1 Introduction

The traditional Transmission Control Protocol/Internet Protocol (TCP/IP) model transmits data packets by selecting only a unique ‘best available network path’ [1]. This model and its classical Transport Layer (L-4) protocols (i.e., Transmission Control Protocol (TCP) [2] and User Datagram Protocol (UDP) [3]) adopt only the single-path communication paradigm. However, they cannot satisfy the fault tolerance demands and QoS requirements imposed by multimedia applications over the Internet. Later, the multi-path communication paradigm-based protocols overcame these insufficiencies of the single-path communication paradigm-based protocols. Multi-pathing activates inverse multiplexing of network resources to send data packets over a set of available network paths instead of a single path. Numerous research efforts from academia, industry, and international standards organizations (e.g., IEEE and IETF) recently adopted the multi-path concept. For example, the research community proposed a plethora of L-4-based policies that rely upon concurrent transmission features. Multi-pathing is also necessary as the two end-hosts must sustain more than one path to guarantee the resiliency and consistency of the network [4,5,6,7,8,9].

The transmission of real-time video requires low End-to-End (EtE) delay and high bandwidth. These restrictions can deteriorate the synchronization between voice and video, leading to poor video quality. Meanwhile, the continuous success of video streaming services (e.g., YouTube) depends on delivering high video quality to the end-users [10, 11]. In such an environment, online real-time video applications (e.g., video-conferencing) demand effective resource management policies that adopt the multi-path concept. Existing wireless technologies and standards (e.g., Long-Term Evolution (LTE), WiFi, and WiMax) and the increasing storage and computational capabilities of new smartphones encourage the mandate for multimedia services. New wireless portable devices have multiple network interfaces to provide smooth and high-quality service provisioning in a heterogeneous wireless environment. Multi-homed devices can increase their throughput using parallel transmissions over numerous paths and bandwidth aggregation. For instance, a good smartphone can transmit data simultaneously if equipped with WiFi and 3G/4G/5G interfaces. Data transmission can occur in the path with the highest throughput, while the backup process can happen in the slower paths. Therefore, multi-homing protocols can cover the fault tolerance demands of multimedia applications [12]. It is noteworthy that single-path L-4 protocols do not support multi-homing and bandwidth aggregation. The multi-homing feature offers two end-user systems to launch a logical association over the available network interfaces. This logical association allows the SCTP sender to convey data to the multi-homed receiver through multiple paths. Initially, SCTP uses a path with the highest throughput as a major path and starts data transmission. The remaining available paths are used for data transmission when the primary path becomes unreachable due to network congestion or connection failure. In case of a path failure, the multi-homing feature of SCTP provides a backup path.

The QoS requirements of multimedia applications are satisfied if the available network resources are appropriately utilized [13,14,15,16,17]. SCTP [18], CMT [19], and Multi-path TCP (MPTCP) [20,21,22] are L-4 protocols that aim to provide appropriate stability between strict QoS requirements and utilize available network resources efficiently. SCTP and MPTCP take advantage of multiple network interfaces and support multi-homing. Concerning fault tolerance, they also provide elective reliability. During the transmission association establishment amid two end-hosts, SCTP and CMT exploit multi-homing. In an already established connection, MPTCP contrasts SCTP by systemizing several TCP subflows simultaneously. MPTCP integration has been done with Apple’s iOS version 7.0. MPTCP smartphones can use the Gigapath commercial service to achieve around 800 Mbps throughput by joining WiFi and LTE networks [23, 24]. Besides, OVH Telecom and Tessares introduced some bandwidth aggregation-based multi-path schemes. OVH Telecom introduced a new product called ‘OverTheBox’ [25], which integrates SOCKS proxies and MPTCP to facilitate users to combine numerous Digital Subscriber Lines (DSLs). Tessares introduced a network service (on top of MPTCP) that performs bandwidth aggregation of multiple network infrastructures (i.e., DSL or LTE) [1, 26].

2 Motivation and Scope of the Article

SCTP initially does not support the notion of simultaneous multi-path data transfer. It motivated Iyengar et al. [19] to introduce the idea of CMT as an extension of SCTP. CMT competently offers SCTP load sharing, fault tolerance, and bandwidth aggregation capabilities [27,28,29]. However, this idea works well for paths having symmetric characteristics (i.e., similar PLR, delays, and bandwidth). Asymmetric path characteristics, which are highly likely for modern Internet arrangements involving numerous service providers, make things extremely challenging for CMT. Each path may have different characteristics, and because of this, it may take different times for the data to reach the destination. As a result, the destination frequently receives unordered data. However, CMT uses Transmission Sequence Numbers (TSNs) and a limited size buffer at the receiver to reorder the data chunk. And the receiver cannot erase the data chunk from the receiver buffer until it receives the ordered data chunk. The continuous unordered data chunk reception leads to the receiver buffer blocking problem [15, 19, 30] that seriously degrades the performance at the application level. The other issue with CMT is that it assumes all paths are disjointed. Hence, the CMT cannot acclimatize its functionality when many bottleneck links get involved in the path. Moreover, the uncoupled congestion control scheme has been implemented on top of CMT. Hence, likewise TCPReno, CMT performs uncoupled (independent) congestion control on each path; therefore, it cannot attain flexible load-balancing, ultimately hampering its fairness and throughput performances. Another drawback of CMT is that it uses a Round Robin (RR)-based data scheduling notion to distribute data over multiple available network paths. This notion does not consider a path’s fluctuating characteristics while scheduling data chunks. It causes the problem of unordered data chunk delivery at the destination, leading to the receiver buffer blocking issue. Due to the continuous unordered data chunk reception, the CMT receiver sends an instant Selective ACKnowledgment (SACK) to the sender. Consequently, the sender needlessly has to reduce the cwnd, whereas the network is not congested. Another problem relates to the policies for selecting the retransmission path that resends the lost data chunk. The recommended path selection policies RTX-CWND [19] and RTX-SSTHRESH [19] choose the path that has the largest cwnd or slow-start threshold (ssthresh), respectively. However, both approaches choose this path randomly in case of an exceptional condition. For instance, a particular situation appears when multiple paths have identical cwnd or ssthresh values. Such random selection may incorrectly choose the path having the maximum PLR and minimum bandwidth and may cause different problems. We conclude that new efficient path selection schemes and retransmission methods are required from the above discussion.

This paper introduces a new DB-CMT scheme and contributes as follows:

  • DB-CMT transmits data chunks over numerous network interfaces (underlying paths) according to their respective traffic load. In DB-CMT, the path load is estimated through delay and cwnd parameters. This new scheduling policy is called DB-DSP.

  • The DB-CMT scheme incorporates a novel retransmission destination selection strategy (RTX-CL) to avoid the random selection of retransmission destinations.

  • The DB-CMT scheme has a new fast retransmission method to reduce the needless cwnd reductions due to unordered data chunk delivery. This original method is called DB-FRP.

  • Confirmation of the effectiveness of DB-CMT by conducting extensive experiments and comprehensive evaluation. The validation of DB-CMT has been carried out on network simulator (ns)-2.

  • The simulation results exhibit the efficacy of DB-CMT and show how DB-CMT outperforms other CMT approaches in terms of throughput and FTT performances.

The arrangement of the paper is as follows. Section 3 presents the related work of CMT and MPTCP-Based policies. Section 4 introduces the proposed DB-CMT scheme. Section 5 presents the simulation setup, comprehensive performance evaluation of considered the CMT schemes. Section 6 presents the summary of assessed simulation results. Section 7 finally concludes the paper.

3 Related Work

This section describes the significant proposals based on multi-path L-4 protocols and the key issues that affect their performance. We have divided this section into two parts which are as follows: (I). SCTP-Based CMT Schemes, and (II). MPTCP-Based Schemes.

