Elsevier

Computer Communications

Volume 178, 1 October 2021, Pages 161-168
Computer Communications

Maintainable stochastic communication network reliability within tolerable packet error rate

https://doi.org/10.1016/j.comcom.2021.07.023Get rights and content

Abstract

The communication networks are complex and considered a stochastic flow network. This throws enormous challenges for the service provider to provide a desired Quality of Service (QoS) to the customer. Due to the stochastic behavior of the network, ensuring QoS requires serious efforts to make the entire system work within the given time constraint, cost, and failure rate. When the communication problem is time-bound, providing a quick and reasonable solution with a permissible error rate is of great importance. Therefore, in this paper, fast solutions to data communication problems are proposed to send the required d units of user’s data from the desired source node to the destination node within some constraints such as permissible error rate ε, time constraint T and maintenance budget constraints B. System reliability and the performance of the proposed approaches are evaluated using minimal paths. All the minimal flow vectors evaluated from minimal paths that satisfy all the above-mentioned constraints are considered for network reliability evaluation. Further, the proposed approaches are observed as faster concerning computation time than the existing approaches.

Introduction

Some of the real-world networks such as communication, rail, electrical, transportation systems, etc., are complex and evolving at a tremendous pace. This throws enormous challenges for the service provider concerning reliability, QoS, maintainability, and scalability of networks. Due to the stochastic behavior of most of these networks, ensuring QoS requires much more sophistication and serious efforts to make the entire system work with optimal delivery time, low maintenance cost, and minimum possible failure rate. These challenges have attracted the attention of researchers working in different domains, and a variety of different approaches have been proposed to provide optimal solutions for some constrained optimization problems (see for example [1], [2], [3]). In this paper, the study is focused on a communication network. Here, the communication network is considered as Stochastic Flow Network (SFN) [4], [5], [6] with unreliable nodes. In SFN, the capacity of the nodes and links are varying in a range of values. The nodes are unreliable so, nodes are considered erroneous and each node can send data with a transmission error rate. In this case, accurate delivery of packets is the prime performance indicator to maintain QoS in the communication network. When the communication problem is time-bound, providing a quick and reasonable solution is also of great importance. Therefore, the prime concern of this paper is to send d units of data from the source node to the destination node within a permissible transmission error rate ε, time constraint T and under maintenance cost B.

The network service provider and the customer agree on a contract to maintain the smooth functioning of the network operation. The service provider ensures the QoS to the customer by measuring some network parameters, e.g. availability, delay, loss of the packets. The transmission of accurate data is the prime concern of any enterprise network. Among all the enterprise networks, the computer network is mostly used for the flow of data or information. The computer network is formed with nodes and links where nodes represent transmission devices, and links represent the connection between them. The transmission link consists of optical cables as well as fiber cables. The transmission device or links have an engineered capacity, and they may fail. The computer network is considered an SFN  [5], [6], [7], [8], [9] where transmission links may have several states and capacity values.

The availability and the robustness of communication networks strongly influence the QoS of the users’ data transmission from some source nodes to the target or destination nodes, system reliability is one of the main concerns. If all the users can send data successfully between the desired nodes then the system is called reliable. The reliability can be calculated for two terminals (only one pair of source node and destination node (2TR)) or for many terminals (mTR). Some of the algorithms are available for finding the shortest path between the desired nodes [4] in a definite network. However, most of the real-life networks are stochastic, and the algorithms [4], although useful, do not provide complete solutions due to multi-criteria optimization issues associated with problems. Researchers made some modifications in the algorithms of shortest path problems and provided some constraint-based optimization techniques [2], [10] to address real-world problems over the past few decades. The constraint can be in the form of transmission time, budget, transmission error rate, and so on. Among all the discussed constraints, numerous methods have been proposed for the successful delivery of the data within a given time bound [6], [11], [12], [13], [14]. Yeh [15], [16] proposed solutions for system reliability evaluation methods for networks having cost and capacity constraints. Yeh [17] also proposed an improved algorithm for an SFN with unreliable node considering the selection of budget constraint-based path sets. However, in the above-mentioned approaches, maintainability was not considered for the evaluation of the performance of the communication system. Maintenance cost is the cost involved in maintaining a network to ensure effective and reliable communication. If an SFN is able to fulfill user’s demand within the given maintenance cost then it is called as maintainable SFN. In some of the studies, SFNs have been analyzed considering the maintenance cost within a specified budget [12], [18], [19]. Some studies are on cloud platform where reliability and availability of the system resources are great concern [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31].

