Reliable Wireless Connections for Fast-Moving Rail Users Based on a Chained Fog Structure

ARTICLE IN PRESS JID: INS [m3Gsc; June 30, 2016;9:36 ]

Information Sciences 0 0 0 (2016) 1–17

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Information Sciences

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Reliable wireless connections for fast-moving rail users based on a chained fog structure

∗ Tian Wang a, , Zhen Peng a, Sheng Wen b, Yongxuan Lai c, Weijia Jia d, Yiqiao Cai a,

Hui Tian a, Yonghong Chen a a College of Computer Science and Technology, Huaqiao University, Xiamen, Fujian Province, PR China b School of Information Technology, Deakin University, Melbourne Burwood, Victoria, Australia c School of Software, Xiamen University, Xiamen, Fujian Province, PR China d Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, PR China

a r t i c l e i n f o a b s t r a c t

Article history: Currently, 3G and 4G networks provide customers with high-speed wireless services al- Received 15 November 2015 most everywhere. However, the wireless connection is often unstable and unreliable, espe-

Revised 13 June 2016 cially for fast-moving end users (e.g., those on trains and buses). To investigate the sever- Accepted 23 June 2016 ity of this problem, we conducted real experiments on fast-moving trains to investigate Available online xxx the quality of 3G connections. From the results, we found that 1) from the temporal per-

Keywords: spective, the 3G connections were not stable and suffered from frequent disruptions of

Reliability connectivity, and 2) from the spatial perspective, the connections that were established Fast-moving rail in different train compartments were largely independent. These two ﬁndings motivate Fog structure us to propose a brand-new fog computing structure, which acts as an intermediate layer Cascade shifting ﬂow problem between the end users and the 3G infrastructure. This new fog structure introduces a series of mutually chained network gateways that are located in different compartments. This structure addresses the aforementioned problem of unstable connectivity and thus ensures reliable wireless service for fast-moving users, such as passengers on trains. We performed a series of theoretical and empirical analyses to evaluate the performance of the newly proposed structure. All of the experimental results suggest that our proposed fog structure greatly improves the reliability of wireless connections on fast-moving trains. © 2016 Elsevier Inc. All rights reserved.

1. Introduction

The popularity of various wireless networks has dramatically increased in recent years. New communication technologies, such as 3G and 4G networks [10,29] , are providing customers with high-speed wireless services. For example, 3G networks support data rates of up to 14.4 Mbps on the downlink and 5.76 Mbps on the uplink for stationary users. They also have reduced latency of nearly 50 ms [36] . As a result, broadband applications can be easily accessed by stationary users in most areas with acceptable signal quality [19] . However, the proliferation of mobile devices, such as smartphones and tablets, and their associated applications has considerably increased along with the growing availability of wireless connectivity [24] . With rising demands for real-time data, such as videos and live streams, customers strongly desire consistent connections with high-speed transmission capability. Considering Hong Kong as an example, an average of 4.5 million people use

Please cite this article as: T. Wang et al., Reliable wireless connections for fast-moving rail users based on a chained fog structure, Information Sciences (2016), http://dx.doi.org/10.1016/j.ins.2016.06.031 ARTICLE IN PRESS JID: INS [m3Gsc; June 30, 2016;9:36 ]

2 T. Wang et al. / Information Sciences 0 0 0 (2016) 1–17 trains (MTR lines) to commute on workdays each week [23] . Train passengers often use their smartphones to watch online videos on services such as YouTube [30] and play games such as Hearthstone [27] . These online video services and games typically have stringent performance requirements, including sufficient connectivity time, short delay, and high bandwidth [37] . For example, online games require consistent network coverage to smoothly deliver streaming data. Support for mobile applications via wireless networks has recently received significant research attention [12,13,25] . In this paper, we focus on the application scenario of wireless services in public transport systems. To investigate whether current wireless networks (e.g., the 3G network) can support the use of wireless services on fast-moving vehicles, we conducted a series of real experiments in trains running over a distance of more than 100 km in total during a period of 3 months. We found that 1) from the temporal perspective, the 3G connections were not stable and suffered from frequent disruptions of connectivity, and 2) from the spatial perspective, the connections that were established in different train compartments were largely independent. These two findings suggest that when the bandwidth of one device is low or the connection has been broken, other devices may still be functioning well with their wireless connections. This inspired us to design a structure that can help to share communication capabilities among neighboring devices through multiple links. This structure can minimize connection disruptions and improve the reliability of connectivity. Accordingly, we propose a novel fog structure [35] for providing wireless services, specifically for fast-moving users on trains. This fog structure is an intermediate layer between the end users and the 3G/4G infrastructure (e.g., Node Bs) and addresses the problem of unstable connectivity problem. This structure consists of a few end devices called Personal Gate- ways ( PGs ) [26] , such as set-top boxes and access points (APs) [38] , deployed at various positions on a train. The PGs are connected and can share their communication capabilities to provide wireless service to different end users on the train. The deployment of our fog structure will provide the following benefits. First, the PGs can have more powerful signal re- ceivers embedded inside. The PGs will therefore establish more reliable connections with Node Bs to support services for end users, especially in fast-moving vehicles. Second, because the connected users and the required network resources may be different for each PG , the network resources can be redistributed among PGs to improve their efficiency of use. Based on the newly proposed fog computing structure, we studied the Cascade Shifting Flow (CSF) problem and ex- amined the wireless services provided to fast-moving users on trains. By mathematically formulating the CSF problem, we were able to solve this problem by limiting the maximum shifting hops of the communication flows, thereby minimizing the maximum delay while maximizing the throughput. Furthermore, we designed a realistic and localized algorithm for flow shifting that collects information from neighboring PGs . The main contributions of this paper as follows:

1. We conducted extensive experiments in the real environment of interest (i.e., trains) to examine the reliability of 3G/4G connections for fast-moving users. The results suggested that the connectivity was not stable or reliable. 2. A new fog computing structure, which consists of a series of chained fog devices, is proposed to improve the reliability of wireless services under fast-moving conditions. 3. We theoretically studied the CSF problem and developed an approximately optimal solution to maximize the availability and reliability of throughput while minimizing the communication delay. 4. Extensive evaluations were performed to validate the effectiveness of the proposed method. The results suggest that the method achieves high throughput, a lower packet loss rate and low communication delay.