3.1 SCTP-Based CMT Schemes

Each path may have different QoS factors like bandwidth and delay. Due to dissimilarity in such characteristics, CMT severely suffers from the issue of receiver buffer blocking, unsolicited cwnd reductions, needless retransmissions, and inaccurate data scheduling [1, 4, 27,28,29, 31, 32]. Iyengar et al. [19] analyzed and indicated that the CMT paradigm suffers from the issue of unnecessary retransmissions. Therefore, considering this issue, the authors suggested a solution known as Split Fast Retransmit (SFR). SFR enhanced the conventional fast retransmission scheme by hosting the concept of a virtual queue per destination. This concept assists SFR in inferring the missing segments more precisely. Moreover, they also identified the cwnd update problem and advocated a cwnd Update scheme for CMT (CUC). CUC handles the after-effects of abridged cwnd growth owing to lesser cwnd updates. From another perspective, Dreibholz et al. [33] recommended the Sender Buffer Splitting (SBS) method, which splits the sender buffer conferring to the existing paths. SBS handles the blocking problem when the receiver blocks data chunks' elimination due to out-of-order delivery. However, SBS suffers from local buffer blocking due to each path’s different delay and bandwidth values. Dreibholz et al. [34] presented a report on SCTP past, present, and future standardization and identified the activities and challenges in the CMT paradigm. Wallace and Shami [27] highlighted various problems related to the CMT scheme, such as unnecessary fast retransmissions, excessive network traffic, receiver buffer blocking, crippled cwnd growth, and naive scheduling. Verma et al. [28] estimated and utilized the path delay factor to adjust the cwnd size and ssthresh value. In this policy, the adaptations in cwnd depend upon packet loss and out-of-order data chunk delivery events. This policy performs minor and significant reductions in cwnd size during out-of-order data chunk delivery and packet loss events. Yang et al. [30] advocated a modified fast retransmission scheme that utilizes both loss rate and delays to reduce the possibility of receiver buffer blocking. These policies [28, 30] use conventional CMT's independent congestion control scheme. Hence, it is necessary to evaluate these policies [28, 30] on the fairness parameter because they might be suffering from the issue of being less fair towards other competing TCP flows. Natarajan et al. [35] suggested a new state, called Potentially Failed (PF) with CMT (CMT-PF), to diminish the receiver buffer blocking that happens due to path failure. This state shows whether the destination is reachable or not. Thus, all the new data packets are forwarded to another alternative path. Yilmaz et al. [36] proposed a Non-Renegable SACK (NR-SACK) policy. This policy eliminates the segment from the receiver buffer without caring for cwnd growth and reordering.

Further, in a heterogeneous wireless network environment, data are sent over heterogeneous paths, and these paths may have different characteristics and QoS parameters. Xu et al. [37] suggested a Quality-Aware adaptive multi-path data transfer policy (CMT-QA) for a distinct network (wireless) environment to schedule data over the numerous paths rendering available path superiority. Xu et al. [38] further enhanced CMT considering the same environment and suggested a Network Coding grounded CMT (CMT-NC). Singh et al. [31] surveyed existing multi-path routing and traffic splitting approaches. They also discussed the problems and challenges of inter-layer cooperation, scalability, stability, buffering, and packet reordering in multi-path provisioning. As a solution to data packet reordering and crippled cwnd growth, Shailendra et al. [39] recommended Multi-path SCTP (MPSCTP). Later, Shailendra et al. [40] appraised MPSCTP to regulate the data transfer on an individual path, rendering the total EtE delay. This method minimizes the average packet delay over multiple available network paths but suffers from lower resource utilization complications due to its identical data dissemination strategy. Shailendra et al. [41] also advocated a Tx-CWND retransmission destination selection method to increase the performance of MPSCTP. Meanwhile, Hwang et al. [42] suggested a network coding-based scheme that deals with the buffer blocking problem of CMT. This scheme utilizes Luby transform codes to minimize the computational overhead and retransmission of data. The scheme’s main objective is to reduce the necessity for retransmissions and in-order delivery. However, there is a reasonable chance that this scheme may suffer from higher per-packet in order delivery delay. It may be because this policy incorporates the usage of block codes and the delay generally increases with the block code size. Verma et al. [43] proposed a delay-based packet scheduling approach that uses the path load variation factor and different threshold variables to schedule the data on multiple paths.

Recently, the application of CMT has been widely recommended (see [44,45,46,47,48,49,50,51,52] and References therein) from the perspective of real-time video traffic transmission. Initially, Wu et al. [44] gave Distortion-Aware CMT (CMT-DA) scheme concerning a heterogeneous network environment. CMT-DA suggests introducing the EtE distortion video model on top of CMT. This scheme minimizes video distortion at the flow level by decreasing the effective PLR. Moreover, in the perspective of high-quality video delivery over critical channel conditions, it is necessary to assess the content factors (i.e., decoding dependency amongst frames (video) and priorities of frame), and the scheme should accomplish segregated frame transmission. Nonetheless, CMT-DA alleviates video distortion without considering the content factors. Regarding this issue, Wu et al. [45] gave a Content-Aware CMT (CMT-CA) scheme considering a heterogeneous wireless environment. CMT-CA reduces video distortion by competently considering the aforementioned content factors and utilizing the limited wireless channel capacity. These schemes [44, 45] offer transmission consistency by relying on the conventional standard of retransmission. Further, Wu et al. [46] suggested a Video and Raptor code-conscious CMT (CMT-VR) scheme that considers the challenges in incorporating the CMT paradigm with real-time video streaming. CMT-VR utilizes the proposed raptor coding mechanism, which offers a frame-level guard for video data. CMT-VR also comprises an online chunk scheduling and retransmission scheme aiming to maximize the channel capacity by mitigating needless retransmissions. The CMT-VR method suggests transmission consistency by relying on the mechanism of raptor codes and a modified retransmission scheme. Typically, the schemes [44,45,46] offer transmission reliability either by traditional or flexible retransmission policies. Undeniably, these schemes suffer from low QoS while dealing with real-time video applications that are highly delay-sensitive. Further, Chen et al. [47] recommended a strict requirement of realizing the inter-packet dependency that previous approaches [44,45,46] do not consider. Generally, in mobile (wireless) broadcast networks, the transmission policies are designed to assist the worst-case user. Whenever any transmission policy deals with the scheduling of real-time video application packets, retransmission is a significant concern before that policy. When considering the critical network environment, a packet can be lost due to many reasons like buffer-overflow and transmission errors. When we consider the case of packet loss due to transmission errors, the previously suggested transmission policies utilize Forwarding Error Correction (FEC) mechanism to detect and correct erroneous symbols. For this, the policies transmit redundant symbols in the form of complementary restoration symbols. These restoration symbols let the receivers restructure the original symbols even if some are not received correctly due to errors in transmission [48]. Further, the authors [47] show their concerns about using traditional fountain codes in the abovementioned approaches. Since such codes cannot offer flexibility in guarding the source-generated symbols, these codes usually have the limited ability to provide an alike type of protection for all source-generated symbols without considering the inter-packet dependency. It might lead to the issue that some original/received or reconstructed symbols may become unusable for the final video restoration when their interlinked references get lost or unrecoverable. Hence, the authors [47] modify fountain codes’ conventional equal protection policy by leveraging the inter-packet dependency in the suggested model. Recently, Chen et al. [49] showed concerns about a strict long-term rate control mechanism requirement for concurrent multi-path video transmission service. Since the policies [44, 50] do not consider the quality measure of long-term video transmission, the buffer usage of the current Intra (I) video frame affects the quality of the next Predicted (P) video frames. It motivated the authors [49] to introduce a novel policy of a long-term rate control mechanism that assists a concurrent multi-path video transmission service.

3.2 MPTCP-Based Schemes

An additional connection-oriented protocol that facilitates multi-homing is MPTCP. The performance of MPTCP is better with the incorporation of middle-boxes in contemporary Internet architecture [4, 20]. Yedugundla et al. [53] studied the performance of CMT and MPTCP for delay subtle traffic and observed that both methods decrease the network delay suggestively in a symmetric packet loss environment. Nevertheless, transmission delay minimization is not up to the mark in an asymmetric delay and loss network environment. However, the applications may still take benefit from an additional feature (i.e., fault tolerance) of multi-path communication without increasing the delay. Multi-streaming is another notion initially utilized in SCTP to accomplish varied network circumstances. MPTCP inherits this feature from SCTP, where Li et al. [54] introduced a Network Coding-based MPTCP (NC-MPTCP) to circumvent retransmission in case of delay. However, Systematic Coding MPTCP (SC-MPTCP) [55] practices redundant code to diminish the needless fast retransmission. Cui et al. [56] advocated an alternative augmented version of MPTCP based on foundation codes. In contrast, Zhou et al. [57] presented the CWnd Adaptation MPTCP (CWA-MPTCP) scheme, suggesting the concept of dynamic adaptations in cwnd of each subflow following its changing EtE path delay. Xu et al. [15] proposed a Cross-Layer Fairness-Driven CMT (CMT-CL/FD) scheme for video transmission over the heterogeneous wireless network to diminish reordering during the transmissions.

