , W B and W S reflect the congestion intensity in three access modes respectively, so we regard the mean passenger sojourn time as the criteria for the congestion intensity in the overall ground access system, When solving the queue congestion problem and reducing the mean passenger sojourn time W , the sojourn time in three access modes should be kept within normal limits, which means the situation that one access mode has a extreme long passenger sojourn time while others have little passenger sojourn time should be avoided. This would be an important consideration in the design of hybrid congestion alleviation strategy. In the last section, we briefly introduce how to model the passenger waiting process in ground transport system based on queueing theory. In this section, we give the mathematic analysis of this model, and explore the corresponding transient solutions and queue lengths. The rule of setting a passenger waiting area size is also introduced in this section. Double-ended queueing model is first introduced in Kendall (1951) , in which there are two queues of taxis and passengers. In Kendall's paper, in order to analyze the behavior of taxi driver, the queues of taxis and passengers are both considered. In our paper, we have assumed that the number of vehicles is unlimited and we only consider the behavior of passengers, so only the queue of passengers is analyzed here. For the passenger queueing model in taxi stand, we have the transient solution P X (t) = [p X,0 (t), p X,1 (t), p X,2 (t), . . . , p X,KX (t)], where p X,j (t) is the probability that there are j passengers waiting for taxis at time t. Here we employ the forth-order Runge-Kutta method (RK4) to calculate the transient solution like Tirdad, Grassmann, and Tavakoli (2016) . The initial condition should be given as P X (0), and the transition matrix of the taxi double-ended queueing model A X is a K X + 1 order square matrix which can be expressed as Davis (1992) : where c X2 is the number of parking spots for every queue channel. According to the Fokker-Planck equation, P X (t), the first derivative of P X (t), can be calculated by the equation In the differential Eq. 4, the left side can be treated as a function, f (P X , t) = P X (t). Define the step size as ∆t, and we have t n = n∆t and P n = P X (t n ). RK4 method compute four quantities κ 1 , κ 2 , κ 3 and κ 4 to obtain P (t n+1 ) (Tirdad, Grassmann, and Tavakoli 2016) . We can obtain the transient solution at every ∆t with the given initial condition. Multiply P (t n ) by vector [0, 1, 2, . . . , K X ] T and the instantaneous expected queue length can be obtained. When the queueing model and the service discipline are given, the number of expected sojourn passengers is L X (λ X , t n , P X (0)), where λ X is passenger arrival rate, t n is time and P X (0) is initial condition. Therefore, the expected passenger sojourn time can be deduced by the Little's law as When the passenger waiting area is full of passengers, the queueing system will lose new arriving passengers, so the effective passenger arriving rate should be modified as As discussed in Section 3.2, the bus service system consists of buying tickets and waiting buses, which can be regarded as a M/M/c/K model with a Min(N, T ) renewal process. The M/M/c/K bus queueing model can be viewed as a filter, in which the input is a Poisson process with passenger arrival rate λ B and the output is also a Poisson process whose rate is related to the input rate. If λ B1 is less than the service rate µ B , the output rate is equal to the input rate. Otherwise, the output rate is µ B . According to the assumption that every passenger has the probability q B to buy a ticket at the ticket window, the parameter of the passenger input Poisson distribution in renewal process can be represented by where p B,KB is a time-varing probability. In general, however, the passenger arrival rate λ B is within normal limits, so p B,KB can be omitted and we have In the process of buying tickets, the transient solution can be computed by RK4 as Section 4.1. The number of expected sojourn passengers can be represented by L B (λ B , t n , P B (0)) and the expected waiting time is The only difference with the RK4 in Section 4.1 is that the transition matrix A B is a K B + 1 order square matrix that can be expressed as: Define the n th bus's departure time in the renewal process as s n and assume that passengers waiting for departure are cleared at s n . The bus service system enters an idle period with Min(N, T ) renewal policy after every clearance, and the renewable time s n is an embedded Markov chain (Deng 1998 ). Define the time from the last renewable time s n−1 until the m th passenger enter the system as t m and the distribution of t m as F m (t). The input is a Poisson process with parameter λ B2 , so the passenger arrival time interval sequence {t m − t m−1 } (0 < m ≤ N ) subjects to a negative exponential distribution with parameter λ B2 . Therefore, F m (t) is a m-order Erlang distribution, and the probability density f m (t) and the distribution function F m (t) can be written as follows: We can find that probabilities of passengers getting service by the T -policy and the N -policy are F N (T ) and 1-F N (T ), and the corresponding expected passenger waiting time is W T B2 and W N B2 respectively. For the T -policy, The update interval T is