The remainder of the paper is organized as follows: Section 2 presents a review of related work. Section 3 introduces our empirical study of 3G/4G connectivity for fast-moving users. We also introduce our new fog computing model in this section. Section 4 discusses the CSF problem, and Section 5 presents our evaluations, followed by the conclusions of the paper in Section 6 .

2. Related work

As a commonly used solution for reliable and fast wireless communication, 3G cellular networks and their related im- proved techniques, such as HSPA , have garnered wide attention [11] . In [21] , Liu et al. reported a large-scale empirical field study of the performance of 3G mobile systems in China. Their measurements were performed in five cities and included three different 3G standards. They observed that for voice service, indoor performance is better than outdoor performance. Specifically, fast movement can lead to an unsteady wireless environment, thereby causing performance degradation in 3G networks. However, their study did not include HSPA . In [18] , Laner et al. investigated the 3G uplink delay based on measurements performed in an operational HSPA network. They provided models for the latency of single network entities and the accumulated delay. Their results showed that the delay is strongly dependent on the packet size, with random components depending on synchronization issues. In [40] , Xu et al. showed that the performance of downloads in 3G/ HSPA mobile networks can be significantly degraded by a concurrent upload saturating the uplink buffer on the mobile device. To miti- gate this problem, they proposed a new algorithm called Receiver-side Flow Control (RSFC) to regulate the uplink buffer on 3G/ HSPA data senders. The above solutions mainly addressed the performance of 3G and HSPA networks in general cases. Recent years have witnessed the development of various applications for mobile devices and smartphones [16] . These mobile applications pose significant challenges for wireless communications in different environments. In [8] , Chen et al. measured the network performance of smart mobile handheld devices (MHDs) in a university campus Wi-Fi network and identified the dominant factors affecting network performance. They found that MHDs tend to have larger local delays in a Wi-Fi network and are more adversely affected by the number of concurrent flows. Moreover, some application-level

T. Wang et al. / Information Sciences 0 0 0 (2016) 1–17 3 protocols cause inefficient use of the network. Beritelli et al. showed that the perceived speech quality of mobile VoIP applications depends on the individual telephone operator when the radio link is not always reliable for the entire duration of a conversation [3] . Thus, they presented an architecture for and a performance evaluation of a dual-stream approach to mobile VoIP applications. In [39] , Xu et al. focused on forecasting network performance for real-time interactive mobile applications. They showed that forecasting the short-term performance of cellular networks is possible in part because of the channel estimation scheme available on the device and the radio resource scheduling algorithm at the base station. Thus, they developed a system interface called PROTEUS to passively collect current network performance and forecast future network performance. This system interface requires global information regarding the network situation. In [4] , Bhatia et al. presented the design and analysis of a scheme for streaming videos that opportunistically takes advantage of “slow fading” variations in the wireless link quality. The proposed scheme works by selectively sending more content to sessions at times when they have better link quality while providing sufficient rate guarantees to prevent buffer underflow. However, these solutions do not address any high-speed scenarios, such as subways or trains. Because subways and rapid buses have become increasingly prevalent in daily life, the question of how to maintain the quality of wireless communication under such high-speed transportation scenarios remains open. In [41] , Yao et al. sought to provide some insight into users’ experience of mobile broadband service in terms of TCP throughput when traveling on a regional train. Compared with metropolitan cities, regional trains are often served by lower data rates but move at higher speeds. They found that using a single broadband provider may lead to a large number of blackouts. In [28] , Pögel et al. proposed to transfer connectivity data from many vehicles to a central server to enable prediction of future network capabilities for other vehicles. They analyzed the characteristics of 3G networks with a focus on vehicular mobility, and they presented an approach for collecting these global data. In [33] , our collaborator Tso and Jia et al. presented an empirical study of the performance of mobile HSPA networks based on extensive field tests. On the one hand, they confirmed that mobility has a large negative impact on the performance of HSPA , as the rapidly changing wireless environment can cause serious service degradation or even interruption. This finding is consistent with that reported in this paper. On the other hand, they also found that throughput performance does not monotonically decrease with increased mobility level; therefore, they char- acterized mobility as a double-edged sword. However, they only analyzed the phenomena reflected by their measurements and did not propose any solutions. In [2] , Abid et al. leveraged the LTE network for vehicle-to-infrastructure communications by using smartphones as an interface. They considered broadband Internet access and entertainment applications such as video streaming, and they presented performance analysis results obtained using an LTE simulator. Thus far, although the researchers mentioned above have analyzed the impact of mobility on wireless communications, they have not proposed any solutions for improving HSPA performance. For providing live TV services on a high-speed train, Chiao et al. developed a mobile live TV system for Taiwan High-Speed Rail (THSR) [9] . Their system delivers specifically live TV programs over the mobile WiMAX network and then uses Wi-Fi multicasting to deliver programs to the terminal devices of railway passengers. In [31] , Song and Dong introduced a scheme for Internet access on high-speed trains based on information-centric networking. They mainly used a central in-network cache on the train to deliver existing content rather than live content to passengers. In [7] , Chang et al. investigated the potential of UDP-based file delivery protocols for high-speed rail reception. They proposed a new protocol for reliable UDP-based unicasting and to support multi-session delivery. They also conducted experiments on the real 802.16e mobile WiMAX network for THSR. In [6] , the authors also proposed a new application-layer forward error correction (AL–FEC) scheme based on the Chinese remainder theorem (CRT) to facilitate streaming service delivery for high-speed rail reception. They evaluated its performance in an emulated environment for simulating high-speed rail reception over WiMAX networks. Although their method can improve network services at the protocol level, it may be difficult to apply in situations with limited network resources. As a kind of extension of cloud computing and services to the edges of networks, the fog approach can provide data, computing, storage and application services to end users [42] . In [5] , Bonomi et al. studied the characteristics of the fog and argued that these characteristics make the fog the most appropriate platform for a number of critical Internet of Things (IoT) services and applications, namely, connected vehicles, smart grids, smart cities and others. In [43] , Zhu et al. considered web optimization within the fog context. They applied existing methods for web optimization combined with unique knowledge that is only available from the fog. In [1] , Aazam et al. discussed the concept and architecture of smart gateways based on the fog. With the help of the fog, the data to be sent can be preprocessed and trimmed to reduce the network burden. In [32] , Stojmenovic et al. summarized the motivation for and advantages of the fog and analyzed its applications in a series of real scenarios. Furthermore, they discussed the security and privacy issues associated with the current fog paradigm. To the best of our knowledge, we are the first to deploy the fog structure in a high-speed moving vehicle scenario. In the study reported in this paper, we set out to provide reliable wireless services to users on fast-moving trains. Instead of a direct link between an end user and the 3G/4G infrastructure, we set up a fog structure that acts as an intermediate layer between the end users and the infrastructure. The fog is able to establish stable connections for end users.