In the past, a significant amount of work has been done concentrating on MPTCP scheduler design. It is the responsibility of a scheduler to distribute data chunks over multiple interfaces (paths). And it is certain that the performance of such multi-path protocols largely depends on their scheduler design. This is because the imprecise scheduling decisions might lead to Head-of-Line (HoL) blocking, out-of-order delivery, and receiver buffer blocking issues, especially when the paths are asymmetric. Undeniably, in such a case, the users perceive low throughput performance as well as high delays, resulting in inferior Quality of Experience (QoE) for the user [58, 59]. Initially, the conventional scheduler in MPTCP utilizes the Round Trip Time (RTT) estimations. This scheduler chooses to transmit over the fast path (i.e., minimum RTT delay path). It prefers to fill the cwnd of the subflow with the minimum RTT before selecting the other subflows with higher RTTs. Now, when any of these scheduled subflows blocks the created connection, this scheduler adapts itself by retransmitting those chunks (i.e., which creates blocking) on the fast path and penalizing the slow path (i.e., higher RTT delay path), which causes that blocking issue. Moreover, this causes non-optimality in bandwidth aggregation since slower paths are underutilized [60,61,62,63]. Further, this scenario worsens when the paths are heterogeneous, where RTTs and the available bandwidth of the paths vary substantially. This further leads to the severe issue of receiver buffer blocking due to high out-of-order deliveries, which ultimately reduces the QoE to the user. Recently, some new schedulers have also been suggested, such as Earliest Completion First (ECF) [64], BLock ESTimation (BLEST) [60], Slide Together Multi-path Scheduler (STMS) [65], and Peekaboo [66]. In particular, to prevent non-optimal bandwidth aggregation problems, ECF includes the bandwidth estimation and the amount of data queued in the sender buffer factors along with MPTCP’s default scheduler. By identifying whether utilizing a slower path for transmitted chunks will cause faster paths to be underutilized, ECF uses the faster path more competently and reduces the receiver buffer blocking. ECF and BLEST schedulers address about HoL blocking issue by suggesting a wait state. By introducing such a state, the scheduler can determine when to halt for more stable conditions to come for scheduling data chunks. Nevertheless, stopping and looking for more stable conditions would cause underutilization, especially when the path properties vary dynamically. Hence, Wu et al. [66] motivated and suggested a new scheduler called Peekaboo that considers the dynamic, varying path properties while transmitting data chunks. This scheme adapts the data chunk scheduling criteria by observing the effects caused by the continuously varying dynamicity level of available network paths. This scheme works in two folds: Firstly, Peekaboo chooses a deterministic approach to deal with varying dynamicity levels of the path by utilizing a self-learning adaptive and BLEST’s halt approach. Secondly, Peekaboo introduces a stochastic modification policy to better handle non-optimal deterministic scheduling decisions. Shi et al. [65] identified that in a constrained buffer environment at the host, the aggregated throughput performance is far limited compared with two single-path TCP connections combined under similar network and buffer configurations. Also, they have acknowledged that the state-of-the-art schedulers require a large buffer on the fast path. So the authors gave a new scheduling scheme called STMS to handle both the issues well. STMS scheduler takes care that the fast path should continuously transmit packets with sequence numbers smaller than those of the slow paths. Hurtig et al. [67] highlighted the low-latency capacity aggregation issue by considering various conventional and new MPTCP scheduling policies. They demonstrated that various MPTCP schedulers could not offer appropriate stability and performance in asymmetric path conditions (primarily when the MPTCP scheduler deals with interactive applications). They cannot utilize the aggregate capacity and do not offer low latency as well. Two schedulers have been suggested to address the problem related to asymmetric characteristics possessed by the paths: Shortest Transfer Time First (STTF) [68] and BLEST scheduler. The STTF tries to reduce the transmission time of each segment, while the BLEST tries to lessen the buffer blocking problem. The STTF scheduler is multi-faceted and needs more resources. However, comparatively, BLEST is a lightweight scheduler. They have extensively designed and implemented these two schedulers mentioned above in the Linux Kernel environment and compared the performance with the default MPTCP scheduler. STTF estimates the probable transmission time of a chunk considering the path properties of all subflows. STTF effectively schedules all the un-transmitted chunks on the fastest existing subflow without caring about the current status of subflow’s cwnd. STTF estimates the probable transmission time for a chunk over a specific subflow considering smoothen RTT (sRTT), traffic status of the subflow, and the amount of data queued in the sender buffer factors. Specifically, the traffic status of the subflow is one factor that differentiates STTF from the other state-of-the-art schedulers. Since most schedulers often blindly assume that the connections are always in the Congestion Avoidance (CA) phase, a hypothesis is often incorrect in the case of short-lived flows. These schedulers, such as BLEST, STMS, ECF, and STTF, have the shared motivation to reduce the buffer blocking problem and keep lower latency in asymmetric paths [69]. They ultimately realize the subflow, which has higher RTT. They schedule the packets to that subflow with higher sequence numbers. Accordingly, these schedulers manage to overcome the problem of out-of-order receptions. Further, a flavor of scheduler based on MPTCP considering ad-hoc network environment called Cross-Layer Adaptive Data Scheduling Policy (CL-ADSP) suggested by Sharma et al. [29]. CL-ADSP considers the paths’ dissimilar properties while scheduling the data chunks. CL-ADSP has been designed and implemented using estimated RTT and average Medium Access Control (MAC) layer retries as a metric in an ad-hoc network environment on top MPTCP. However, when the RTT estimations are utilized as a network congestion metric, a lesser channel utilization may be attained in the existence of reverse traffic. Recently, Gao et al. [70] suggested a new packet-level-based load balancing scheme called Adaptively Adjusting Concurrency (AAC), considering high latency and packet reordering. AAC makes reasonable amendments in the number of chosen paths based on identifying differences in their properties. Table 1 summarizes SCTP (CMT) and MPTCP-Based schemes, while Table 2 presents their advantages and disadvantages.

Table 1 Summary of SCTP/CMT-based and MPTCP-based schemes
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Table 2 Advantages and disadvantages of SCTP/CMT-based and MPTCP-based schemes
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4 The DB-CMT Scheme

The conventional CMT and CMT-PF exploit the RR data scheduling strategy to transmit data over multiple network paths. The RR data scheduling strategy initially sends an equivalent amount of data on each path. However, as the load on the network increases over time, the number of incoming ACKs via multiple paths will also get affected, causing multiple timeouts and retransmissions in the network. Due to this, the size of the cwnd will change continuously. Hence, different amounts of data can be sent by this scheduling scheme depending on the condition of each path. As a result, a slower path delivers fewer amounts of data than a faster path. Therefore, the receiver receives out-of-ordered data packets. As the frequency of unordered data packets increases, the receiver buffer gets blocked. Consequently, higher Negative ACKs (NACKs) get generated, further reducing the size of cwnd unnecessarily, reducing channel utilization, and ultimately leading to inferior throughput performance. Typically, each path's delay, bandwidth, and PLR can vary comprehensively in a multi-path environment. Therefore, for efficient multi-path communication, we need a data scheduling (or distribution) scheme to take care of the parameters mentioned above efficiently. Initially, we suggested an Adaptive data chunk scheduling policy for CMT (A-CMT) [71] which acclimatizes the transmission rate rendering to bandwidth and delay of the path. For this, we considered path delay as a foremost factor which certainly shows a path's current traffic status precisely because each path's delay constantly varies when the load on the path changes. Thus, we presented an A-CMT policy, and the purpose of this policy is to estimate the expected and the actual transmission rate accurately. In A-CMT, we assessed the variation between these delays ​​and adapted the cwnd growth policy accordingly. This paper proposes a DB-CMT scheme consisting of a cwnd adaptation policy (originally from A-CMT). On top of A-CMT, we are suggesting two new approaches, which are as follows: (I). Path Selection Policy, and (II). Fast Retransmission Policy. The schemes (i.e., CMT-PF, CMT-QA, and A-CMT) implemented on top of CMT are having an issue with their fast retransmission policy. According to their fast retransmission policy, these schemes state that whenever there is a need to perform fast retransmissions, always perform fast retransmissions on a path with a larger cwnd size or ssthresh. This is because these policies assume that if a path’s cwnd size is sufficiently larger than that of the other path, that path is running more seamlessly. And at that point of time (i.e., when a scheme requires fast retransmission), if the paths have the same cwnd sizes, all these policies randomly select a path and perform fast retransmission. Such random selection may inaccurately choose the path having the maximum PLR or minimum bandwidth and may cause more retransmissions, buffer blocking, and losses. So we believe that retransmission is also overhead in itself, and in this way if such random selections are made, it further severely affects the delivery performance of any scheduler. We propose modifying the conventional fast retransmission policy to handle this issue well.

