1 Introduction

An emerging connected vehicle paradigm, the VIoT [1,2,3,4,5], interconnects vehicles with other vehicles, humans, and machines for optimal sharing of traffic and non-traffic-related information for safe and comfortable commuting. VIoT was formed as an inevitable division of the intelligent transportation system (ITS) [6,7,8] to improve data sharing and better resource management for semi or fully autonomous vehicles. VIoT shares the vehicle information from the intelligent embedded sensors to the cloud or a diverse group of users through a fixed hotspot or roadside unit (RSU). The vehicle-to-everything (V2X) paradigm [9,10,11] of VIoT solely relies on dedicated short-range communications (DSRC) [12,13,14,15,16] for device-to-device (D2D) information exchange.

The VIoT operates in a 5.9 GHz radiofrequency with 10 MHz seven non-overlapping channels operating in a 75 MHz radio spectrum. VIoT also caters to support non-vehicle safety services, such as file sharing, mailing service, toll payment, e-shopping, e-payment, and acts as a mobile hotspot for last-mile wireless internet connectivity. The internet remains the backbone of the VIoT ecosystem; the boundless global web traffic and data center traffic depends on TCP [17,18,19] to deliver data packets between end systems. Figure 1 displays the vehicular transmission model in different modes.

Fig. 1
figure 1

VIoT communication networks

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TCP incorporates flow control [20], congestion control [21], and error control mechanisms, ensuring the successful in-sequence transmission of each information byte between sender-receiver processes. TCP's bottleneck control mechanism comprises a slow start (SS), congestion avoidance (CA), and CR mode. In the SS mode, the source device fixes the SS threshold (SSThresh) and doubles the source window (Wnd_) rate for each successful acknowledgment. On exceeding the SSThresh, the source device initiates the CA phase and gradually increments the transmission rate by one data packet for each RTT. TCP starts the transmission rate control process when the source device infers packet loss by a timeout or three duplicate acknowledgments (3DUPACK). The source device trims down the Wnd_ rate of TCP connections during the congestion control process by a commensurable rate reduction factor of 0.5. In the CR phase, the Wnd_ increments one packet per RTT until the equilibrium point. Figure 2 displays the Wnd_ growth or transmission pattern of additive increase and multiplicative decrease (AIMD) traffic connection for each iteration or RTT.

Fig. 2
figure 2

Transmission pattern of RFC6582 traffic connections

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The majority of web servers around the globe widely adopt RFC 6582 [22] congestion control approach due to its lesser implementation complexity and faster mechanism to detect incipient network bottleneck conditions. In addition, the proper functioning of the congestion control algorithm in each phase results in optimal throughput performance. However, the existing RFC 6582 implementation remains inappropriate for the vehicular environment due to the following deficiencies.

Spurious rate control initiation: The RFC 6582 algorithm invokes rate control based on the timeout condition. This assumption results in triggering a spurious rate decrement process for non-congested RTT jitter or packet losses that arise due to frequent route breakage and radio channel losses. The spurious rate control phenomenon severely destabilizes the throughput stability of TCP traffic flow in the wireless links.

Slow convergence rate: TCP implementation in the CR phase is plagued by the slow Wnd_ update function that leads to additional RTTs to finish the flows, results in increased communication latency between end systems.

Fairness disparity among TCP flows: From Fig. 1, it is observed that the existing Wnd_ growth in the CR phase maintains a fairness disparity among the concurrent TCP flows, i.e., flows with higher and lower transmission rates maintain a massive variation in sharing the network bandwidth.

The DART implementation proposed in this article modifies the rate adjustment model and Wnd_ growth function to overcome the limitations of TCP connections under the VIoT environment. The later part of the article is arranged into five sections. Section 2 briefs contemporary literatures on independent congestion control algorithms developed for wireless scenarios. Section 3 narrates the operation of the UAR + SLC algorithms in vehicular networks, and Sect. 4 explicates the fairness and convergence model of the DART approach based on the optimization theory. Section 5 briefly outlines the vehicular simulation outcomes of the proposed and existing algorithms under diverse scenarios. Finally, Sect. 6 presents the proposed UAR + SLC implementation conclusion and discusses the future direction of the work.