3. The fog structure on trains

In this section, we ﬁrst present several real experiments conducted to test the 3G service available on trains and analyze the results in Section 3.1 . Then, we describe the proposed fog structure in Section 3.2 and the design of the Personal Gateways in Section 3.3 .

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Fig. 1. Sending and receiving throughput in the ‘from’ direction.

Fig. 2. Sending and receiving throughput in the ‘to’ direction.

3.1. Measurements of 3G service on trains

To test the 3G service available on trains, we performed measurements on the MTR lines in Hong Kong. We used two devices located in different compartments to measure the throughput for sending and receiving data available on the train. These two devices, denoted by L A and L B , were two laptops of different brands. For a long experimental duration, we chose the East Rail Line between Lo Wu station and Mong Kok East station. To consider the influence of the direction of motion of the train, we conducted each experiment twice, once with the train moving in each direction, which are labeled as the ‘from’ direction and the ‘to’ direction with respect to Mong Kok East. In each direction, we recorded thousands of measurements regarding the network throughput for sending and receiving data. To present the results clearly, we selected 100 time points at equal intervals and plotted their corresponding measurements for the two devices in the same figure for comparison. The results are shown in Figs. 1 and 2 , wherein Figs. 1 a and 1 b show the throughput measurement results for sending and receiving data, respectively, in the ‘from’ direction and Figs. 2 a and 2 b show the throughput measurement results for sending and receiving data, respectively, in the ‘to’ direction. We can see that the real-time throughputs of the two devices are generally independent. Moreover, when one device suffered from a low throughput, the other often enjoyed a high throughput. For instance, in Fig. 1 a, when L B was receiving almost no wireless service at the 80th time point, L A could still achieve a throughput of more than 100 Kb. Similar situations are also evident in Fig. 1 b at the 53rd time point, in Fig. 2 a at the 80th time point and in Fig. 2 b at the 50th time point. The reason for these discrepancies is that the network quality can be widely variant between different devices because there may be different numbers of passengers in different compartments and the wireless signal may be more or less unstable at different locations along the train. Because there is no exchange of network resources between devices, it is difficult to ensure that a single device will receive enough bandwidth for its wireless services. This situation leads us to propose the deployment of an interface between users’ wireless devices

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Fig. 3. An illustration of the fog structure established on a train. and the 3G/4G infrastructures to optimize the distribution of limited network resources throughout a train and enhance connectivity.