To lessen the receiver buffer blocking issue, fast retransmission issue, and to improve the utilization of available bandwidth, DB-CMT incorporates the three new policies, which are as follows: (I). D-DSP, (II). RTX-CL, and (III). D-FRP. Figure 1 shows the design of DB-CMT, which contains an SCTP sender, SCTP receiver, and ‘n’ asymmetric wired communication paths. On the sender side, there are three vital DB-CMT modules (i.e., D-DSP, RTX-CL, and D-FRP), compound interfaces (I-1, I-2, …, I-N), and a sender buffer. The chunks will be reassembled and collected inside the receiver buffer at the receiver side if the router has done the fragmentation of data chunks. D-DSP aims to transmit data chunks over multiple network paths with respect to their conforming traffic load. D-DSP estimates a path load by utilizing their corresponding delay and cwnd parameters. Meanwhile, RTX-CL manages to lessen the absurdness of selecting the retransmission destination. Finally, D-FRP reduces the problem of the needless cwnd reductions due to unordered data chunk reception at the receiver side.

Fig. 1
figure 1

The DB-CMT design

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This work proposes a data chunk scheduling policy that transmits more data chunks through the minimum delay path that minimizes the out-of-order data chunk delivery. This scheduling policy estimates each path’s actual and expected data transmission rate. The approximation of these mentioned rates utilizes RTTi, cwndi, and minimum RTT (RTTmin_i) parameters of any ith path in the network.

$${\text{Act}}_{\text{Rate}\_\mathrm{i}}=\frac{{\text{cwnd}}_{\text{i}}}{{\text{RTT}}_{\text{i}}}$$
(1)
$${\text{Exp}}_{\text{Rate}\_\mathrm{i}}=\frac{{\text{cwnd}}_{\text{i}}}{{\text{RTT}}_{\text{min}\_\mathrm{i}}}$$
(2)
$${\text{D}}_{\text{i}}=\left({\text{Exp}}_{\text{Rate}\_\mathrm{i}}-{\text{Act}}_{\text{Rate}\_\mathrm{i}}\right)*{\text{RTT}}_{\text{min}\_\mathrm{i}}$$
(3)

where ActRate_i is the actual transmission rate, ExpRate_i is the expected transmission rate, and Di stipulates the load on the ith path. When the traffic on the ith path surges, the value of Di rises consistently. The proposed policy utilizes the Di factor to schedule the data chunk over multiple paths.

4.1 D-DSP Module in DB-CMT

In our policy, the source approximates an expected and the actual transmission rate for each destination based on Eqs. (1) and (2). Then, based on the estimation of these rates, we have calculated the factor Di using Eq. (3). Now, two threshold variables, λ, and δ, decide the path traffic intensity. Typically, whenever the path traffic intensity is high and the sender tries to increase the size of cwnd, it ultimately causes network congestion. Thus, the proposed approach uses λ and δ threshold variables to send data according to path traffic intensity. If the path traffic intensity is low, the λ threshold is triggered. Meanwhile, δ will be triggered when the path has a high traffic intensity. The initial values of λ and δ are chosen to render the threshold estimation scheme introduced in our preceding work [71]. As shown in Eq. (4), if the Di factor is smaller than that of λ, the path has smoother traffic. Consequently, the sender can increase the size of cwnd by one Maximum Transmittable Unit (MTU). Next, if the Di factor is more significant than δ, the path has sufficient traffic. Hence, the sender keeps the size of cwnd as is. Conversely, suppose the Di factor is superior to that of λ and inferior to that of δ. In that case, this shows that the path is not carrying enough traffic, and there is a possibility that we can transmit some more traffic on that (shown in Algorithm 1). Consequently, the sender can increase the size of cwnd according to the growth factor shown in Eq. (4). This technique can control the aggressiveness of cwnd growth and subsequently offers adequate time to settle the network congestion condition. Also, this reduces the possibility of buffer blocking at the receiver end.

$${\text{cwnd}}_{\text{i}+1}=\left\{\begin{array}{l}{\text{cwnd}}_{\text{i}}\quad if \hspace{2mm}{ \text{D}}_{\text{i}}>\delta \\ {\text{cwnd}}_{\text{i}}+\left(\frac{\text{MTU}}{2}\right)\quad if \hspace{2mm} \lambda <{\text{D}}_{\text{i}}< \delta \\ {\text{cwnd}}_{\text{i}}+MTU\quad if \hspace{2mm} {\text{D}}_{\text{i}}<\lambda \end{array}\right.$$
(4)
figure a

4.2 RTX-CL Module for Path Selection Policy in DB-CMT

Iyengar et al. [19] initially proposed five path selection policies to decide the data chunk retransmission path. RTX-SSTHRESH and RTX-CWND select paths with either maximum cwnd or maximum ssthresh factors. If numerous paths have identical cwnd or ssthresh, these schemes can randomly choose the retransmission path. In such a random selection process, there is a possibility to select the path with low QoS parameters, such as low available bandwidth and higher loss rate. To solve this problem, we propose the RTX-CL path selection policy that chooses the best retransmission path according to the highest cwnd and lower loss rate. Initially, RTX-CL selects the retransmission path with the highest cwnd. If multiple paths have the same highest cwnd, it checks the lowest loss rate amongst the destinations chosen in the previous steps. If the policy cannot find one path, then RTX-CL selects one path randomly. The algorithm for the proposed RTX-CL is shown in Algorithm 2. To verify the RTX-CL policy, we designed, implemented, and analyzed the scheme on ns-2.35 [72]. For this, we compare the performance of the RTX-CL retransmission path selection scheme against the RTX-CWND and RTX-LOSSRATE policies. The network topology utilized for the simulation is shown in Fig. 2. In this considered topology, PATH-1 has a fixed PLR of 1%, while the PLR of another path (i.e., PATH-2) varies between 1 and 10%. Meanwhile, we have shown the considered values for delay and bandwidth of both paths in Fig. 2. The SCTP sender S has S1 and S2 interfaces, while SCTP receiver D has D1 and D2 interfaces. The SCTP sender S transmits the FTP traffic to receiver D. The receiver buffer size is 64 KB (default), and the link queue has been configured with a drop-tail queuing policy of 50 packets size.

Fig. 2
figure 2

Network topology

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figure b

Figure 3 shows the throughput performance of different retransmission path selection policies with variable PLRs. Here, DB-RTX-CL, DB-RTX-CWND, and DB-RTX-LOSSRATE use the proposed DB-CMT, while CMT-RTX-CWND and CMT-RTX-LOSSRATE use the customary CMT scheme. As discussed earlier, RTX-CL selects the initial retransmission path with a larger cwnd size. If every path has the same cwnd, this method chooses a path with the minimum PLR. However, RTX-CWND and RTX-LOSSRATE select the retransmission path based on the largest cwnd and smallest PLRs.

Fig. 3
figure 3

Throughput performance of CMT and DB-CMT using different RTX policies

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It is evident from the results (shown in Fig. 3) that as the PLR increases, the throughput performance of all retransmission path selection (RTX) policies declines significantly. In this analysis, CMT-RTX-CWND outperforms CMT-RTX-LOSSRATE, while the DB-RTX-CL achieves higher throughput performance than other retransmission policies. From Fig. 4, it is evident that DB-RTX-CL has fewer average retransmission timeouts than other retransmission policies. Figures 3 and 4 confirm that RTX-CL can be an optimal retransmission policy for networks with higher PLRs.