constant, so it is easy to get For the N -policy, the update interval subjects to the distribution F N (t), and W N B2 is exactly the residual life of the renewal process. We have where E[t] and E[t 2 ] are the first moment and the second moment of distribution F N (t) (Deng 1998 ). According to the above formulas, the mean passenger waiting time under the Min(N, T )-policy can be expressed as The expected passenger sojourn time in airport bus queueing system W B (t) is the sum of adding the passenger waiting time in the ticket and renewal process and we have For the subway queueing model, the order of passing the security check and buying tickets may be reversed in different subway stations. In the security check first case, the passenger arrival rate λ S1 = λ S . If λ S1 is less than the overall service rate n 1 µ S1 , the passenger output is exactly its input. Otherwise, the passenger output rate is equal to the service rate, so the output is a Poisson process of n 1 µ S1 . Furthermore, every passenger has the probability q S to queue up for tickets, so the passenger arrival rate for tickets is λ S2 = q S min(n 1 µ S1 , λ S ). In the ticket first case, passengers without any prepaid-card, month-card or e-card should first buy one-way ticket at the ticket window with a probability q S . We have λ S2 = q S λ S and λ S1 = min(λ S2 , n 2 µ S2 ) + (1 − q S )λ S . Numbers of sojourn passengers in the security check and ticket system are independent. If the passenger waiting area sizes are unlimited in these two systems, the sizes of their transition matrices will be positive infinity for this M/M/c/∞ model. For numerical implementation, we choose an appropriate and relative large passenger waiting area size, and the original M/M/c/∞ queueing model can be replaced by a M/M/c/K model approximately. Now, transient solutions of these systems can be computed by RK4 respectively. The passenger sojourn time in overall subway service system can be written as: W S (t) = L S1 (λ S1 (t), t, P S1 (0)) λ S where t 3 , M and B are the walking time to the subway platform, the train headway and the staying time of a train at the platform respectively. In this paper, for the sake of simplicity, we consider the security check first case for simulation. There are also some subway stations that have no security check process in other countries. In that case, the passenger sojourn time can be simply obtained by deleting the L S2 part, which will not be analyzed in detail here. Setting of passenger waiting area size can avoid the loss of passenger revenues, which is an important research subject in passenger equilibrium behaviors. In Naor (1967) , the passenger waiting area size in the observable M/M/1 queueing model based on social and individual interests has been explored. In this section we will set the proper passenger waiting area size based on individual interests. We make the following assumptions: (1) Each passenger in a queueing system has the same unit time cost C. (2) When the service is successfully received, each passenger obtains the same numerical utility R related to the service quality. (3) The mean time of receiving service is 1 µ . Theorem 1. Let the individual interests of passengers who join the queue be positive, the passenger waiting area size D should be: where [ ] is the represent of bracket function. Proof. Proof When a new passenger arrives in a certain queueing system, if there are j − 1 passengers in the system at present, his revenue can be written as If I j is positive, the newly arrived passenger will join the queue, otherwise leave. If the newcome passenger choose to join the queue, the number of passengers already in the queue D − 1 should satisfy If he is the last one who is allowed to enter the queue, D also should satisfy Therefore, Considering D should be an integral, we can obtain Eq. 24 now. Based on the above discussion, we develop a hybrid congestion alleviation algorithm aiming at alleviating congestion in the airport ground access system by adjusting the transport capacity (arrival rate of taxi and the service rate of bus ticketing), optimizing passenger share rates and providing passenger access mode choice guidances. When there is congestion at the queueing system, airport manager can take two measures to alleviate it. The first one is enhancing the transport capacity which is carried by adjusting the number of open taxi queue channels and the bus ticket counters here. The second is guiding passengers to change their access mode choices through broadcasting, manual guidance or other methods. Because the priority should be given to the preference of passengers themselves, the airport manager first considers the method of enhancing the transport capacity. If the congestion still exists when every taxi queue channel or bus ticket counter has been opened, the guidance on passenger access mode choices will be started. Transport capacity adjustment following the principle of minimum system cost will be proposed in this section. We take taxi queue channel adjustment as the example to introduce this principle which is similarly taken in bus ticket counter adjustment. For the queueing cost, we first obtain the current arrival rate λ X and the initial condition P X (0) in the taxi queueing model. In practical situation, P X (0) can be obtained by real-time passenger flow counters or surveillance