2 Background and Related Works

Over three decades, TCP's congestion avoidance algorithm has undergone several modifications [23] to sustain a stable data rate among multiple traffic flows under both wired and wireless conditions. This literature briefly reviews the recent developments of independent congestion avoidance approaches developed to improve TCP's throughput stability in lossy wireless links. CERL + [24] method derives two parameters (queuing delay and RTT delay) for predicting the bottleneck wireless link. The sender initiates rate adjustment when the derived delay parameter is higher than the threshold level. Rather than of reacting to packet drop, CERL + relies on delay parameter estimation for Wnd_ deflation. However, the Wnd_ growth function in the CR phase is similar to the RFC 6582 approach, resulting in a slow convergence rate.

TCP Wave [25] approach implements a unique burst-based transmission of packets instead of traditional Wnd_ based packet transmission. The WAVE algorithm tracks the wireless network dynamics based on ∆RTT computation, derived from average RTT and minimum RTT (RTTmin) values. The source node initiates a reduction in burst size when the derived ∆RTT is higher than the tolerated bottleneck level β.

FIT [26] algorithm is yet another derivative of RFC6582, where a newer Wnd_ increment mechanism is introduced in the CR phase based on the traffic flows. Furthermore, FIT implements a new rate adjustment mechanism instead of the traditional rate halving method. However, the FIT algorithm reacts to non-congested losses of lossy radio links that cripple TCP's throughput capability. TCP-LoRaD [27] predicts the bottleneck wireless link based on the queuing delay parameter. However, the Wnd_ growth pattern of TCP-LoRaD in the CR phase resembles the RFC6582 model resulting in a slower convergence and bandwidth sharing inequality among multiple traffic flows.

ACC [28] is yet another method to improve AIMD traffic flow under lossy radio conditions. The ACC approach solely relies on packet latency to initiate the transmission rate adjustment process. First, the sender derives the queuing delay of a wireless link by computing the RTT values of the current and old packet. The source device starts the rate adjustment process where the threshold value lesser than the obtained RTT (ζ × qmax). In the CR phase, the ACC algorithm implements a linear Wnd_ increase similar to RFC 6582, resulting in a slow data throughput to attain the steady state or maximal point.

Vegas [29, 30] based end-to-end congestion avoidance implementation estimates RTT delay parameter to invoke the rate adjustment process. However, the Vegas approach fails to update the latest RTTmin value for wireless topology change. The discrepancy in computing RTTmin leads to spurious initiation of a congestion control process that cripples TCP's throughput performance. Pegas [31], modification of Vegas algorithm implements a particle swarm approach in fixing the new RTTmin value for dynamically changing topology. Pegas captures dropped packet count, RTTmin, and current transmission rate as the input parameter for setting the dynamic RTTmin value for each packet interval. However, PSO implementation at the sender side requires more computation parameters for obtaining a new RTTmin value for each packet interval. Similarly, G-vegas [32] employs grey prediction theory, and D-TCP [33] uses the cuckoo search optimization technique to estimate the dynamic RTTmin value based on the wireless dynamics.

However, the Vegas-based approaches perform worse under diverse TCP traffic conditions due to RTT fluctuations [26] in wireless conditions. Table 1 summarizes the behavior of recent AIMD congestion avoidance algorithms under lossy wireless networks. However, the AIMD approaches Wnd_ growth pattern severely compromise the steady-state convergence of the TCP flows. The additive Wnd_ growth in the CR phase cripples the throughput rate and requires additional RTTs to complete the TCP flow.