In all the discussed research works, performance standards of communication networks are defined using several criteria such as packet transmission time within a time constraint, budget constraint and by sending data through a constrained quickest path. However, in the above-mentioned papers, the accuracy rate is not considered for the transmission of data between the desired nodes; source and destination. In the real-world communication network, node may be unreliable and may send data with some transmission errors. The rate of error transmission at any node is computed as the ratio of incorrectly received data packets to the total number of packets received, termed as packet transmission error rate (PTER). A packet is declared incorrect if at least one of the bits is erroneous in it. Packet transmission error rate is considered a key performance index of QoS in computer networks. While PTER is an important factor reflecting the QoS in large networks, it always remains a challenge to estimate it accurately. Earlier, statistical sampling of network traffic is used to estimate PTER [32]. The packet transmission error rate is considered by the researchers working in different areas, e.g., wireless network, cognitive radio network, etc. Choudhury et al. [33] optimized the user throughput by varying the physical layer data rate and corresponding payload size based on PTER constraint in a wireless local area network. Zhan et al. [34] used channel coding based approach to minimize PTER without retransmission of packets in a low latency constrained based application. Yong et al. [35] provided an upper bound to evaluate the PTER of a conventional transmission system of a wireless network. Nadir et al. [36] derived an upper bound of the probability of packet error in the cognitive radio networks. Zhang et al. [37] optimize the spectrum sensing time and PTER in cognitive IoT. While PTER serves as one of the most important quality measures, delivery latency is undoubtedly another fundamental measure for QoS. Lin et al. [6] studied delivery reliability of a communication network under a permissible PTER and latency to incorporate the practice followed in service level agreements between service providers and customers. They consider an SFN where each component has a range of flow states and a permissible PTER. System is found as reliable if user can send a specified data amount d from the desired source and destination nodes without the PTER exceeding a fixed permissible error rate η. A path from a source node to destination node is called as minimum if the path contains no cycle and removal of a link from the path disconnect both the path between both the nodes. A minimal path based approach is used to find all the minimal path vectors (MPVs) to find the lower boundary points for (d,T,B,η) such that the network delivers user’s demand d under the permissible error rate η. From the literature survey, it motivated us to find system reliability considering most of the constraints such as time, packet transmission error rate, maintenance cost.

The present work aims to provide system reliability of a SFN within some constraints. The approach is an extended version of Lin et al. [6] approach for Maintainable Stochastic Flow Networks (MSFNs) with the strategy that those MPVs that cross the PTER are checked and eliminated early in the analysis. This results in a considerably smaller set of qualified MPVs which leads to reduction in the complexity of system reliability evaluation to a great extent. Since, nodes are also assumed to have stochastic behavior in [6], the same assumption is made in the present work. This means each component of the given network changes its state randomly over a finite range. All possible MPs that can send the maximal amount of data within time constraint T, maintenance budget constraint B and tolerable PTER ε are generated to evaluate the system reliability. Two approaches are proposed to evaluate performance of the system. In the first approach, MPs are used for the creation of MPVs having multiple disjoint paths from the desired source node to the destination node. All the generated MPVs are employed to evaluate system reliability. Once the most reliable, maintainable and error tolerable MPV is obtained, data is sent through the associated multiple disjoint paths simultaneously to reduce the delivery latency. A second approach is presented for fast and reliable data transmission under the given constraints. Instead of evaluating reliability for the entire network, a threshold probability of successful data transmission under the given constraints is set. The first path that crosses the threshold is selected to minimize system overhead in data delivery. Sometimes, it is not possible to find disjoint paths that fulfills all desired constraints (time, maintenance budget, probability threshold, tolerable packet error rate (TMPE)). In that case, user’s data is split into multiple segments, and the process is repeated until one can find a set of disjoint paths that satisfies TMPE constraints.