videos. Assume that λ X will not change over the next period of time. The number of currently open taxi queue channels is m and the predicted queue length in time t e is L X ( λX m , t e , P X (0)), which are used for obtaining the total time cost of passengers in the queueing system. Define the unit time cost per passenger who is in the queue as C p , the unit operating time cost of one dispatcher in charge of a taxi queue channel as C a and the unit time cost per passenger who switches to the other access modes in that the queue length reaches its waiting area size K X as C n . Therefore, the unit time cost in the taxi queueing system is Calculate C X for each m ∈ (1, 2, ..., c X1 ) and select the m minimizing C X as the number of open queue channels in this period, and we have In this section, we introduce multinomial logit (MNL) model to calculate passenger share rates and the method of successive weighted average (MSWA) to optimize it in the airport ground access mode choice problem. MNL model can calculate the probability of passengers choosing each option according to the corresponding utility approximately. In this paper, the passenger choice probability can be regarded as the passenger share rate of each access mode. From the perspective of passengers, they always want to maximize their own interests when choosing a ground access mode to leave the airport. The utility of a certain transportation mode can be estimated by journey time, costs, convenience, queueing time, safety, stability and other factors. The probability of the n th passenger choosing the i th option in the option set C n is P n (i) = P (U in ≥ U jn , ∀j ∈ C n , i = j), where U in is the utility of the i th option. V in , the linear weighted sum of k different reference factors, is the systematic component of U in . θ k i is the independent variable of the k th factor in the i th option and η k i is the corresponding weight. in , the random part of U in , subjecting to a Gumbel distribution. Therefore, for the given V in , the probability P n (i) can be rewritten as Interested readers can refer to Train (2009) for more details. According to the above assumption, P n (i) is the same for any n, and the corresponding passenger arrival rate Q i can be expressed as where λ is the passenger arrival rate in the airport. In the airport ground access mode choice problem, choices of passengers are determined by different reference factors among which queueing time is treated as the dynamic part, and others, such as expense costs and travel time, are treated as the static part. For the dynamic part, queueing time influences the number of passengers in the i th access mode and is influenced by it as well. Passengers make choices among three access modes with probabilities of α (0) , β (0) and γ (0) based on static utilities under the assumption that initial queue lengths in every transport queueing system are all zero. At present, the queueing time has no effect on choice probabilities. After passengers make their first choices, a flow assignment among ground access modes is formed, the queueing phenomenon occurs and waiting time starts to influence the ground access mode choice. Then probabilities in passenger choices change and the passenger flow is redistributed among different ground access modes. The queueing time also changes and in turn affects passenger choices again. Finally, the passenger flow assignment and the queueing time tend to be balanced and stable after several iterations. The whole iteration process can be modeled by MSWA, which is summarized as follows, and the corresponding flow chart is illustrated in Fig. 3 . (1) The iteration starts from l=0 and queue lengths are all 0. Define the static utilities of taxi, airport bus and subway as S X , S B and S S respectively. In Eq. 34, systematic component where χ (l) is the step size in the l th iteration and d is a given constant. Here we choose d = 1. (4) If the error G between v (l+1) and v (l) in last iteration satisfies where is the given threshold, we can deem that the iteration converges, which means passenger share rates and queueing time reach equilibrium, and regard v (l+1) as the final solution. Otherwise, return to Step2, set n = n + 1 and re-execute the loop. Combine the transport capacity adjustment strategy with the passenger choice guidance algorithm and we can obtain a hybrid congestion alleviation strategy. We set a fixed time interval T k as the update cycle of the congestion control strategy. The control algorithm is carried out every T k to decide the number of open taxi queue channels and bus ticket counters and whether it is necessary to implement a passenger guidance. If yes, calculate the optimal passenger share rates and generate the guidance. The process of hybrid congestion alleviation strategy can be summarized as follows. Firstly, obtain the current arrival rate λ, passenger share rates α, β and γ of taxi, airport bus and subway and queue lengths in all queueing systems including L X , L B (queue length for bus tickets), L S1 (queue length for subway security check) and L S2 (queue length for subway tickets). Secondly, find the appropriate number of open taxi queue channels and bus ticket counters by Eq. 30 and calculate the predicted passenger queueing time in fixed time t e (t e < T k ) using RK4 according to the current queue length and passenger arrival