Table 1 Comparison of AIMD congestion avoidance approaches
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3 The Proposed DART Approach

The DART implements UAR and SLC algorithms which require modification in TCP's congestion control and recovery mechanisms. The UAR algorithm is a three-step process responsible for the rate tuning at the sender side. Step 1 implements a bottleneck prediction (T_bottle) parameter to determine the incipient link congestion instead of a packet loss effect. The T_bottle parameter is computed based on the average RTT (RTTavg) and RTTR_min values. As mentioned in [34], the RTTavg values are computed from the recent five samples. The RTTR_min is the minimum RTT value among the recent five samples that minimize the impact of RTT fluctuation in T_bottle prediction. When the estimated T_bottle rate is superior (0.7) than the threshold (γ) rate, the sender begins the rate adjustment process. The γ value is fixed as 0.7 based on the repeated trials using wireless internet RTT measurements. Lesser γ value results in a spurious timeout due to frequent RTT fluctuations. A higher γ value allows the sender to respond slowly to bottleneck conditions. The T_bottle parameter is derived as

$$T\__{{bottle}} = \frac{{RTT_{{avg}} - RTT_{{\min }} }}{{RTT_{{avg}} }}$$
(1)

Step 2 implements the utilization prediction (Wutility) parameter to initiate a proportionate reduction mechanism during the rate adjustment process. The sender identifies low and high rate TCP flows based on the δ threshold value (δ = 0.5), estimated based on the current Wnd_ level (Wi) and maximum receiver capacity Wmax or initial SSThresh. The source node implements two rate decrement factors based on the utilization levels. The Wutility parameter and rate decrement factor is derived as

$$W_{utility} = \frac{{W_{i} }}{{W_{\max } }}$$
(2)
$$\begin{array}{*{20}l} {W_{utility} < \delta ;} \hfill & {low\,rate\,flow} \hfill \\ {W_{utility} \ge \delta ;} \hfill & {high\,rate\,flow} \hfill \\ \end{array}$$
(3)

Rate reduction procedure for high bandwidth utilized TCP flow is computed as

$$W_{{i_{(k + 1)} }} = \,W_{i} *.0.5\,\,\,;\,W_{utility} \ge \delta$$
(4)

Rate reduction procedure for low bandwidth utilized TCP flow is computed as

$$W_{{i_{{(k + 1)}} }} = W_{i} *\left\{ {\left( {1 - \frac{{W_{i} }}{{W_{{\max }} }}} \right)} \right\};W_{{utility}} {\text{ }} < \delta$$
(5)

Step 3, the UAR algorithm implements a modified fast retransmit mechanism during the packet loss state, resulting in retransmission of missing data packets within the current RTT without invoking the rate reduction process.

The SLC algorithm is responsible for the Wnd_ increment mechanism in the CR phase with a faster recovery rate and minimum fairness disparity among traffic flows. The SLC algorithm introduces a new dynamic Wnd_ update pattern that allows the traffic flow to enter the steady-state transmission point at a faster rate with the least fairness disparity. The steady-state point is an equilibrium state where the source device transmission rate matches the link capacity. The Wnd_ increase pattern of the CR phase is given as

$$W_{i(k + 1)} = W_{i(k)} + \frac{{\left( {4*W_{\max } } \right)}}{{W_{i(k)} }}$$
(6)

The DART approach finite state machine (FSM) model is represented in Fig. 3. The FSM model specifies interactions among different transition states and their impact on the transmission rate.

Fig. 3
figure 3

FSM model of DART approach

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3.1 Fairness and Convergence Efficiency Analytical Validation

The proposed DART approach’s bandwidth fairness and transmission efficiency performance are validated using an analytical model and compared against CERL + , TCP-LoRaD, and RFC 6582 approaches. The fairness and convergence efficiency analytical equations are derived based on Jain’s model [35]. In wireless conditions, the fairness performance of TCP flow is influenced by Wnd_ growth pattern and channel conditions [36, 37]. The DART implementation practices a packet latency/T_bottle parameter to initiate the Wnd_ decrement process. Let γ(t) be the T_bottle threshold value; rs represents the source node dispatching rate, rm represents the highest attainable dispatching rate of the source node, WLc represents the wireless link capacity and RTarget is the steady-state point. The source device dispatching rate matches the wireless link capacity (RTarget = WLc) in the steady-state point. The RTarget value is taken as the maximum dispatching rate (rm) attained by the sender and expressed as the function of time

$$r_{s} (t) = \left\{ {\,r_{{_{y1} }} (t),r_{{y_{2} }} (t),r_{{y_{3} }} (t),....r_{{y_{m} }} (t)} \right\}$$
(7)