Fig. 4
figure 4

Average retransmission timeout of CMT and DB-CMT with different RTX policies

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4.3 D-FRP Module in DB-CMT

In the fast retransmission phase, every time CMT obtains four duplicate SACKs, it assumes this event as congestion. Subsequently, CMT reduces the aggressiveness of cwnd growth by blindly halving it out of the current cwnd size. But this approach of cwnd reduction is inappropriate because duplicate SACKs are also received when the destination gets unordered data chunks- the frequent reductions in the cwnd lead to a problem of compromised throughput performance. When congestion surges, the RTT factor rises, whereas the unordered data chunk delivery may not increase the RTT. If we comprise delay (path) as a significant factor in cwnd reduction, it will appropriately regulate the reduction in cwnd growth instead of carelessly reducing it to half. Therefore, the proposed method comprises the up-to-date path’s cwnd and RTT as a cwnd lessening factor. This factor is self-sufficiently estimated for each path while getting four duplicate SACKs. Eq. (5) shows the proposed cwnd reduction policy.

$${\text{cwnd}}_{\text{i}+1}={\text{cwnd}}_{\text{i}}-\frac{{\text{cwnd}}_{\text{i}}*({\text{RTT}}_{\text{i}}-{\text{RTT}}_{\text{min}\_\mathrm{i}})}{{\text{RTT}}_{\text{i}}}$$
(5)

The (RTTi—RTTmin_i)/RTTi provides a constant factor (ω) that changes in accordance with RTTi variation. The value of ω will be significant when RTTi variation is large, and if RTTi variation is smaller, ω will be small. Now, in Eq. (5), we estimate the next cwnd by using cwnd*ω. The cwnd*ω shows the extra buffer consumed by the current flow on the ith path. Therefore, when congestion is detected due to packet drop or buffer blocking, the source reduces the cwnd according to the extra buffer consumed by the current flow on the ith path. As a result, Eq. (5) reduces the size of cwnd to a lesser amount when ω is small. As ω increases, the reduction in cwnd also increases. The ω lessens the size of cwnd of the current path by a significant amount if congestion occurs, while cwnd decreases with the trivial amount during the situation of unordered data chunk delivery (shown in Algorithm 2). The selection of the retransmission path is also made according to the proposed RTX-CL path selection policy.

5 Performance Evaluation

We performed simulation experiments with some imperative CMT variants. Section 5.1 presents the network and topological arrangements for the simulated CMT variants. In Section 5.2, we present and discuss the performance evaluation of DB-CMT with CMT [19], CMT-PF [35], CMT-QA [37], and A-CMT [71] using ns-2 on different sets of bandwidth values scenarios. Further, ns-2 includes the latest CMT module developed initially and modeled by the University of Delaware, US.

5.1 Simulation Environment

We have realized two types of network environments to evaluate the performances of all the CMT schemes, which are as follows: (I). Network environment where bandwidth is sufficiently available (i.e., CASE-1) and (II). Network environment where bandwidth is extremely limited (i.e., CASE-2). Our main objective behind realizing such environments is that we will be able to assess the performance of all the schemes in both kinds of situations in a much better way. Figure 5 displays the network topology used for our performance assessment. This network structure has an SCTP sender having S1 and S2 interfaces and an SCTP receiver with D1 and D2 interfaces. Along with this, we have configured two routers (denoted R-1 and R-3) which are single-homed devices. To simulate severe congested circumstances at these routers, we also configure cross-traffics. We inject multiple cross-traffics to simulate the background traffic for heavy data exchange. This cross-traffic is produced by a Constant Bit Rate (CBR) generator attached over a UDP connection. These end-hosts interconnect through two disjoint paths (PATH-1 and PATH-2). The parameter configurations of both paths are listed in Table 3. Initially, the parameter settings of both paths are default and similar; hence, we change some specific parameters of PATH-2 at a time while keeping the parameters associated with PATH-1 constant. Consequently, we configure dissimilar paths’ characteristics, and further, we evaluate the individual impact of parameters on the performance of the simulated schemes. All the simulation results presented are estimated by normalizing the results over several runs, which makes the consequence of the loss rate and cross-traffic on different simulated schemes more accurate and not affected by any other stochastic factors.

Fig. 5
figure 5

The network topology

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Table 3 Simulation parameters
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To simulate CASE-1, we have configured 10% fixed PLR on PATH-1 and variable PLR (which varies between 0 and 10%) on PATH-2. In particular, the delay and bandwidth of each attached link are shown in Fig. 5 as BandWidth (BWIJ), Delay (DIJ) (where IJ are the corresponding nodes to which a link is directly connected), and their actual values are presented in Table 4 for this simulation setup. However, to simulate CASE-2, we have configured a 1% fixed PLR on PATH-1 and the variable PLRs (varies between 1–10%) on PATH-2. The corresponding delay and bandwidth values for this simulation setup are shown in Table 4. Additionally, the source (SCTP) is attached with an FTP traffic generator, and the simulation time of this setup is 200 secs. Also, this topology has two UDP senders, U1 and U2, and two UDP receivers, U11 and U22. The U1 and the U11 are attached to R1 and R4, while U2 and U22 are attached to R2 and R3 routers. The UDP sources U1 and U2 are connected with the CBR traffic agent, while the SCTP source is attached to an FTP traffic agent. This simulation setup is organized with a drop-tail queuing scheme, and the default queue magnitude is 50 packets. DB-CMT uses the proposed RTX-CL in this simulation arrangement, while CMT and CMT-PF are organized with an RTX-CWND retransmission scheme. We do not comprise enormously low traffic throughout the simulations. Table 3 shows the other necessary simulation parameters utilized for the performance assessment.

Table 4 Bandwidth and delay configurations
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5.2 Simulation Results and Discussions

This section presents the performance evaluation of DB-CMT against CMT, CMT-PF, A-CMT, and CMT-QA based on metrics such as average throughput (kbps), cwnd size variations, and FTT. In Sect. 5.2.1, we examine the performance and behaviour of DB-CMT where bandwidth is sufficiently available (CASE-1). In Sect. 5.2.2, we investigate the performance of DB-CMT in a network environment where bandwidth is highly limited (CASE-2), and finally in Sect. 5.2.3, we perform the statistical analysis for the simulated CMT schemes.

5.2.1 Experimental Analysis of All Simulated CMT Schemes on a Sufficiently Available Bandwidth Network Environment

We investigate the performance of DB-CMT when bandwidth is sufficiently available in a network in terms of throughput with a 1 Mbps UDP background traffic rate. Figure 6 shows the variations in average throughput (kbps) for the entire simulation period. This experiment aims to confirm the competence of all the simulated CMT schemes to efficiently handle packet losses, which substantially impact the throughput performance. As shown in Fig. 6, as the PLR increases, throughput continually decreases for all the simulated schemes. The drop in throughput performance of CMT, CMT-PF, CMT-QA, A-CMT, and DB-CMT is around 74.31%, 75.80%, 73.67%, 72.48%, and 71.68% respectively. At a PLR of 1%, DB-CMT yields 11.33%, 13.30%, 7%, and 5.31% improved throughput performance against CMT, CMT-PF, CMT-QA, and A-CMT, respectively. While at a maximum PLR of 10%, DB-CMT’s throughput performance is 27.09%, 29.83%, 15.10%, and 9.03% higher than CMT, CMT-PF, CMT-QA, and A-CMT, respectively. While at an average PLR of 5%, DB-CMT’s throughput performance is 6.23%, 18.11%, 10.77%, and 7.07% higher than that of CMT, CMT-PF, CMT-QA, and A-CMT, respectively.

Fig. 6
figure 6

The average throughput performance comparison between simulated CMT schemes with respect to varying PLRs

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In particular, as the PLR increases, the chances of higher cwnd growth reductions increase. It increases the probability of higher transmission delay as well. Here, the throughput performance of CMT drops seriously on increasing PLRs (i.e., 1773 kbps to 455 kbps) because it reduces its cwnd size immediately as soon as it senses the packet loss. However, CMT-PF also does not offer substantial performance (i.e., 1843 kbps to 446 kbps) because it cannot precisely recognize packet drop due to short-term route failures in most cases. Also, CMT and CMT-PF utilize an RR-based scheduling scheme without considering the path quality factors. Hence, these schemes cannot efficiently utilize bandwidth and offer around 888 kbps and 867 kbps average throughput. In fact, initially, the scheduling scheme incorporated in CMT and CMT-PF schedules and transmits the same amount of data on all available network paths without considering any quality factors. However, CMT-QA offers 6.19% and 8.76% improved performance than CMT and CMT-PF because it can detect packet losses and congestion-induced path failure well on time and further assist the scheme in dynamically adapting its scheduling decisions. Moreover, A-CMT suggests 8.89%, 11.53%, and 2.54% improved performance against conventional CMT, CMT-PF, and CMT-QA schemes. This is because A-CMT utilizes the paths’ quality factors (i.e., delay and bandwidth) as a crucial aspect of chunk scheduling and schedules more chunks on a path having lower delay and higher available bandwidth. Furthermore, DB-CMT outclasses CMT and CMT-PF schemes by offering 16.21% and 19.03% improved performances and suggests 9.43% and 6.72% better performance than CMT-QA and A-CMT. DB-CMT offers such performance because it eradicates the randomness in selecting a path during the fast retransmission procedure when the paths possess the same cwnd sizes at any point of time. Such random selection inaccurately chooses the path in CMT, CMT-PF, CMT-QA, and A-CMT schemes having the maximum PLR and minimum bandwidth and causes more retransmissions, buffer blocking, and losses. Meanwhile, DB-CMT also uses a delay and bandwidth-aware data chunk scheduling policy to distribute data over multiple paths, further assisting the scheme in effectively scheduling data over qualitative paths.