rate. Finally judge whether the expected queueing time exceeds the given W * . If yes, calculate the new passenger share rates α (l+1) , β (l+1) , γ (l+1) by MSWA and start a passenger guidance based on the gap between α, β, γ and α (l+1) , β (l+1) , γ (l+1) , otherwise directly stop the algorithm. The algorithm flow chart is illustrated in Fig. 4 . The proposed algorithm is simulated in MATLAB 2017a. In section 6.1, we predict the variation of queue length under different passenger arrival rates obtained by RK4. In section 6.2, we simulate the transport capacity adjustment through the example of taxi arrival rate adjustment. In section 6.3, the process of convergence and reduction of mean queueing time with MSWA is explored under different groups of initial static utility. In section 6.4, numerical results of being with and without the congestion alleviation strategy are shown by a specific example. Typically, in section 6.4, we consider changes in the airport under the influence of the epidemic and set up two groups of experiments. The commonest strategy for preventing the spread of epidemic taken in airport queues is strictly controlling the interval between passengers, so the waiting area size will become much smaller. Besides this, another most obvious change is the significant reduction in passenger flow, and then it cames the decreasing number of airport servers controlled by airport managers for saving unnecessary costs. Taking these effects into consideration, the different / parameters of these two groups of experiments are the waiting area size K X and K B , the number of subway security servers and ticketing counters n 1 and n 2 and the overall passenger arrival rate λ. Among them, K X and K B can be calculated by Equation 24 based on transport revenue R, service rate µ and time cost C p . After epidemic, airport managers strictly control the queueing interval being no less than one meter, so the K X and K B under the epidemic background are reduced to two-thirds lower than normality. In the hybrid congestion alleviation strategy, the number of servers of taxi and bus can be automatically adjusted to the lowest to save costs, so only the number of subway security check and ticket counter needs to be fixed to 1 which is different from that in normality. The data of passenger arrival rate are chosen from the real date of two certain days in BCIA before and after the epidemic. The experimental parameters were obtained by combining the estimation with the field investigation at BICA, and details are illustrated in Table 1 which are used in Section 6.3-6.4. The M/M/c/K model is widely used in this paper to predict the variation of queue lengths in different queueing systems, such as subway and bus tickets, and the transient solution can be computed by RK4, so we choose one certain M/M/c/K model to expound the process here. In this M/M/c/K model, parameters are set as µ = 0.5, c = 8, K = 100, P (0) = [1, 0, 0, . . . , 0], t = 0.005. According to whether the system utilization ρ is less than 1 or not, the queueing system can be steady or not. Select four arrival rates of passengers, λ = 3, 6, 9, 12. For λ = 3, ρ = 0.75 < 1, and the queue length will tend to be stable over time. For λ = 6, 9, 12, ρ = 1.5, 2.25, 3 (≥ 1), and the queue length will increase continually. The expected instantaneous queue lengths within 30 units of time can be calculated by RK4, as shown in Fig. 5 . For λ = 3, the increase of queue length tends to be 0 from the 15 th unit of time. For λ = 6, 9, queue lengths increase continually but do not reach the waiting area size K yet. For λ = 12, the queue length increase so fast that it reaches the passenger waiting area size K in 30 units of time. We can find that the faster the passenger arrival rate is, the faster the queue length will grow and the more serious the congestion will be with the accumulation of passengers, which is consistent with the theory of stable distribution in queueing model. When the passenger waiting area is full, the system will lose new arriving passengers. In the ground access system of this paper, passengers who are lost by taxi and bus systems will switch to subway immediately, which will affect the effective passenger arrival rate related to p K according to Eq. 4. As illustrated in Fig. 6 , we also present probabilities of passenger loss p K and effective passenger arrival rates λ * in 30 units of time under different initial passenger arrival rates λ. It can be found that the greater the initial passenger arrival rate λ is, the greater the probability of passengers loss will be. Moreover, with the increase of time, the probability of passenger loss will continue to increase and the expected queue length with unsteady condition will be closer to passenger waiting area size K. According to Fig. 6 , for λ = 3, 6, probabilities of passenger loss are little and can be ignored, and the effective arrival rate λ * (30) = λ. For λ = 9, the probability of passenger loss is 0.3415 and the effective arrival rate decreases to 6, which means losing 3 passengers per unit time. For λ = 12, the queue length will be equal to the passenger waiting area size and 8 passengers will be lost per unit time. Now, the congestion where more than half of the new-arriving passengers have to change their choices appears, which is not the airports manager want to see. In practical, the manager