The source node increment rs for non-congested state γ(t) = 0 (γ < 0.7) and lessen rs for an increase in network load γ(t) = 1 (γ ≥ 0.7).

$$\begin{array}{*{20}l} {\gamma (t) = 0,} \hfill & {non\,congested\,state} \hfill \\ {1,} \hfill & {congested\,state} \hfill \\ \end{array}$$
(8)

Figure 4 illustrates the communication model of the proposed DART approach.

Fig. 4
figure 4

DART approach communication model

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The sender updates its dispatching rate rs(t + 1) based on γ(t) and follows an additive Wnd_ increment pattern for γ(t) = 0 and multiplicative Wnd_ decrement pattern for γ(t) = 1. The Wnd_ increment and decrement patterns are expressed as

$$\begin{array}{*{20}l} {r_{s} (t + 1)} \hfill & {W_{I} + r_{i} (t),\gamma (t) = 0} \hfill \\ {} \hfill & {W_{D} *r_{i} (t),\gamma (t) = 1} \hfill \\ \end{array}$$
(9)

The ri (t) represents the current dispatching rate, rm (t) is the maximum dispatching rate, WI and WD denotes additive Wnd_ increment pattern and multiplicative decrement pattern. For the DART approach, WI and WD are derived from the Eq. (4), (5), and (6) as

$$W_{I} = \frac{{4*r_{m} }}{{r_{{_{i} }} }}$$
(10)
$$\begin{array}{*{20}c} {W_{{_{D} }} } & {1{\text{ - }}\frac{{r_{{_{m} }} }}{{r_{i} }};\,r_{i} (t) \le \delta } \\ {} & { = \frac{1}{2};\,r_{i} (t) > \delta } \\ \end{array}$$
(11)

On substituting (10) and (11) in (9), the equation can be modified as

$$\begin{aligned} r_{s} (t + 1) & = \frac{{4*r_{m} }}{{r_{{_{i} }} }} + r_{i} (t),\quad \gamma (t) = 0 \\ & = 1 - \frac{{r_{m} }}{{r_{i} }}*r_{i} (t);\quad r_{i} (t)\delta \,\gamma (t) = 1{\text{ }} \\ & = \frac{1}{2}*r_{i} (t);\quad r_{i} (t) > \delta \,\gamma (t) = 1{\text{ }} \\ \end{aligned}$$
(12)

The DART approach flow efficiency equation is developed based on the TCP fairness and convergence vector diagram displayed in Fig. 5. Let rs1 (x-axis) and rs2 (y-axis) are the two source devices sharing the bottleneck wireless link. The midpoint on the graph represents the efficiency of the two flows. The region below the efficiency midpoint is the underutilization, and above is the congested state. The flows (rs1 and rs2) attain its transmission efficiency when rs1 = rs2 = RTarget = WLc. The convergence rate is an essential component in attaining the efficiency of the TCP flow. The convergence rate denotes the pace at which the source device transmission rate attains the equilibrium state. The dispatching rates of the TCP flows get lessened when rs (t) reach the equilibrium condition and again attain the steady-state point in repeated cycles.