3.2. Fog structure

For deployment on trains, we propose a fog structure that offers several benefits for network services on trains. First, the fog provides data processing capacity, which can be used to execute several complex algorithms to optimize performance. Second, the fog is much closer to the end users than is the 3G/4G infrastructure. This can help to guarantee the stability of the wireless signal for connecting devices [22] , especially in circumstances of high-speed motion. Third, the fog offers data storage capacity, which provides the possibility of extending mobile applications and wireless services. The fog is composed of several network devices called Personal Gateways ( PGs ), which are evenly distributed along the train, commonly one or two per compartment. As shown in Fig. 3 , these PGs are crucial components of the network infrastructure on the train. On the one hand, these PGs act as an interface layer for wireless services. In a given compartment, passengers can connect their mobile devices to a PG via a short-distance wireless connection, such as a Wi-Fi network [17] . All network services are provided by the PG , which will communicate with Node Bs to obtain bandwidth resources via a 3G or 4G network. On the other hand, these PGs also act as nodes in a wired network on the train. They are arranged along the train like a linear bus network, and each node has two neighbors except those at the two ends. Using this wired network, the PGs are able to communicate with their neighbors to transfer flows. Here, we provide an overview of the process by which the fog optimizes the network services on the train. First, the PGs establish wireless connections with Node Bs, which can provide network resources to the PGs in the form of bandwidth. The amount of resources provided depends on the communication technology used for the connection. The PGs can then distribute these resources to their end users. This step is transparent to the end users, and they will not observe any difference compared with a direct connection. Second, a PG will communicate with its neighbors in accordance with their current network conditions. As discussed in Section 3.1 , when one PG has little available bandwidth, its neighbors may still have extra bandwidth available for additional services. In this situation, the exhausted PG will transfer some of its flows to its neighbors based on a suitable established rule. The bandwidth will be distributed among several PGs during this stage. Af- terward, the network burden for certain PGs will be mitigated. Again, the entire operation is transparent to the passengers. The details of the transfer rule will be discussed in Section 4 . Moreover, as the network edge extension of cloud computing, the fog can provide additional services beyond wireless communication. With commercial cooperation, it is possible for popular mobile applications to deploy some content buffer in the fog. If the content that a user is requesting is available in the fog, then it can be provided directly to the user without connecting to a Node B, especially for certain streaming media such as videos [14] . The entire process executed in the fog will be presented in Section 4.8 .

3.3. Design of the personal gateway architecture

The PG is the basic unit of the fog structure on a train. It is a kind of smart network equipment with computational power and storage capability. On the one hand, it relays communications between end users and Node Bs, just like an ordinary access point. On the other hand, it should also optimize wireless service by means of established settings and

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Fig. 4. An illustration of a Personal Gateway ( PG ). buffered content. Its overall module architecture and function are depicted in Fig. 4 . As shown, a PG consists of 6 different modules. The AC module contains protocol stacks to communicate with Node Bs and obtain cellular network resources. Similarly, the NH module is responsible for providing short-distance wireless network connectivity to end users on the train. For the extendability of future applications, the NH module is compatible with multiple network specifications such as Wi–Fi, WiMAX and Bluetooth. The MS module contains the initial settings of the PG . It can execute the optimization algorithm and handle any exceptions that arise during operation. The BS module is controlled directly by the MS module. Its primary responsibility is to process data flows in accordance with the MS module’s operation, such as shifting flows to or from neighboring PGs . It can also buffer some Internet content in advance. The modules described above provide the main wireless service to the end users. Other modules can provide certain types of assistance. The database module can store information regarding the operation of the PG for maintenance. The UM module handles operations for connecting end users.

4. Cascade shifting ﬂow problem

In this section, we ﬁrst introduce the relevant problem for improving the communication reliability on trains in Section 4.1 and then presented a simple example of the problem in Section 4.2 . To solve this problem, we adopt several assumptions, as described in Section 4.3 , and we then analyze its optimal solution in Section 4.4 . To relax the optimal solution, we analyze both a special case and the general case of the problem in Sections 4.5 and 4.6 , respectively. Subsequently, a localized algorithm is presented in Section 4.7 . Based on this algorithm, an algorithm for providing wireless service based on the fog structure is proposed in Section 4.8 .

4.1. Problem description

We now formally deﬁne the Cascade Shifting Flow (CSF) problem.

Definition 1. Cascade Shifting Flow ( CSF ) problem: Consider a train that is composed of n compartments: c 1 , c 2 , . . . , c n . In each compartment, there is a PG with available bandwidth bi , which is connected to two adjacent PGs (ci and ci +1 ) via a wired link. A user will communicate only with the PG in his or her compartment. The user-driven data flow produced | − | in a compartment i is fi and can be shifted to compartment j over i j shifting hops. The objective is to minimize the maximum shifting hops (delay) of all user flows under the constraint that all final data flows in each compartment must ∗ ≤ satisfy fi bi .

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Fig. 5. The initial user ﬂows distributed on the train.

Fig. 6. The optimal user ﬂows after scheduling.

4.2. A simple example

We illustrate our problem with an example. Consider an instance of the current user ﬂows and available bandwidths on a train, as shown in Fig. 5. Suppose that there are 4 compartments, c1 , c2 , c3 and c4 , with the corresponding PGs PG1 , PG2 ,

PG3 and PG4 , respectively. The current user flows in the compartments are {1, 3, 2, 2}, respectively, and the current available bandwidths of the PGs are {3, 0, 2, 3}, respectively. Because the available bandwidth of PG2 is zero, that PG cannot offer any service at this time; however, 3 data flows are being produced in the corresponding compartment. To allow these data flows to be served, we must shift these 3 flows to other PGs , satisfying the requirement that in each compartment, the final user flow must be less than or equal to the available bandwidth for that compartment, but under the constraint that the maximum number of shifting hops is minimized.

One naïve solution is that we can first shift 2 flows from PG2 to PG1 and then shift 1 flow from PG2 to PG4 , with 1 and 2 shifting hops, respectively. After this shifting process, each data flow can be served by the PGs , and the maximum number of shifting hops is 2. However, this is not the optimal solution, as we can achieve the same results with a maximal shift of 1 hop. To shift 1 flow from PG2 to PG4 , we can first shift that flow to PG3 and then shift 1 of PG3 ’s own flows to PG4 . We call this shifting process “cascade shifting”. Using this method, we shift 4 flows, each with a cost of 1. The user flow distribution after the optimal solution is applied is as shown in Fig. 6 .

4.3. Assumptions

We adopt the following assumptions in this paper.