can adjust taxi queue channels for increasing the service rate or(and) release an appropriate guidance for passengers in access mode choices to avoid this situation in advance. In order to satisfy the choices of passengers as far as possible, the airport manager should first consider adjusting the service rate in queues. We take taxi queue channels adjustment as example and assume that there are up to 4 queue channels for passenger to wait and taxi to drive from storage tank into the taxi stand. Set the passenger arrival rate λ X (passenger/minute)∈ {2, 5, 8, 11, 14, 17, 20, 23, 26, 29} and initial queue lengths are 0, and we can obtain expected queue lengths and system costs at t e = 30(minute) when different numbers of taxi queue channels are open. As illustrated in Fig.6 , the second to fifth columns represent the obtained system costs and the sixth column is the number of open taxi queue channels m minimizing cost with the relevant λ X . We can find that when λ X is relative small, the queueing system can keep smooth without opening all channels. In order to minimize the operation cost, we choose to open m taxi queue channels. When λ X ≥ 11, all queue channels should open to restrain the growth of passenger time cost. When all the service have been adjusted to its upper limit, if the passenger congestion still exits, an appropriate guidance strategy should be generated and released in time. Here we present a feasible guidance strategy based on the optimal passenger share rates obtained by MSWA. In order to demonstrate the effectiveness of MSWA in the optimization of passenger share rates, we choose λ = 44 and different groups of transport static utility values as below and explore their impacts on passenger queueing time. Case 1 S X = 0.5, S B = 1, S S = 0.3, Case 2 S X = 0.3, S B = 0.5, S S = 1, Case 3 S X = 1, S B = 0.3, S S = 0.5. Set the weights of static utilities and queueing time as 1:1, and open all 4 taxi queue channels and 2 bus ticket counters. The queueing time, passenger share rates and convergence errors of these cases are shown in Figs. 7-9. From Fig. 7 , we find that the passenger mean queueing time shows a downward trend with iterations, so the queue congestion can be alleviated to some extent. Especially for Case 2, the abnormal situation that it takes overlong time for taking subway caused by initial static utilities can also be eliminated. For the purpose, alleviating the congestion in the whole ground access queueing system, some increase of queueing time in a certain access mode is acceptable. According to the discussion in Section 3 and parameters in Table. 1, the service process of taxi is the simplest and its service rate is relative high, so, for reducing the mean queueing time, taxi tends to share more passengers and the corresponding queueing time after optimization increases in all three cases. Passenger share rates is initially determined by static utilities and begins to fluctuate with the start of iterations, as illustrated in Fig. 8 . At first, the share rate of taxi increases and the share rate of subway decreases sharply, but the share rate of bus decreases gently due to the T -policy. They converge to certain values, however, after several iterations. The same changing trend appears in these three cases, but convergence values are different due to different initial static utilities. In summary, the initial and the final passenger share rates are heavily influenced by static utilities, but the changing trend during the converge is up to service rules and rates. As shown in Fig. 9 , iterative errors decrease within the given limit after several iterations, which means the passenger share rate optimization method is convergent and feasible. Therefore, we can concluded that the MSWA can reduce the mean queueing time by optimizing passenger share rates. As mentioned before, the hybrid congestion alleviation strategy consists of transport capacity adjustment and passenger guidances. We simulate queueing systems under implementation of the hybrid congestion alleviation strategy in one day when taxi, airport bus and subway are all running, and compare the queueing time with that without the passenger guidance. The different results under epidemic situation and normality are also analyzed. The time period selected for simulation in one day is 8:00-16:00, and the corresponding data of passenger arrival rate under normality and epidemic obtained from BCIA are shown in Fig. 10 . Set static utilities as S X = 0.72, S B = 0.56 and S S = 0.68, and substitute them into Eq. 34 as V in . We have P (X) = 0.356, P (B) = 0.302 and P (S) = 0.341 which are the initial passenger share rates α, β, γ at 8:00. Basically, the queueing system information is unknown for passengers, so if the airport manager do not take any measures on passenger access mode choices, α, β and γ are passenger share rates under self-selection for the whole time period. When implementing the passenger guidance, the manager should update it every T k = 30 minutes from 8:00. The update process can be summarized as follow. (1) Predict the queueing time after t e = 30. (2) Calculate the ideal numbers of taxi queue channels and bus ticket counters which should be open. Numerical simulation results before and after implementing the guidance and under epidemic situation and normality are shown in Table. 3, Fig. 11, Fig. 12 and Fig. 13 . Table. 