Fig. 5
figure 5

Efficiency and fairness vector representation

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The condition for the convergence efficiency of TCP flow is derived as

$$\begin{array}{*{20}l} {\gamma (t) = } \hfill & {0 \Rightarrow \sum {r_{s} (t + 1)} } \hfill & { > \,r_{m} (t)} \hfill \\ {\gamma (t) = } \hfill & {1 \Rightarrow \sum {r_{s} (t + 1)} } \hfill & { < \,r_{m} (t)} \hfill \\ \end{array}$$
(13)

The independent congestion avoidance algorithm’s efficiency is crippled severely by negative feedback phenomena due to spurious rate decrement process for packet loss conditions. However, the DART approach invokes rate adjustments solely based on the T_bottle parameter, which considerably minimizes negative feedback phenomena and improves the TCP flow efficiency in wireless conditions. The convergence efficiency of the DART approach is derived by substituting Eq. (12) in (13)

$$\gamma (t) = 0\left( {\frac{{4*r_{{_{m} }} }}{{r_{{_{i} }} }} + r_{i} (t)} \right) > r_{m} (t)$$
(14)
$$\begin{array}{*{20}l} {\gamma (t) = } \hfill & {1 \Rightarrow \left( {1{\text{ - }}\frac{{r_{{_{m} }} }}{{r_{i} }}} \right)*r_{i} (t) < r_{m} (t);\,r_{i} (t)\delta } \hfill \\ {} \hfill & { = 1 \Rightarrow \left( {\frac{1}{2}*r_{i} (t)} \right) < r_{m} (t);\,r_{i} (t) > \delta } \hfill \\ \end{array}$$
(15)

Equation 15 denotes the utilization level based on the proportionate reduction for γ(t) = 1 condition. Equation 14 represents the Wnd_ increment pattern for γ(t) = 0, which results in a quicker convergence pace towards the midpoint efficiency line. Similarly, the efficiency equation for RFC 6582 based TCP flows (CERL + and TCP-LoRaD) are derived as

$$\gamma (t) = 0 \Rightarrow \left( {\frac{1}{{r_{{_{i} }} (t)}} + r_{i} (t)} \right) > r_{m} (t)$$
(16)
$$\gamma (t) = 1 \Rightarrow \left( {\frac{1}{2}*r_{i} (t)} \right) < r_{m} (t)$$
(17)

Figure 6 displays the convergence efficiency analysis of RFC 6582 and DART in the CR phase. The convergence efficiency Eqs. (14, 15, 16 and 17) are validated by substituting the values rm = 36 and the initial ri value = 18. The Wnd_ growth oscillates between the minimum and steady-state point in repeated cycles. The graph shows that DART accomplishes a faster convergence pace than RFC 6582, i.e., the DART algorithm reaches efficiency midpoint within fewer RTTs.

Fig. 6
figure 6

Efficiency Convergence of DART vs. RFC6582 Wnd_ growth

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Fairness study measures the bandwidth distribution among two separate TCP traffic flows (rs1 and rs2) sharing the same bottleneck wireless link of WLc. The fairness convergence is attained among the competing flows when the fairness index F(rs) moves towards unity, i.e., rs1 = rs2. The dispatching rate of the rs1 (t) or rs1 (t) is below/above the fairness line in graph (Fig. 5) results in unfairness among sharing network bandwidth the competing flows. The F(rs) index is derived using Jain's equation as

$$F(r_{s} ) = \frac{{\left( {\sum {r_{si} } } \right)^{2} }}{{n\left( {\sum {r_{si}^{2} } } \right)}}$$
(18)

The Eq. 18 can be modified as

$$F(r(t + 1)) = \frac{{\left( {\sum {r_{{_{si} }} (t + 1)} } \right)^{2} }}{{n\left( {\sum {r_{{_{si} }} (t + 1)^{2} } } \right)}}$$
(19)

Altering Eq. (19) based on WI and WD variables

$$F(r(t + 1)) = \frac{{\left( {\sum {W_{I} + W_{D} r_{i} (t)} } \right)^{2} }}{{n\sum {\left( {W_{I} + W_{D} r_{i} (t)} \right)^{2} } }}$$
(20)

where

$$W_{I} \ge 0,\quad 0 \le W_{D} < 1$$
(21)