(1) The user flows are uniformly and independently scattered throughout the train. When the number of flows is large, the number of flows in a compartment of length l will be Poisson distributed [15] . Therefore, this assumption is reasonable. ≤ (2) The total number of user flows is less than or equal to the total available bandwidth of the train, that is, fi bi . > In fact, our solution also works when fi bi . We adopt this assumption solely for convenience of analysis.

(3) The bi and fi values are all integers. This assumption will not always hold, but this approximation does not strongly inﬂuence the overall problem.

4.4. Optimal solution

We construct a graph G ( V , E ) in which each compartment is represented by a vertex. We add a directional edge ( i , j ) = | − | | − | from ci to cj with the cost hij i j . That is, a ﬂow can be shifted from ci to cj with i j shifting hops. Let the number of ﬂows shifted from ci to cj be denoted by xij ; then, the shifting problem can be transformed as follows:

Minimize Max{ h ij }∀ x ij >0 (1a)

s.t. x ji − x ij ≤ b i ∀ i (1b) j j

x ij ≤ f i ∀ i (1c) j

x ij ≥ 0 ∀ i, j (1d)

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In this optimization problem, Eq. (2) is the flow conservation condition, which requires that the final flow in compartment i (the number of flows shifted to ci minus the number of flows shifted out of ci ) is less than the available bandwidth in that compartment. Eq. (3) states that the total number of flows moving out of ci should not be larger than the initial flow in ci . In this formulation, every flow will be shifted at most once between compartments. Based on this transformation, the problem can be solved using linear programming algorithms.

4.5. A special case of the CSF problem

A special case of the CSF problem exists in which the available bandwidth for each PGi is the same. This section focuses on the solution for this special case. We have the following theorem regarding this special case of the CSF problem.

Theorem 1. Suppose that the total data ﬂow is N. If the available√bandwidth bi is the same as all others in the CSF problem, ∗ ( N logN ∗ ) 1 then the maximum number of shifting hops for any user ﬂow is O N n w.h.p . Proof. Suppose that the total length of all compartments on the train (henceforward, “all compartments on the train” are

= L referred to simply as the “train”) is L, such there are n l total compartments. We ﬁrst divide the train into N subsections,

N each of length L . The basic idea is to match the N user flows to the N subsections. Obviously, if we can achieve this perfect match, then the N user flows are “evenly distributed” among all compartments. Consider the case of matching N randomly distributed flows to the same number of subsections on the train by maximally matching a distance of D , where D is the maximum number of shifting hops in our problem. Let the neighborhood of a subinterval R on the train be denoted by N (R ) . By Hall’s Theorem [15] , there exists a perfect match with a maximum moving distance D between the flows and subsections if and only if for every subinterval R on the train, the number of flows contained in R , denoted by f R , is N ( ) , S smaller than or equal to the number of subsections contained in R denoted by N (R ) . We define the discrepancy of any subinterval of the train as the absolute value of the difference between the expected number of flows contained in that interval and the actual number of subsections contained in that interval.√According to the discrepancy theorem of [20,34], we know that w.h.p. , every subinterval has a discrepancy of at most O ( M logN + logN) , where M is the number of the √ ≤ ( + ) ( ∗ ) subsections in a subinterval. Obviously, M N; thus, O M logN logN can be rewritten as O N logN . Based on these = ( ∗ ) , results, if we let D O N logN we can achieve the desired perfect match. That is, each user flow only needs to move ( ∗ ) ∗ a maximum of O N logN subsections to arrive at its corresponding subsection. The number of subsections N logN is

∗ ∗ L L contained within the length N logN N √of the train, where√ N is the length of each subsection. Thus, we ultimately ﬁnd ∗ ∗ N logN ∗ L = N logN ∗ , that the ﬂows only need to be shifted by N l N n which is the number of hops required to arrive at the corresponding compartments.

4.6. The general case of the CSF problem

By the general case, we mean that the available bandwidth of each compartment is not a constant and that these bandwidths may not be equal to each other. We assume that in a time interval T , which may be the interval required for the exchange of beacon information among the PGs , the available bandwidth B for each compartment follows a Poisson distri- −B k ( , ) = e B bution, f k B k ! . We wish to obtain similar results to those in Section 4.5, that is, we wish to determine the bound on the maximum number of shifting hops in this general case. We have the following theorem regarding this general case of the CSF problem.

Theorem 2. Suppose that the total data ﬂow is N, the total available bandwidth is M, and the available bandwidth bi for

e −BB k each c follows the Poisson distribution f (k, B ) = . Then, w.h.p., the maximum number of shifting hops for any user ﬂow √i k ! ξ ∗logξ is O ( ξ ∗ n ) , where ξ = Min { M, N} .

Proof. The proof has two steps. First, we divide the train into√ N subsections and match the user flows to the N subsections. ∗ ( N logN ∗ ) According to Theorem 1, this will require a maximum of O N n hops. Second, we divide the train into M subsections and match the available bandwidth to the M subsections. The basic idea is to first shift the flows to their corresponding subsections and then shift√ them again to their corresponding compartments. If we can complete the second shifting process ∗ ( M logM ∗ ) with a maximum of O M n hops, the theorem is proven. To prove the second step, we assume that the total available bandwidth M is uniformly distributed throughout the train. When M is large, the number of flows in a compartment of length l will be Poisson distributed with a mean of

Ml L [15]. Using an approach similar to the proof of Theorem 1, it is not diﬃcult to show that when the train is uniformly

1 − ( 1 ) α In this paper, the term “w.h.p.” is used as an abbreviation for “with high probability”, which means “with probability exceeding 1 N for any constant α ≥ 1”.