Afterward, we apply the concept of the confidence interval to estimate the average throughput and FTT (evaluated parameters ‘ep’) performance variations via Eq. (6).

$${\text{P}}_{\text{r}}(\overline{\text{M} }- {\text{Z}}_{(1-\updelta /2)}*(\mathrm{SD}/\sqrt{n} ) \le {e}_{p} \le \overline{\text{M} }+ {\text{Z}}_{(1-\updelta /2)}*(\mathrm{SD}/\sqrt{n} ))= 1-\updelta$$
(6)

where \(\overline{\text{M} }\) is the sample mean, SD is the sample standard deviation, n is the sample size, ‘1-δ’ is the confidence level, and ‘Z(1-δ/2)’ is a function of ‘1-δ/2’, which can be refer through Table 5.

Table 5 Confidence level and equivalent Z score
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Besides, we also evaluate the confidence intervals on the considered parameters for the simulated schemes. Though to reduce their difficulty level in observation, the values of those intervals are not only shown in Fig. 7, but we have also added the table (Table 6) explicitly. In Table 6, we show the confidence intervals with a 95% confidence level concerning simulation results shown in Fig. 6. Also, each simulation point underwent repetition twenty times, and we confirmed the reliability of the obtained simulation results with a 95% confidence level. Figure 7 depicts the plots showing the average throughput performance and the conforming 95% confidence intervals for changing PLR.

Fig. 7
figure 7

Average throughput of all the simulated CMT variants with 95% confidence interval

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Table 6 Analysis of the evaluated schemes via statistical parameters based on average throughput (kbps)
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Figure 8A–E shows the variations in cwnd growth for the entire duration of the simulation. The results have been obtained for CMT, CMT-PF, CMT-QA, A-CMT, and DB-CMT, and these results specify the amount of traffic (in terms of bytes) over network paths (PATH-1 and PATH-2). To perform this analysis, we set 2% PLR on PATH-1 and 10% on PATH-2. In general, when we consider all the cases (Fig. 8A–E), we can comprehend that all the simulated CMT schemes have an initial cwnd size of 4380 bytes. This is because the traditional CMT scheme suggests a policy (i.e., cwndInitial = min (4*MTU, max (2*MTU, 4380 bytes))) to initialize cwnd initially. Also, the implementation of CMT schemes (i.e., CMT-PF, CMT-QA, A-CMT, and DB-CMT) given herein follow the traditional CMT implementation. It is evident from results (Fig. 8A–E) that the size of cwnd growth on PATH-1 is much larger than on the PATH-2 because the PLR on PATH-1 is smaller than the PATH-2. Figures 8A and B show the variations in cwnd growth for CMT and CMT-PF schemes. In CMT, the average cwnd growth on PATH-1 and PATH-2 is about 12845 bytes and 6306 bytes. In CMT-PF, the average cwnd growth on PATH-1 and PATH-2 is around 12361 bytes and 6042 bytes. In CMT-QA, the average size of cwnd growth on PATH-1 and PATH-2 is nearby 15585 bytes and 8685 bytes. In A-CMT, the average cwnd growth on PATH-1 and PATH-2 is near 14197 bytes and 7775 bytes. While, in DB-CMT, the average size of cwnd growth on PATH-1 and PATH-2 is nearby 16965 bytes and 9606 bytes. These results signify that CMT and CMT-PF schemes fail to achieve appropriate channel utilization when PLR on a path gets severe. DB-CMT, CMT-QA, and A-CMT suggest improved channel utilization performance on CMT and CMT-PF. Specifically, if we consider the case of PATH-2, which has 10% PLR, CMT-QA offers 37.70% and 43.74% improved performance than CMT and CMT-PF (shown in Fig. 8C). In the same scenario, A-CMT suggests 23.27% and 28.68% improved performance than CMT and CMT-PF (shown in Fig. 8D). However, DB-CMT offers 16.34% and 4.50% improved performance than CMT-QA and A-CMT. DB-CMT outperforms CMT and CMT-PF by providing 52.30% and 59.01% improved performance. Also, DB-CMT suggests 10.65% and 23.54% better channel utilization than CMT-QA and A-CMT (shown in Fig. 8E).

Fig. 8
figure 8

A–E Variations in cwnd growth in simulated CMT schemes

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Figure 9 shows the change in throughput (kbps) for the entire duration of the simulation. The CMT, CMT-PF, CMT-QA, A-CMT, and DB-CMT policy results indicate the traffic over simulated paths (i.e., PATH-1 and PATH-2) when a 64 KB receiver buffer is used. In addition, the PLR of PATH-1 and PATH-2 is 10% and 0%, respectively. Initially, the throughput of all the CMT schemes increases rapidly because all the policies quickly probe the available channel capacity. And, the Slow-Start algorithm in all the schemes doubles the cwnd size repetitively. We can observe variations in throughput for all the simulated CMT schemes due to congestion and buffer blocking induced packet losses. Then it recovers after cwnd amendments and fast retransmissions. When we compare DB-CMT with the rest of the simulated CMT schemes, it is clear that DB-CMT tolerates packet loss better and utilizes the obtainable aggregate bandwidth competently. For a particular instance, after 200 s of simulation time with a 64 KB receiver buffer, DB-CMT offers 13.87%, 9.40%, 6.45%, and 4.78% improved average throughput than CMT, CMT-PF, CMT-QA, and A-CMT, respectively.

Fig. 9
figure 9

Throughput (kbps) comparison between simulated CMT schemes

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In the next simulation, we investigate the effects of asymmetric loss rate on FTT performance. To perform this analysis, we have set 2% PLR on one path (PATH-1) and 10% on the other (PATH-2). In contrast, other important simulation configurations remain identical, as shown in Tables 3, 4, and Fig. 5. Figure 10 shows the results plots showing the average FTT (s) performance and the conforming 95% confidence intervals (shown in Table 7) for changing file sizes. These results show that as the file size increases, the FTT also upsurges. These results clearly show that the FTT is highest in the case of the CMT compared to other schemes. In the case of CMT, the average FTT (concerning changing file sizes) is around 229.17 s, while it is around 217.76 s, 216 s, 212.45 s, and 209.47 s in CMT-PF, CMT-QA, A-CMT, and DB-CMT, respectively. Due to its conventional scheduling scheme, CMT takes more time to transmit each size file. However, in this scenario, CMT-PF suggests some improvement in average FTT (i.e., around 5.23% lesser than the CMT) because it recognizes packet drop as a result of short-term route failures to some extent. Moreover, CMT-QA suggests comparable performance with respect to CMT-PF and A-CMT. Further, DB-CMT takes the minimum time to transmit each file size compared to other simulated schemes. DB-CMT takes 9.80%, 4.07%, 3.15%, and 1.68% lesser average FTT then CMT, CMT-PF, CMT-QA, and A-CMT respectively. DB-CMT takes 26.19% and 19.04% less time to transmit a 10 MB file than CMT and CMT-PF. While for the same scenario, DB-CMT suggests 9.52% and 7.14% lesser average FTT performance than CMT-QA and A-CMT. Moreover, DB-CMT takes 9% and 4.26% less time to transmit an average file size of 50 MB than CMT and CMT-PF. DB-CMT suggests 3.79% and 1.89% lesser FTT for the same scenario than CMT-QA and A-CMT. However, for the case of a maximum file size of 90 MB, DB-CMT suggests 8.20%, 2.91%, and 2.90% lesser FTT performance against CMT, CMT-PF, and CMT-QA, respectively, and suggests comparable performance (i.e., 1.08% lesser FTT) against A-CMT scheme. For minimum file sizes (i.e., ranges from 10 to 40 MB), the average FTT performances of CMT, CMT-PF, CMT-QA, A-CMT, and DB-CMT are around 116.87 s, 111.42 s, 109.23 s, 107.10 s, and 105.15 s, respectively. For maximum file sizes (i.e., ranges from 60 to 90 MB), the average FTT performances of CMT, CMT-PF, CMT-QA, A-CMT, and DB-CMT are around 341.25 s, 323.66 s, 322.30 s, 317.25 s, and 313.30 s, respectively. Also, we estimate the confidence interval for these results.