3 shows the transport capacity adjustment based on minimum cost during this time period. Fig. 11 illustrates the variation of passenger share rate with the hybrid congestion alleviation strategy obtained every T k during the time period. In Fig. 12 , the black curve represents the mean queueing time under the original passenger share rate, while the red curve is the mean queueing time after adjusting the passenger share rate. Fig. 13 shows the variation of queueing time of taxi, bus and subway during this time period. We can find that, in normality, the queueing time from 8:00 to 10:00 of red curve and black curve is exactly the same, which represents that queueing time does not exceed 20 minutes during this period and the taxi queue channel and bus ticket counter are not all open, so the passenger guidance is not implemented. Correspondingly, passenger share rates in normality before 10:00 remain fixed as well, as shown in Fig. 11a . At 10:00, the prediction shows that the passenger waiting time of subway at 10:30 under the current passenger arrival rate will exceeds 20 minutes even if all taxi queue channels and bus ticket counters have opened, so the passenger guidance starts. From now on, as shown in Fig. 12a and 13a, the passenger waiting time of all access modes becomes different from that without guidance. After that, the gap of mean queueing time between before and after optimization keeps growing over time, which implies that taking measures on passenger congestion earlier may alleviate the congestion better. In addition, from Fig. 10a , the passenger flow after 10:00 is almost no less than that before 10:00, and the passenger flow has been increasing after 12:00. Therefore, all taxi queue channels and bus ticket counters are open after 10:00, and passenger guidances has been in progress from 10:00 to 16:00. In Fig. 12b , the small passenger flow situation under epidemic, there is only a black curve which represent being without passenger share rate optimization exists. That is because the queueing time of all three ground access modes are no more than 20 minutes during the day, so adjusting the service rate is enough to control the queueing time. In can be concluded that, under normality, the large passenger flow would cause serious queue congestion even when the transport capacity has been adjusted to the maximum. Therefore, most of the time with normal situation, appropriate passenger guidances are needed to alleviate queue congestion and evacuate passengers quickly. Under the epidemic situation, due to the greatly re- Table 3 .: The number of open taxi queue channels and bus ticket counters during a time period. the order of T k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 normality taxi 1 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 bus 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 epidemic taxi 1 1 1 1 1 1 2 2 2 1 2 2 2 2 1 1 bus 1 1 1 1 1 1 1 1 1 Figure 11 .: optimized passenger share rate every T k from 8:00 to 16:00. duced passenger flow, even if the size of passenger waiting area and the transport capacity are reduced, queue congestion would not occur. A little adjustment on transport capacity can dynamically alleviate queue congestion. These results show that our hybrid congestion alleviation strategy can be applied to various situations. In this paper, we propose a hybrid airport ground access system congestion alleviation strategy based on transport capacity adjustment and passenger guidance, and develop queueing and service models consisting of three common airport ground access modes based on the queueing theory. Firstly, the developed model can predict the queue length according to the current passenger arrival rate and simulate the basic ground access service process in airports. It can also be adjusted and improved according to practical situations in different airports. Secondly, after implementing the developed MSWA independently, optimal passenger share rates are obtained and the corresponding mean queueing time is decreased. Finally, by implementing the hybrid congestion alleviation strategy based on real passenger arrival data, the mean queueing time can be reduced sufficiently and the passenger congestion in the ground access system can be alleviated effectively. In numerical experiments, we analyze some methods for epidemic taken by airport managers and set two groups of parameters for experiments, in which the results show some differences under these two methods but both can alleviate the queue congestion in airport ground access system. Although the proposed model and algorithm show some good results concluded above, there is a long way to go to realize the high efficient coordination of airport ground access modes. First of all, the queueing time prediction is only based on the current passenger arrival rate, so considering the combination of passenger flow and queueing time predictions for higher precision deserves further (a) normality period. study. Secondly, in practice, not all passengers would like to follow the airport guidance, so the probability of passengers following the guidance needs to be considered in the future. Furthermore, the effectivenesses and advantages of the proposed model and method shown in the MATLAB simulation needs to be further verified in the airport. 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