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divided into M subsections,√ the maximum number of shifting hops from the current subsections to the corresponding band- ∗ ( M logM ∗ ) width is bounded by O√ M n √w.h.p . Obviously, the total number√ of shifting hops from the users to the corresponding ∗ ∗ ∗ ( M logM ∗ + N logN ∗ ) x logx PGs√is bounded by√ O M n N n . When√ x is large, x is a monotonically decreasing function; therefore, ∗ ∗ ξ ∗ ξ ( M logM ∗ + N logN ∗ ) ( log ∗ ) , ξ = { , } O M n N n can be rewritten as O ξ n where Min M N .

4.7. Localized ﬂow shifting algorithm

The computing cost may be very high for the optimal algorithm presented in Section 4.4 because it is an integer linear programming ( ILP ) problem. Another problem with this optimal algorithm is that it requires the collection of information for the entire train, which may lead to unacceptable delay and much more beacon information exchange.√ ξ ∗ ξ From the previous section, we know that the optimal solution can be obtained with a maximum of O ( log ∗ n ) shifting √ ξ ξ ∗logξ hops w.h.p . This suggests that we can collect only the state information for the O ( ξ ∗ n ) neighbors of each PG to design a localized algorithm. In this section, we present our localized optimal shifting√ algorithm. The basic idea is to divide all of ξ ∗logξ the compartments on the train into several subsections, each of size k = O ( ξ ∗ n ) . In each subsection, the PGs exchange beacon information with each other. Below, we present the localized algorithm for each subsection. Our localized algorithm is presented in Algorithm 1 . In our algorithm, the available bandwidths and the user ﬂows are

Algorithm 1 Localized cascade shifting flow ( L-CSF ). , , . . . , Input: the flows f1 f2 fk that are distributed in different compartments from 1 to k, respectively; the √bandwidths ξ ∗ ξ , , . . . , = ( log ∗ ) b1 b2 bk that are available for different compartments from 1 to k, respectively; and the value k O ξ n , which is the size of each subsection; , , . . . , Output: the flow states s1 s2 sk among PGs 1 to k; 1: s 1 = b 1 − l 1 ; 2: output s 1 ; 3: i = 2 ; /* the iterator for the outer loop */ = − 4: si fi ; 5: j = 1 ; /*the iterator for the inner loop*/ − i 1 < 6: if j=1 s j 0 then /* shifting flows */ + ≥ ≤ 7: while bi s j 0 && j i do = + 8: bi bi s j ; /* update bi */ = 9: s j 0; /* update s j */ 10: j = j + 1 ; 11: end while = + 12: s j bi s j ; 13: end if − i 1 ≥ 14: if j=1 s j 0 then /* shifting bandwidths */ + < ≤ − 15: while si s j 0 && j i 1 do = + 16: si si s j ; /* update si */ = 17: s j 0; /* update s j */ 18: j = j + 1 ; 19: end while ≥ 20: if j i then /* calculate si */ = + 21: si si bi ; 22: else = + 23: s j si s j ; = 24: si bi ; 25: end if

26: output si ; 27: i = i + 1 ; 28: end if 29: if i < k then 30: goto step 4; 31: end if

all regarded as elements that can be shifted. Obviously, if we allocate an amount of bandwidth m from ci to cj , then there are m flows that can be shifted from cj to ci . For each PG ci , we first add a variable si to denote the flow state of ci . If si is a positive number, it means that ci has a maximum bandwidth of si available to its left-neighbor (henceforth, we refer to

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ci +1 as the “right-neighbor” of ci and to ci −1 as the “left-neighbor” of ci ). If si is a negative number, it means that ci has si = = − , flows that need to be shifted to its right-neighbors. For example, if si −1 3 and si 2 then ci can shift 3 flows to ci −1 and = − , shift 2 flows to ci +1 . Initially, we let si fi which means that ci has fi flows to be shifted to its right-neighbor. The basic idea of the algorithm is to “push” the redundant flows or redundant available bandwidth from c1 to ck one by one. If ci , , “pushes” bandwidth to ci +1 then ci +1 first shifts its own flows to ci , and if ci “pushes” flows to ci +1 then ci +1 first provides its own bandwidth to ci . For ci , we calculate the total number of flows remaining to it. If the number is negative, then the bandwidth should be used to satisfy those flows as much as possible. To this end, those flows that cannot be satisfied ≤ should be gradually shifted from c1 to ci . Specifically, the available bandwidth of ci can be updated according to all sj (j i), and then, those sj values can also be updated. Afterward, if the total number becomes positive, it means that the flows ≤ remaining to ci can all be satisfied after the shifting of the flows. Therefore, all sj (j i) should be updated from left to right, and then, si can be output. The procedure continues until all compartments in this subsection have been optimized. Using this method, the maximum shifting hops can be minimized. In Algorithm 1 , the length of every subsection is k . For every compartment, the algorithm traverses all of the compartments to its left. Therefore, the time complexity of Algorithm 1 is O ( k 2 ), and consequently, this algorithm can be executed by every PGs very rapidly. For PGs in the same subsection, because the input is the same, each PGs can obtain a common solution and can perform the shifting process independently. In other words, after the beacon exchange process, the PGs no longer need to negotiate with each other and can simply complete the shifting process locally.