Fig. 10
figure 10

Average FTT (s) vs. File size of all the simulated CMT variants with 95% confidence interval when an asymmetric loss rate exists

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Table 7 Analysis of the Evaluated Schemes via some Statistical Parameters on the basis of Average FTT (s)
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5.2.2 Experimental Analysis of the Simulated CMT Schemes on a Limited Bandwidth Network Environment

Figures 11, 12, 13, 14 compare the throughput performance of DB-CMT with CMT, CMT-PF, and CMT-QA for receiver buffer sizes 32 KB, 64 KB, and 128 KB, respectively. This simulation study demonstrates that the receiver buffer size affects the performance of CMT variants. It shows that as a receiver buffer size increases, the throughput of CMT variants increases. Figure 11 shows the throughput variations with the PLR when the receiver buffer size is 32 KB. CMT and CMT-PF show a linear throughput deviation because both methods use the RR-based data chunk scheduling policy. However, CMT-QA uses the path quality-based data distribution policy. Consequently, it achieves a better result compared to CMT and CMT-PF. Meanwhile, DB-CMT uses a delay and bandwidth-aware data chunk scheduling policy to distribute data over multiple paths. It is evident from Fig. 11 that DB-CMT performs better than the CMT, CMT-PF, and CMT-QA at all PLR values. At a minimum receiver buffer size (32 KB) case, DB-CMT’s overall throughput performance is 7.45%, 5.93%, and 2.45% higher than CMT, CMT-PF, and CMT-QA, respectively.

Fig. 11
figure 11

Average throughput vs. PLR at 32 KB receiver buffer size

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Fig. 12
figure 12

Average throughput vs. PLR at 64 KB receiver buffer size

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Fig. 13
figure 13

Average throughput vs. PLR at 128 KB receiver buffer size

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Fig. 14
figure 14

Average throughput performances of all the simulated CMT variants with 95% confidence interval on varying receiver buffer size considering minimum, average, and maximum PLR

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In the 64 KB receiver buffer size case, DB-CMT’s average throughput is 13.42%, 12.04%, and 8.07% more than CMT, CMT-PF, and CMT-QA, respectively. While at a maximum receiver buffer size (128 KB) case, DB-CMT’s overall throughput performance is 15.05%, 15.26%, and 2.38% higher than that of CMT, CMT-PF, and CMT-QA, respectively (shown in Figs. 12 and 13). In Table 8, we show the confidence intervals with a 95% confidence level with respect to simulation results in Figs. 11, 12, 13. Also, each simulation point underwent repetition twenty times, and we confirmed the results’ reliability with a 95% confidence level. Figure 14 depicts the results plots showing the average throughput performance and the conforming 95% confidence intervals for changing receiver buffer sizes.

Table 8 Analysis of the Evaluated Schemes via some Statistical Parameters on the basis of Average Throughput (kbps) considering PLR cases on changing receiver buffer sizes
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Also, we examine the performance of DB-CMT for different receiver buffer sizes concerning time. In this simulation setup, PATH-1 and PATH-2 have a PLR of 1% and 5%. We run two simulations to study the effect of receiver buffer size 32 KB and 64 KB on throughput for 200 s. Figures 15, 16 show that as the buffer size increases, the throughput of all the approaches also increases. Initially, the throughput of all the approaches increases rapidly because of network capacity probing (Slow-Start phase). After the Slow-Start phase, the network identified throughput variations due to packet losses (all mechanisms recover from packet loss by reducing the cwnd and retransmission of lost packet). Therefore, we show only the throughput variation part of CMT variants in Figs. 15, 16. CMT and CMT-PF show lower throughput because they cannot competently tolerate packet losses. However, CMT-QA tries to manage packet losses more effectively. As a result, CMT-QA offers better throughput than CMT and CMT-PF. But, DB-CMT uses a delay-based fast retransmission policy to adjust cwnd more effectively to improve the available bandwidth utilization. Thus, DB-CMT achieves better throughput than CMT, CMT-PF, and CMT-QA.

Fig. 15
figure 15

Throughput vs. simulation time at 32 KB receiver buffer

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Fig. 16
figure 16

Throughput vs. simulation time at 64 KB receiver buffer

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Next, we examine the performance of DB-CMT, CMT, CMT-PF, and CMT-QA in terms of average FTT in lossy and lossless network environments. Figures 17, 18, 19 presents the average FTT performances of all the simulated CMT variants on symmetric and asymmetric PLR when the file size varies from 10 to 90 MB. Both paths have background traffic of 150 kbps. The rest of the simulation configuration remains the same, as shown in Tables 3 and 4 and Fig. 2. First, we examine the performance of DB-CMT in a lossless network environment. Figure 17 shows the average FTT performance of the CMT variants when both paths have a PLR of 0%. The results clearly signify that as the file size increases, FTT increases as well. Here, CMT and CMT-PF offer comparable average FTT performances (585.79 s and 584.37 s) because both approaches use RR scheduling to transmit data over multiple paths. However, CMT-QA transmits data on each path according to their path quality. Thus, CMT-QA offers 1.20% and 1.03% less average FTT performance than CMT and CMT-PF. Further, DB-CMT estimates the load of each path and schedules the data according to path load variation. Therefore, DB-CMT schedules more data on the least loaded path and less on the heavily loaded path. As a result, DB-CMT takes less FTT compared to CMT, CMT-PF, and CMT-QA. In fact, DB-CMT offers 2.80%, 2.63%, and 1.75% lesser FTT than CMT, CMT-PF, and CMT-QA, respectively.

Fig. 17
figure 17

Average FTT vs. file size when a symmetric loss rate exists

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Fig. 18
figure 18

Average FTT vs. file size when an asymmetric loss rate exists

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Fig. 19
figure 19

Average FTT performances of all the simulated CMT variants with 95% confidence interval on symmetric/asymmetric PLRs considering minimum, average, and maximum file sizes

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Figure 18 shows the average FTT performance of all the simulated CMT variants when both paths have an asymmetric PLR. In this simulation setup, PATH-1 has a 1% PLR while PATH-2 has a 2% PLR. Figure 18 shows that as file size increases, the FTT of all CMT variants increases as well. However, the difference in FTT between all CMT variants also increases due to a dissimilar PLR of each path. Figure 18 shows that CMT and CMT-PF take similar time due to their similar packet scheduling policy over the multiple available paths. However, CMT-QA takes less time than CMT and CMT-PF because it uses a data distribution policy based on path quality. On the other hand, DB-CMT achieves better performance as compared to CMT, CMT-PF, and CMT-QA due to its delay-based data chunk scheduling policy. Thus, DB-CMT takes less time to transfer all file sizes in a dissimilar PLR scenario. In the case of symmetric PLR paths, the DB-CMT’s FTT performance difference was relatively small compared to other approaches. Still, as the substantive difference in the PLRs of the paths came in, this difference proved to be moderately large. DB-CMT suggests 5.61%, 6.06%, and 5% lesser average FTT performance than CMT, CMT-PF, and CMT-QA, respectively. This proves that DB-CMT is capable of handling the asymmetric PLRs of multiple paths to a larger extent. Figure 19 shows the average FTT performance of all the simulated CMT variants with a 95% confidence interval on symmetric and asymmetric PLR cases (Table 9).

Table 9 Analysis of the evaluated schemes via some statistical parameters on the basis of average FTT (s) considering symmetric/asymmetric PLR cases
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5.2.3 Statistical Analysis for the Simulated CMT Variants

In this sub-section, we concisely present the basics of the regression analysis notion. This notion directly deals with discovering the correlation between the independent variable (say ‘x, x = (x1, x2, x3,…, xn)’) and a dependent variable (say ‘y, y = f(x)’), which is called predictive or regression model). In fact, this kind of model measures the closeness (strength) of that association, discounting the random and outlier values (noises) and predicting the most exact value of the dependent variable ‘y’ on a value of independent variable ‘x’ with a minimum error [73]. This kind of model is based on the Sum of Squares (SoSs), the best conceivable mathematical means to predict the dispersion of points (data). The ultimate objective of this model is to estimate the minimum possible SoSs and plot a line that comes as close as possible to the simulated data.

