Modeling congestion considering sequential coupling applications: A network-cell-based method

https://doi.org/10.1016/j.physa.2022.127668Get rights and content

Highlights

  • The impact of sequential coupling on traffic congestion is investigated.

  • Sequential coupling applications are modeled as network cells and their connections.

  • A network-cell-based metric to evaluate application quality is presented.

  • The proposed method is applied to modeling congestion of real metro systems.

Abstract

Sequential coupling of applications is the major cause of traffic congestion and low application quality. Modeling traffic congestion under sequential coupling applications is the primary means to explore congestion mechanism, which can further support application design and adjustment to improve application quality. Existing congestion models concentrate more on traffic flow modeling based on network components, with little consideration of the influence of network application and its coupling. This paper proposes a network-cell-based congestion model for describing dynamics of congestion propagation under sequential coupling multi-applications. First, the basic characteristics of network applications are analyzed, and network applications are abstracted into network cells as functional units, which is specifically described from three perspectives: Structure, function and connection. The dynamic process of network can be modeled as intracellular reaction (single application function behavior) and intercellular interaction (coupling behavior of multi-applications). Furthermore, a network-cell-based metric to evaluate application quality is presented, and the implementation algorithm of the model is also given. Numerical simulations are implemented with comparison of typical information flow model to verify the model. Moreover, the proposed model is applied to Chengdu Metro system case to show the applicability. Furthermore, the influence of sequential coupling on congestion is further investigated, and the results show that the larger coupling strength corresponds to less congestion in peak period. This study provides guidance for application design and management to improve application quality of transportation networks.

Introduction

Application quality of network systems has been paid much attention [1], [2], [3], [4], [5], [6], [7], [8], which is greatly affected by traffic congestion under coupling multi-applications. In transportation systems, multiple lines of transit and metro systems are typical applications, which can be combined in sequence to transport passengers from place to place. When a certain line congests, coupling lines are prone to be congested because of passengers’ re-routing choice, which may further lead to unexpected travel delay and low quality of metro lines. Modeling the congestion evolution triggered by user demands for multi-applications is significant in congestion mechanism analysis, which can further guide the network application design and management to improve the application quality [9].

Exploring network applications and the coupling between them is the basis of congestion modeling. Network application is the function provided by the network systems [10], [11], such as messaging [12] and Web browsing [13] in communication networks, passenger transporting [14] in transport systems. The capacity of different applications shows different, which is more determined by application configuration at application layer rather than the capacity of a certain node or edge from physical layer. For public transportation systems, especially metro systems, various metro lines are different network applications, which can satisfy different travel demand of passengers. The capacity of a certain application is determined by many functional attributes, such as departure time interval, capacity and direction of lines [15], [16]. With the expanding scale of the transportation systems, driven by various travel demands, multi-applications are combined under complex sequential coupling at application layer. For instance, during the traveling to another place, passengers may take different subway lines. The traffic flow distribution caused by various route choices is typical result of sequential coupling, which may lead to traffic congestion and excessive waiting time. Studying network congestion under sequential coupling application is of great significance, which can further benefit the design and adjustment of the applications.

Previous research on congestion models can be classified into two categories: local congestion model and global congestion model. Research on congestion models originated from the theory of probabilities and telephone conversations proposed by Erlang [17], in which congestion was regarded as the traffic accumulation caused by queuing. The queuing models are composed of three parts: Arrival process, queuing discipline and service process [18], [19], which can describe the traffic transmission process of each node. The congestion models based on queuing theory have been widely applied, such as M/M/1, M/M/C, M/D/1, etc. [20], [21]. In these models, the first letter denotes the inter-arrival time distribution, the second letter denotes the service time distribution and the last letter denotes the number of servers [18]. The inter-arrival time distribution and service time distribution are mainly determined by data analysis, in which exponential distribution is the common assumption [22]. Local congestion models concentrate more on local congestion dynamics of each node, in other words, the dynamics of nodes is modeled under strict and restrictive assumptions [23], which is difficult to extend to model congestion propagation and evacuation in whole network.