4.8. Optimized wireless services based on the chained fog structure

In wireless services based on the fog, there are three kinds of participants, i.e., end users, PGs and Node Bs. During the initialization stage, every PG has an established wireless connection with a Node B. These connections can be provided by cellular networks, such as 3G and 4G networks. The PGs are able to obtain network resources from the Node Bs, and the amount of resources available depends on the communication technology used and the connection conditions. Subsequently, every PG provides access point (AP) service to the compartment in which it is located by establishing a short-distance network, such as a Wi-Fi network. After initialization, the PGs are in the service stage. End users can connect to the PGs in the same manner as they would connect to an AP. Because the end users obtain network services via the PGs , these PGs can check the user flows to see whether they are requesting buffered streaming content, e.g., videos. If so, the PGs are able to provide this portion of the flows immediately without fetching them again from the Node Bs. More importantly, every k sequential PGs form a subsection. The PGs in a subsection execute Algorithm L-CSF to optimize their flow loads. The entire process is presented in Algorithm 2 . For a total of n compartments, the time complexity of this algorithm is O ( n ).

Algorithm 2 Optimized wireless services. Input: value of k , which is the size of each subsection; Output: optimized wireless services; 1: for Every PG do 2: PG establishes connection with a Node B; 3: PG establishes AP service; 4: PG provides wireless service to connecting end users; 5: end for 6: for Every PG do 7: if End user asks for buffered content then 8: PG provides the buffered content immediately; 9: end if 10: end for 11: Every k PGs form a subsection; 12: for Every subsection do 13: PGs in the subsection execute Algorithm L-CSF; 14: end for

5. Evaluation

To validate the effectiveness of our proposed algorithm, we conducted extensive simulations using MATLAB 8.3. We sim- ulated the network scenario on a train where the flows and bandwidths are both Poisson distributed. Some general parameters are listed in Table 1 . As part of the evaluation, three other algorithms were also considered for comparison. The first is the greedy scheduling algorithm. In this algorithm, a PG collects bandwidth information from its two neighboring PGs . If it has flows that need to be shifted, it transfers them to the neighboring PG with more redundant available bandwidth. The second is the right-hand scheduling algorithm, in which a PG will shift its redundant flows to its right-neighbor PG . The last is the raw algorithm,

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Table 1 Simulation parameters.

Parameter Value

Simulation instances 10 0 0 Unit size of ﬂows (kb) 1 Unit size of bandwidth (kb) 1 Flow size (kb) Poisson distribution with λ = 10 Bandwidth (kb) Poisson distribution with λ = 20 The value of k 20

Fig. 7. Maximum number of shifting hops vs. ﬂow size.

in which there is no scheduling of flows and the PGs simply transmit their own flows. For convenience of discussion, our proposed algorithm is referred to as CSF , the greedy scheduling algorithm is referred to as GRD , the right-hand scheduling algorithm is referred to as RTH , and the raw algorithm is referred to as RAW . In the simulations, these four algorithms were compared based on three metrics, i.e., the maximum shifting hops , the packet loss rate and the packet transfer rate . Among them, the maximum shifting hops is a special metric for the CSF problem defined in Section 4 . The packet loss rate is the ratio of the number of lost flows to the total number of original flows. It reflects the quality of the wireless flows because a high packet loss rate means that many packets cannot be sent out. Finally, the packet transfer rate is the ratio of the number of successfully transferred flows to the total number of flows. Because no packets are shifted in RAW at all, this algorithm was not considered in the simulations addressing the maximum shifting hops or the packet transfer rate. In the first simulation study, the factor that was varied was the flow size, which was increased from 10 kb to 20 kb. Fig. 7 plots the results for the maximum number of shifting hops for CSF , GRD and RTH as a function of the flow size. It is apparent that the maximum number of shifting hops generally increases with increasing flow size for all algorithms. Among them, CSF had the lowest maximum number of shifting hops. Therefore, from the perspective of the flows, this algorithm achieves the objective of the CSF problem as stated in Section 4 . Specifically, for a flow size of 20 kb, the maximum numbers of shifting hops for GRD and RTH are approximately 610% and 650% larger, respectively, than that for CSF . The reason is that in CSF , the PGs share bandwidth with their neighbors. When flows from neighbors arrive, the PGs will send them preferentially, thereby limiting the maximum number of shifting hops. Fig. 8 shows histograms illustrating the performances of CSF , GRD , RTH and RAW . It is evident that the packet loss rate increases with an increasing flow size for all algorithms. Obviously, RAW has a much higher packet loss rate than the other algorithms because it has no mechanism for flow scheduling. For further clarity, we also provide Fig. 9 , which plots only the results for the other three algorithms, excluding RAW . It is seen that RTH has the highest packet loss rate among these three algorithms. CSF exhibits slightly better performance compared with GRD as the flow size increases. This is because CSF and GRD distribute the flows more intelligently than RTH does. In Fig. 10 , the packet transfer rate results for these three algorithms are presented. The figure shows that as the flow size increases, the packet transfer rates all increase to some extent, and the differences among the algorithms gradually grow. CSF exhibits a steeper rising tendency than the other algorithms for flow sizes between 15 kb and 20 kb. Specifically, for a flow of 20 kb, CSF outperforms GRD and RTH by approximately 200%. A higher packet transfer rate means that the flows are distributed more evenly to improve the performance of the wireless network. Meanwhile, for CSF , the maximum number of shifting hops does not increase considerably with a higher packet transfer rate, as shown in Fig. 7 . In the second simulation study, the factor that was varied was the bandwidth, which was increased from 10 kb to 20 kb with the flow size fixed at 10 kb. Fig. 11 shows the results for the maximum number of shifting hops for CSF , GRD and RTH

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Fig. 8. Histogram: packet loss rate vs. ﬂow size.

Fig. 9. Packet loss rate vs. ﬂow size.