Mathematically, a linear regression is stated by Eq. (7).

$$y=b\left(x\right)+a+\varepsilon$$
(7)

where ‘a’ is stated as Y-intercept, it is the anticipated value (mean) of variable ‘y’ when all ‘x’ variables are zero. ‘b’ is defined as the slope of the regression line, which shows the rate of change in variable ‘y’ as the ‘x’ variable deviates. ‘ε’ is the random error which shows the deviation between the predicted and the actual value of a dependent variable. We have applied the linear regression analysis to predict the next value of throughput for the simulated methods, dependent on a PLR factor. Now, we need to understand and estimate the quality of the regression model applied to our data set. The factors such as p-values and R-Square (R2) are the essential criteria to assess the quality of the regression model. R2 is the determination coefficient which is basically utilized as an indicator of the goodness of fit. It indicates how many the number of points come over the regression line. Specifically, R2 can be computed by Eq. (8).

$${\text{R}}^{2}=1-({\text{Sum}} \;{\text{Squared}}\;{\text{ Regression }}\left(\text{SSR}\right)/{\text{Total}}\; {\text{SoSs }}(\text{TSoSs})),$$
$${\text{with}}\;{\text{SSR}}=\sum_{i=1}^{n}{({y}_{i}-\widehat{{y}_{i}})}^{2}\; {\text{and}}\;{\text{TSoSs}}= \sum_{i=1}^{n}{({y}_{i}- \overline{y })}^{2}$$
(8)

Here, ‘\(\overline{y }\)’ is the mean value of simulated data points (actual y value) ‘yi’ and ‘\(\widehat{{y}_{i}}\)’(predicted y value) is calculated by placing ‘xi’ value into the considered regression model ‘y = f(x)’, SSR is the summation of residual (ri) squared (i.e., ri = \({y}_{i}-\widehat{{y}_{i}}\)) and TSoSs is the summation of the distance the simulated data is far from the mean all squared. The value R2 criterion ranges from 0 to 1 (i.e., R2 \(\upepsilon\) [0,1]). Here, in our scenario, after applying such linear regression analysis separately on each simulated CMT variant’s data set, we got the regression analysis results shown in Table 10. These results show how well the estimated linear regression equalities (shown in Eqs. (9–13)) fit our simulated data. After applying linear regression to each simulated method, we get the following equations for each method:

$${\text{CMT}}: {\text{y }} = \, - {115}.{\text{63x }} + { 1465}.{1}$$
(9)
$${\text{CMT}}{-}{\text{PF}}:{\text{ y }} = \, - {12}0.{\text{7x }} + { 147}0.{5}$$
(10)
$${\text{CMT}}{-}{\text{QA}}:{\text{ y }} = \, - {122}.0{\text{6x }} + { 1577}.{4}$$
(11)
$${\text{A}}{-}{\text{CMT}}:{\text{ y }} = \, - {122}.{\text{86x }} + { 1557}.{3}$$
(12)
$${\text{DB}}{-}{\text{CMT}}:{\text{ y }} = \, - {127}.{\text{82x }} + { 1671}$$
(13)
Table 10 Regression statistics for simulated CMT variants
Full size table

Here, Multiple R is the correlation coefficient and measures the strength of association (linear) between two variables. The value of the Multiple R criterion ranges from -1 to 1, and its absolute value shows the strength of the association. The more will be the absolute value, the stronger the association. If its value reaches close to 1, then there is a strong positive association. Here, from the results shown in Table 10, it can be perceived that in all the simulated CMT variant cases, the value of the Multiple R criterion is close to 1; hence, there is a strong positive relationship between the dependent variable (throughput) and the independent variable (PLR). Apart from this, it can also be understood from the results shown in Table 10 that the R2 criterion amongst all the CMT variants is close to 0.85. It means that 85% of our simulated data values fit the regression analysis model. Moreover, 85% of our considered dependent variable (throughput) are explicated by the independent variable (PLR). To visualize the association between the two considered variables, we plot the results, which are shown in Fig. 20A–E.

Fig. 20
figure 20

A–E: Regression results for the simulated CMT variants

Full size image

6 Summary of Assessed Simulation Results

This section summarizes the complete impact of our suggested scheme (DB-CMT) in a multipath environment. We compared DB-CMT with the conventional RR-based data scheduling scheme, i.e., CMT. Moreover, we compared and analyzed DB-CMT against adaptive versions of CMT such as CMT-PF, CMT-QA, and A-CMT in an environment where bandwidth is sufficiently available. First, we compared the throughput performance of DB-CMT with CMT, CMT-PF, A-CMT, and CMT-QA when the PLR varies between 0 to 10% with a 64 KB receiver buffer size (default). Then, considering the same environment, we compared the cwnd growth variations with respect to the simulated CMT schemes. By performing a thorough analysis of throughput and cwnd growth variations, it has been confirmed that DB-CMT tolerated packet loss better and utilized the obtainable aggregate bandwidth competently than other simulated CMT schemes. Afterward, in the same network environment, we compared and analyzed the FTT performance on asymmetric loss rate situations with respect to the simulated CMT schemes. We thoroughly analyzed those FTT results and found that DB-CMT takes the least FTT to transmit each size of the file compared to other simulated CMT schemes.

Furthermore, we also compared and analyzed DB-CMT against adaptive versions of CMT in an environment where bandwidth is extremely limited. We compared and analyzed the throughput performance of DB-CMT with CMT, CMT-PF, and CMT-QA when the PLR varies between 1 to 10%. For performing analysis and comparisons, we run a group of three types of simulations (i.e., for the receiver buffer sizes of 32 KB, 64 KB, and 128 KB) to understand the impact of different receiver buffer sizes on the throughput performance of the simulated schemes. It has been perceived that the throughput performance of all simulated schemes surges with an upsurge in the sizes of the receiver buffer. The lower the buffer size is, the greater the possibilities are (1) of triggering the receiver buffer blocking issue, (2) of transmitting NACKs, and (3) of reducing cwnd size by the sender. Consequently, such a situation leads to the problem of lower channel utilization, ultimately leading to inferior throughput performance. This simulation study validates that the receiver buffer size affects the throughput performance of all the considered CMT variants. Comparing DB-CMT with the rest of the simulated CMT schemes, it is clear that the DB-CMT scheme is better at utilizing the obtainable aggregated bandwidth from different links in this environment.

Then, we further assessed the average FTT performances with varying file sizes in symmetric and asymmetric loss rate situations. We compared the FTT performances for DB-CMT, CMT, CMT-PF, A-CMT, and CMT-QA. DB-CMT utilizes a new delay-based data chunk scheduling, a new retransmission path selection policy (RTX-CL), and a fast retransmission policy. DB-CMT estimates the transmission load of each path and schedules the data according to the path load variation. Consequently, DB-CMT can schedule more data on the least loaded path and less on the severely burdened path. For this reason, DB-CMT achieves more throughput and less average FTT performances.

Based on the simulation results obtained, the following statements can be claimed:

  1. 1.

    The proposed delay-based data chunk scheduling scheme for CMT can transmit more data chunks through the minimum delay variation path that subsequently minimizes the out-of-order data chunk delivery and further minimizes the possibility of receiver buffer blocking. Hence, it later reduces the likelihood of cwnd growth reductions and further assists DB-CMT in maintaining the better utilization of the obtainable aggregated bandwidth from different links.

  2. 2.

    In the DB-CMT scheme, the source approximates an expected and the actual transmission rate for each destination. Based on these estimations, DB-CMT efficiently assesses the load on a path. This technique can control the aggressiveness of cwnd growth and subsequently offers adequate time to settle the congestion condition in the network.

  3. 3.

    DB-CMT comprises a new retransmission path selection policy (RTX-CL) which chooses the best retransmission path according to the highest cwnd and lower loss rate. This scheme effectively eliminates the issue of randomness in the path selection process if numerous paths have identical cwnd or ssthresh factors.

  4. 4.

    DB-CMT also includes a delay-based fast retransmission policy which eradicates the problem of the conventional fast retransmission policy. Specifically, due to the four SACKs receptions, the traditional fast retransmission policy blindly reduces the cwnd size to half. But, SACKs can also be received when the receiver gets unordered data chunks. Hence, such frequent reduction in cwnd size leads to the issue of compromised throughput.

  5. 5.

    DB-CMT scheme can considerably improve the throughput performance on varying PLRs with varying receiver buffer sizes by transmitting more data chunks through a minimum delay variation path. Moreover, DB-CMT can also improve the FTT performance on varying file sizes compared to other simulated CMT schemes.

7 Conclusions

This paper proposed a new delay-based concurrent multipath transfer policy (DB-CMT) for simultaneous multipath transmission. DB-CMT has a new delay-based data chunk scheduling policy, a new retransmission path selection policy (RTX-CL), and a fast retransmission method. The proposed data chunk scheduling policy transmits a large amount of data over a less loaded path, while RTX-CL selects the retransmission path whose cwnd is larger and the PLR is lower. Simulation results showed that the proposed RTX-CL policy achieves better throughput and retransmission timeout results. Moreover, the overall performance of DB-CMT is better regarding throughput, FTT, and cwnd growth.