Therefore, global congestion models attract many scholars, such as cell automata, cascading failure model [24], [25], [26], [27], information diffusion dynamic model [28], [29], [30]. Cellular automata is typical microscopic model, in which the network space is often divided into be two-dimensional square cells and traffic congestion is described by passengers’ dynamics in cells [31], [32]. The rules describing passengers’ behaviors are local, i.e., passengers’ movement is affected by state of neighbor cells at physical layer. However, traffic congestion is more influenced by global rules from application layer, such as the various route choice of passengers and train time interval in metro systems, which leads to heterogeneity of passengers’ behavior and complexity of microscopic model. Load-capacity models for modeling cascading failures depicted the load redistribution process from failing components to adjacent normal components at mesoscopic level [25], which has been widely used in transportation systems [33]. Considering the variations in load capacity and functionality, Guo et al. [34] explored the effect of the heterogeneity in nodal load capacity and types of nodes on cascading failures. The coupling relationship in these models was the connection of nodes at physical layer. However, the coupling between nodes shows more complex with logic relations [35], [36], [37]. To concretely describe traffic dynamics close to reality, information flow model was proposed, in which the user demands were modeled as OD (Origin–Destination) pairs [8] and network application is simply described as the processing ability provided by each node. The dynamic process included traffic generation, transmission, and removal [38]. Considering traffic is only the operation result of applications, recent studies have realized the impact of applications on congestion propagation, and defined three categories of applications based on application path, including random, customized, and routine applications [39]. Based on this, Zhang [39] studied the impact of three types of applications on network performance, and further proposed an optimization method of network topology under a given application scenario based on genetic algorithm. Zhang [40] analyzed that the traffic flow distribution under different application scenarios showed great difference, and evaluated node importance under multi-applications, which could further help to allocate network resources. To simulate real network, more details are considered in global congestion models, such as network topology [41], node capacity [42], characteristic of traffic flow [43], routing strategy [44], application feature [45], transmission of travel decisions and experiences [46], etc., which are all acting on network components at physical layer finally. It will lead to the complexity of model in congestion analysis. Furthermore, it is difficult to extend existing models when considering more application attributes and sequential coupling from application layer. However, application concentrate more on logic rules, not confined to a certain component in network systems.

Inspired from the research on systems biology, complex diseases, such as cancer and tumor, are considered to be caused by pathological changes at cellular level [47], [48], and directly affected by the changes of cell function and intercellular behaviors. Organism is the most complex network systems, and diseases are the most complex network failure. The study of pathogenesis at cellular level more focuses on the behaviors of cells than that of single molecules [49], since cell is the basic structural and functional unit of organism [50], and cell-based research benefits the understanding of function changes in diseases and simplifies the complexity of modeling as well.

In this paper, each application in the network is modeled as a network cell, then the multi-applications can be described as multiple network cells through cell connection. Furthermore, the congestion evolution under the network multi-application with sequential coupling can be described as the congestion propagation process based on network cells, cell connections and cell operation rules. A network-cell-based congestion model considering sequential coupling applications is proposed. For the proposed model, we compared it with the information flow model, and verified the model based on theoretical derivation and simulation analysis. To prove the applicability, we applied the proposed model to Chengdu Metro System, and analyze the phase transition point in three typical periods: Peak period, flat hump period and low peak period. Simulation results indicate that our model can effectively describe the congestion process considering sequential coupling applications. It can further support planning and adjusting multi-applications considering sequential coupling to guarantee application quality.

Section snippets

Functional unit of network: Network cell

Network application is a variety of functions provided by the network to users, which can be simply understood as the OD (Origin–Destination) with different processing function, such as metro lines in the transportation network and data transmission in the computer network. In this paper, we aim to investigate applications in metro and bus systems, a representative of routine applications. Through analysis of application operation, network application is regarded as the basic unit of network

A network-cell-based congestion model considering sequential coupling applications

Because of limited resource, congestion is often triggered by extra user demands beyond maximum capacity. In this section, a novel network-cell-based congestion model is proposed, in which congestion propagation is regarded as cell responses affected by external-cellular environment. Here, external environment is used to describe user demands for applications, and cell operation rules are established to model the interactions between users and network applications. Moreover, a

Model validation

In this section, we analyze the effectiveness of the proposed model through comparison with information flow model. In the network-cell-based congestion evolution model, there exist user traffic generation from external environment and removal at functional site on network cells. Similarly, the widely-studied information flow model also has typical characteristics of traffic generation, transmission and removal.

We compare and analyze the simulation results of the proposed model and the

Case study

To prove the applicability, the proposed model is applied to Chengdu Metro System. In this section, we first investigate the topology and application attributes of Chengdu Metro System, which is the basis of modeling and parameter setting. Then, the congestion model based on network-cell is established. Moreover, congestion propagation during different periods is simulated, such as peak period, flat hump period and low peak period. Simulation results indicate that our model can describe the

Conclusions

With various user demand increasing, multi-applications are coupled in sequence to provide service, which greatly affects the congestion propagation. Previous congestion models mainly focus on traffic dynamics on physical layer, with little consideration of the impacts of application configuration and its coupling from application layer. To investigate congestion evolution under sequential coupling applications, this paper proposed a network-cell-based congestion model, in which network

CRediT authorship contribution statement

Xin Zhang: Conceptualization, Methodology, Writing – original draft, Writing – review & editing. Ning Huang: Methodology, Funding acquisition, Project administration. Lina Sun: Methodology, Validation, Investigation. Xiangyu Zheng: Validation. Ziyue Guo: Resources.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 61872018) and National Natural Science Foundation of China (Grant No. 61773044).

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