Fig. 10. Packet transfer rate vs. ﬂow size.

as a function of the bandwidth. As seen, the maximum number of shifting hops decreases with increasing bandwidth for all algorithms. Among them, CSF has the lowest maximum number of shifting hops. Specifically, for a bandwidth of 10 kb, the maximum numbers of shifting hops for GRD and RTH are approximately 360% and 420% larger, respectively, than that for CSF . These results show that CSF is able to effectively decrease the maximum number of shifting hops. Fig. 12 shows histograms illustrating the performances of CSF , GRD , RTH and RAW . It is evident that the packet loss rate decreases with an increasing flow size for all algorithms. The figure shows that RAW has a much higher packet loss rate than the other algorithms. Hence, we also present Fig. 13 , which shows the results only for the other three algorithms, excluding

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Fig. 11. Maximum number of shifting hops vs. bandwidth.

Fig. 12. Histogram: packet loss rate vs. bandwidth.

Fig. 13. Packet loss rate vs. bandwidth.

RAW , for clearer observation of their behavior. It is apparent that RTH has the highest packet loss rate among these three algorithms. CSF exhibits slightly better performance than GRD , especially for a bandwidth close to 10 kb. In Fig. 14 , the packet transfer rate results for these three algorithms are presented. The figure shows that as the flow size increase, the packet transfer rates for all algorithms decrease and eventually nearly converge. CSF exhibits a steeper declining tendency than the other algorithms for bandwidths between 10 kb and 15 kb. Specifically, for a bandwidth of 10 kb, CSF outperforms GRD and RTH by approximately 200% and 270%, respectively. In the third simulation study, the factor that was varied was the value of k , increasing from 15 to 25 with the flow size and the bandwidth both fixed at 10 kb. k is equal to the number of compartments, i.e., PGs , in a single subsection. Fig. 15

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Fig. 14. Packet transfer rate vs. bandwidth.

Fig. 15. Maximum number of shifting hops vs. the value of k .

Fig. 16. Histogram: packet loss rate vs. the value of k . shows the results for the maximum number of shifting hops for CSF , GRD and RTH as a function of k . In this figure, all curves are increasing to some extent. CSF has the lowest maximum number of shifting hops. Specifically, for a k of 25, the maximum numbers of shifting hops for GRD and RTH are approximately 450% and 350% larger, respectively, than that for CSF . The results show that the performance of CSF is not strongly influenced by the value of k . Fig. 16 presents histograms illustrating the performances of CSF , GRD , RTH and RAW . The figure shows that the packet loss rate decreases with increasing k for all algorithms except RAW , because RAW operates completely independently of the value of k . Therefore, we also provide Fig. 17 , which contains the results for only the other three algorithms. It is evident that RTH has the highest packet loss rate among these three algorithms. Generally, CSF exhibits slightly better performance than GRD .

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Fig. 17. Packet loss rate vs. the value of k .

Fig. 18. Packet transfer rate vs. the value of k .

In Fig. 18 , the packet transfer rate results for these three algorithms are presented. The ﬁgure shows that as the value of k increases, the packet transfer rate also increases to some extent for all algorithms. The increases for GRD and RTH are smaller than that for CSF , for which the packet transfer rate increases by approximately 30%. At larger values of k , CSF can distribute the ﬂows more evenly among the PGs with only a slight increase in the maximum number of shifting hops, as shown in Fig. 15 .

6. Conclusion

Recent years have witnessed a dramatic increase in the popularity of wireless network services in public places. With the widespread use of mobile devices and networks, users typically require some kind of reliable and effective wireless service at all times, even during their daily commutes via fast-moving vehicles, such as subways in the city or high-speed railways for cross-country travel. In the study reported in this paper, we conducted extensive real experiments on the quality of 3G connections for end users. On the MRT lines in Hong Kong, we recorded thousands of measurements of the network throughputs for sending and receiving achieved by two wireless devices. From these measurements, we found that the current 3G service is far from stable. When one device’s network quality is good, the other’s may still be poor. These findings led us to propose a fog structure with the intent of improving the reliability of communications on trains. The proposed fog structure is an intermediate layer between the end users and the 3G/4G infrastructure (such as Node Bs) and addresses the problem of unstable and unreliable connections. It comprises a few end devices called Personal Gateways ( PGs ) distributed throughout different compartments of the train, which can cooperatively share their communication capabilities to connect end users to the 3G/4G infrastructure. We then formulated the Cascade Shifting Flow (CSF) problem and proved that its optimal solution can be obtained with high probability using only limited local information. Based on this finding, we designed a distributed flow-shifting algorithm to solve the problem. Extensive simulation results show that the algorithm can improve the connectivity and reliability of wireless services by reducing the packet loss rate with a bounded delay. Accord- ing to these simulations, our algorithm can reduce the packet loss rate by approximately 40% compared with the worst result, and the maximum number of shifting hops (delay) can be reduced more than 600% compared with other algorithms.

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In our future work, we intend to conduct further real experiments involving the practical deployment of chained fog networks on trains to test their performance and the effectiveness of the algorithm. Moreover, the proposed fog structure can also be used in other public transport systems, such as buses and steamers. We plan to continue our research concerning these different scenarios. We believe that the proposed fog structure is a promising solution schema for many practical scenarios to improve the reliability of wireless connectivity.

Acknowledgment

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61572206 , 61370 0 07 , 61305085 , U1536115 , the National China 973 Project under Grant No. 2015CB352401, the Chinese National Re- search Fund (NSFC) Key Project under Grant No. 61532013, the National Key Technology Support Program under Grant No. 2015BAH16F00/F01, the Natural Science Foundation of Fujian Province of China under Grant No. 2014J01240, and the Pro- motion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University under Grant No. ZQN-PY308.

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