Both the proposed approaches are different to each other. In the first approach, the best suitable path is selected for user’s data transmission without compromising in the QoS of the system. But, it is a time consuming process and increases time complexity. In the second approach, a faster yet reliable set of disjoint paths is found for data communication. The second approach assigns more priority on the time complexity than the selection of the best suitable path.

Major contributions of the paper are summarized below:

  • Find all the minimal paths and minimal path vectors in the MSFN.

  • Send data through the most reliable, maintainable and error tolerable MPV using Method 1 in Section 3.1.

  • Fast and reliable data transmission by applying threshold probability under the given constraint using Method 2 in Section 3.2.

The paper is organized as follows. Section 2 is used to show problem formulation. Section 3 presents the proposed approaches for the selection of disjoint path sets under the decided TMPE constraints. Section 4 discusses the approach for the computation of system reliability evaluation. In Section 5, computational complexity of the proposed approaches are computed. Section 6 illustrates the working of both the approaches using a toy network. Section 7 concludes the proposed work and enlighten some future scope of the work.

Section snippets

Problem formulation

Let, G=G(N,E,L,X,C,W,ε) be an MSFN where, N={ni|1i|N|} as the set of nodes and E={ej|1j|E|} as the set of links. The nodes and links are communication devices that need different amount of time to start their functioning in terms of data transmission in the network. Here, the start up time for each element is named as lead time. The lead time vector is expressed as L={li|1i|N|+|E|} which contains lead time of nodes/links. The flow vector X is represented as X={xm|1m|N|+|E|} (xm is the

Proposed approaches

This section addresses two problems; Problem 1, Problem 2 by proposing two solutions in Method 1 and Method 2, simultaneously. The detailed description about the methods are provided in the following sections.

System reliability evaluation approach

In this section, it is aimed to provide formulation for the system reliability for the user’s successful data delivery in the SFN. For that, the user selects a quickest path or a set of disjoint paths within (T,B,ε) constraints. While finding the solution, it is required to concentrate on system overhead minimization. Two different approaches are discussed in the present work. Basic aim of first approach is to generate all possible disjoint sets of MPs which can send d units of data within (T,B,

Computational complexity

In this section, computation complexities of the proposed methods (in Section 2) for system reliability evaluation is discussed.

Mathematical analysis

The steps of the proposed approaches (in Section 2) are well explained with the help of a directed toy network containing 5 nodes and 8 links (shown in Fig. 1). As the network is an SFN so, the node/link bi has various flow levels ranging from minimum value 0 to capacity cbi along with the probability of their occurrences. All the necessary information about the nodes/links are provided in Table 2. It contains cost, lead time, error rate and capacity levels with their occurrence probability.

Conclusions and future scope

In this paper, system reliability of the SFNs under time, maintenance budget and tolerable PTER constraints has been studied. With an aim to provide a solution to the problem of data transmission in an MSFN under the defined constraints, two different approaches are proposed. In the first method, system reliability is evaluated for all possible generated MPs that can send given amount of data within the constraints; time T, maintenance budget B and a tolerable PTER ε (i.e., TMPE constraints).

CRediT authorship contribution statement

Suchi Kumari: Conceived the idea and discussed it with all co-authors, Formulated problems, Developed the proposed approaches. Rajesh Kumar: Formulated problems, Developed the proposed approaches. Seifedine Kadry: Evaluated the system reliability and proofread the paper. Suyel Namasudra: Calculated computational complexity and write up of this work. David Taniar: Analyzed the proposed approaches mathematically.

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.

Acknowledgment

I am thankful to Prof. Aparajita Ojha for supporting in my early research work related to this area.

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