By substituting Eq. (14) and (15) in (20), the fairness index of the DART approach is derived as

$$F(r(t + 1)) = \frac{{\sum {\frac{{4*r_{{_{m} }} }}{{r_{{_{i} }} }} + 1{ - }\frac{{r_{{_{m} }} }}{{r_{i} }}*r_{i} (t)}^{2} }}{{n\sum {\frac{{4*r_{{_{m} }} }}{{r_{{_{i} }} }} + 1{ - }\frac{{r_{{_{m} }} }}{{r_{i} }}*r_{i} (t)} }},\,\,r_{i} (t) \le \delta$$
(22)
$$F(r(t + 1)) = \frac{{\sum {\frac{{4*r_{{_{m} }} }}{{r_{{_{i} }} }} + \frac{1}{2}*r_{i} (t)}^{2} }}{{n\sum {\frac{{4*r_{{_{m} }} }}{{r_{{_{i} }} }} + \frac{1}{2}*r_{i} (t)}^{2} }},\,\,r_{i} (t) > \delta$$
(23)

Table 2 displays the fairness and efficiency analytical equations of proposed and existing approaches.

Table 2 DART, CERL + , RFC6582 and TCP-LoRaD fairness and efficiency equations
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Figure 7 displays the Wnd_ growth function of RFC 6582 and DART approaches in the CR phase based on the fairness equations in Table 2. The rm value is taken as 36; the initial ri value for high utilized flow is taken as 18, and the low utilized flow is taken as 6. The graph shows that DART accomplishes a minimum disparity among the competing flows within fewer RTTs. Conversely, RFC 6582 has a slower flow convergence rate and larger fairness disparity gap between high and low-rate TCP flows.

Fig. 7
figure 7

Fairness Convergence of DART vs. RFC6582 a DART Wnd_ growth and b RFC6582 Wnd_ growth

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The pseudocode for DART implementation in SS, CA and CR phases are given as.

figure h

3.2 Simulation Results and Analysis

The DART approach performance is validated using the vehicular simulation approach under varying node mobility and varying traffic load scenarios. The DART, RFC6582, CERL + , and TCP-LoRaD congestion avoidance algorithms are evaluated based on average throughput, average end-to-end packet latency, fairness, and transmission efficiency metrics. The experiments conducted using the network simulator (NS-3) [38, 39] in a closed road formation, as shown in Fig. 8. The vehicle mobility traces are generated using VanetMobiSim [40, 41] and ported into the simulation. The vehicular network features are incorporated using WAVE library modules [42]. Table 3 summarizes the parameters of vehicular simulation experiments.

Fig. 8
figure 8

Closed road formation scenario in PyViz [43, 44] visualizer

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Table 3 Vehicular simulation parameters
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3.3 Mobility Analysis

The mobility analysis measures the congestion avoidance algorithm performance under varying vehicle speed conditions. The vehicle speed varies between a minimum of 5 m/s to a maximum of 20 m/s in closed road simulation experiments, and Fig. 9 displays the simulation outcomes. The DART approach achieves an average throughput of 9.82 Mbps in low speed road conditions and yields an improvement of 26.57, 11.91, and 9.26% against the RFC6582, TCP-LoRaD, and CERL + approaches. In the 20 m/s vehicle speed condition, the DART attains an average throughput of 5.57 Mbps, and the existing methods encounter a throughput lag of 49.55% (RFC6582), 36.98% (TCP-LoRaD), and 34.11% (CERL +). In vehicular networks, frequent connection failure occurs due to vehicle mobility conditions, triggering timeout at the sender side. Under such circumstances, the DART approach re-transmits only the lost packet without invoking the rate adjustment that considerably stabilizes the throughput rate. Furthermore, the DART rate adjustment based on T_bottle prediction and faster convergence rate in the CR phase improves the throughput rate than the existing approaches. However, the TCP-LoRaD and CERL + in high mobility conditions attain a lesser average throughput performance due to its slow convergence rate in the CR phase.

Fig. 9
figure 9

Congestion avoidance approaches performance under mobility conditions a average throughput b mean delay c transmission efficiency and d fairness

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Similarly, the DART approach yields a lesser mean delay during packet transmission compared to the other approaches. The DART approach attains a 19.67, 14.74, and 9.26% lesser RTT packet delay than RFC6528, TCP-LoRaD, and CERL + approaches in the low vehicle speed conditions. The DART approach attains similar mean delay performance in the high speed conditions. During simulations, it is noted that the rate adjustment based on T_bottle prediction allows the sender to push more data packets when the link delay is low, minimizing mean packet latency during transmission. Conversely, the slow convergence rate and RTT fluctuation in bottleneck prediction of CERL + and TCP-LoRaD increase the mean delay of data packets to finish the flow.

The number of successful data packets delivered to the destination determines the transmission efficiency. The wireless link quality and the queuing delay are the two prime factors determining packet transmission efficiency in vehicular networks. The DART approach attains an average efficiency between 97.31 and 99.12%, and the existing approaches reach efficiency between 95.25 and 98.11% in diverse mobility conditions. The fairness metric evaluates equitable bandwidth distribution among the competing TCP flows in the network. The DART approach attains average bandwidth fairness of 95.25% in diverse mobility.

Conversely, the existing approaches achieve 92.09% bandwidth fairness among traffic flows in mobility conditions. The DART approach proportionate rate adjustment and SLC algorithm significantly contribute to the equitable sharing of network bandwidth among different flows. However, the fairness capability of the existing approach is crippled primarily due to its flat-rate decrement mechanism and Wnd_ growth pattern in the CR phase.

3.4 Traffic Load Analysis

The traffic load analysis measures the performance of the congestion avoidance approach under varying TCP traffic conditions. The experiments were conducted by increasing the traffic load from two to eight pairs of a source–destination process with an average vehicle speed of 10 m/s. Figure 10 displays the outcomes of the proposed and existing approaches. The DART approach attains the average throughput rate of 10.12 and 7.37 Mbps under minimum and maximum traffic load conditions, with 29.11, 12.68, and 10.23% improvement against RFC6582, TCP-LoRaD, and CERL + approaches under varying load conditions. Furthermore, the DART approach congestion prediction assisted proportionate rate adjustment, and a faster convergence rate considerably contributes to achieving a higher throughput rate.

Fig. 10
figure 10

Congestion avoidance approaches performance under traffic load conditions a average throughput b mean delay c transmission efficiency and d fairness

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During packet transmission under diverse traffic load conditions, the DART approach attains 22.44, 17.04, and 13.09% lesser mean delay than RFC6528, TCP-LoRaD, and CERL + approaches. The DART approach Wnd_ growth pattern allows the sender to the swift packet transfer during the low link delay conditions that minimize mean packet delay. Conversely, the existing approaches' slow transfer rate in the CR phase increases the mean delay of data packets to finish the flow.

The DART packet transmission yields a higher efficiency of 95.32–99.12% in diverse load conditions due to its capability to infer queuing delay that minimizes packet loss associated with buffer overflows. However, transmission efficiency is degraded due to radio channel loss that induces considerable packet drop in the DART and existing approaches under vehicular networks. Similarly, DART proportionate rate decrement and SLC algorithm in the CR phase allow multiple flows to attain a 95.32% fair distribution of resources. However, the traditional Wnd_ growth pattern of similar AIMD approaches achieves 92.56% fairness under diverse traffic conditions.

4 Conclusion

The DART congestion avoidance approach proposed in this article intends to improve TCP traffic throughput, convergence rate, and equitable bandwidth distribution under VIoT networks. The DART initiates a proportionate rate adjustment mechanism based on the T_bottle parameter that considerably lessens needless throughput reduction during packet losses in wireless conditions. Furthermore, the modified Wnd_ growth pattern in the CR phase significantly boosts the convergence rate and maintains the equitable distribution of network bandwidth among low and high utilized flows. The analytical equations derived based on Jain's model verifies the improvement in fairness and convergence rate performance over the existing schemes. The experiment outcome under two scenarios proves that DART attains considerable throughput, transmission efficiency, and equitable bandwidth distribution improvement with the least mean delay in packet transmission. The proposed DART approach's future variant is customized to support the multipath TCP implementation under vehicular networks.