Congestion control is one of the main obstacles in cyberspace traffic. Overcrowding in internet traffic may cause several problems; such as high packet holdup, high packet dropping, and low packet output. In the course of data transmission for various applications in the Internet of things, such problems are usually generated relative to the input. To tackle such problems, this paper presents an analytical model using an optimized Random Early Detection (RED) algorithmbased approach for internet traffic management. The validity of the proposed model is checked through extensive simulationbased experiments. An analysis is observed for different functions on internet traffic. Four performance metrics are taken into consideration, namely, the possibility of packet loss, throughput, mean queue length and mean queue delay. Three sets of experiments are observed with varying simulation results. The experiments are thoroughly analyzed and the best packet dropping operation with minimum packet loss is identified using the proposed model.
Internet of Things (IoT) refers to direct communication between the physical and digital world [
Formerly, the IoT was designed to use different types of sensors to gather data from the environment to store and process it automatically and reduce human efforts [
 Achievement of lowest packet dropping possibility: It can be achieved when the optimum function is increased by the threshold value. It is expected to generate minimum packets drop possibility in comparison to other functions.
 Highest throughput in the network delayed due to achievement of minimum proliferation: The best possible operation should attain a low delay of the network at the highest throughput in comparison to other operations.
 Discover the best possible size of the average queue: The computed mean of the size of the queue should consider being the best perspectives to the highest threshold in comparison to other operations.
Recently, there is a huge demand for application services that operate at immensely high speed on the Internet. Additionally, this high speed is desired to be delivered while accommodating all of the QualityofService (QoS) parameters. The principal significance is to ensure the QoS in certain delaysensitive applications in the network of smart devices. The memory capacity of the existing switches and routers is limited. Therefore, usually, incoming web traffic goes beyond the extrovert buffer size. When the buffer is overflown congestion takes place that leads to network collapse and loss of packets. Congestion also causes packet delays during the transmission. Hence, insufficient information is retrieved and it drastically degrades the standard of internet services. Therefore, an efficient traffic queue management model is required to overcome the network congestion.
This research article presents an optimized analytical model for traffic queue management in a network. The main objective is to obtain a mathematical solution that is optimum and results in enhanced performance metrics. This objective is fulfilled by taking into consideration and observing two tasks. (1) Decreasing the mean queuing delay and increasing the throughput after its execution in the proposed analytical model. Similarly, its evaluation and comparison to other operations in Sharma et al. [
This section provides a detailed review of the existing algorithms and techniques such as the Tail Drop (TD) and RED methods that are used for internet traffic congestion control. Similarly, a detailed overview is provided for the analytical model presented in Sharma et al. [
Over the year’s researchers have proposed several techniques to manage the congestion in the internet traffic. One of the classic buffer management approaches is known as TD technique. The TD approach was developed to overcome the gridlock and was applied on routers [
RED method recognizes the congestion in advance and gives a response to the transmitter by either dropping or marking packets even if the space of buffer is ready for use [
To control the network congestion, several researchers have also focused on using other algorithms such as the Decentralized Traffic Aware Scheduling (DeTAS) algorithm, Constrained Application Protocol (CoAP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods. In Accettura et al. [
To evaluate the performance of the proposed model, it is necessary to compare it to an existing model. The model presented in Sharma et al. [
Every entrance accompanies an individualistic Bernoulli procedure to a limited buffer capacity (
The analytical model proposed by Sharma et al. [
Symbol  Description 

P  Packet loss 
Packet arrival  
Zero packet departure  
Zero packet arrival  
Threshold value  
System volume  
Initial coefficient  
MQM  Mean queue length 
W  Mean waiting time 
S  Throughput 
PL  Probability of packet loss 
As already stated the model proposed in this research paper is based on the model presented in Sharma et al. [
Several of the packets are dropped, the probability is taken such that the threshold value equal to or greater than
Suppose that the proposed model utilized a discretetime queuing system, dependent on a specific unit of time to obtain performance metrics equations, called a slot. The finite buffer space (
1) The following sequence of steps is used to find the STD measuring expression using virtual mathematics to obtain the performance metrics and balanced equation from the new model. The symmetry probability equations given below are obtained under the supposition
Generally, the equations can be represented as,
For
In the general case, the following equations are obtained,
For
For
2) For each value of =
3) Using the normalized equation
4) For substituting and finite queue length results obtained in
5) To compute the “Mean Queue Length” (MQL) an expression is created from the firstorder derivative which is obtained in step (4) evaluated at Z = 1 as shown below:
6) Using a few rules [
a) The period where a random customer gets into the system and leaves the system is the waiting time
b) Throughput (S) is the number of customers passing through the system per unit.
7. Some of the random customers find no waiting room to hold them as they reached the destination.
where
The probability of Packet Loss enlarged from zero to
Experimental simulations are carried out to analyze and observe the performance metrics expression resulting in the four typical packets dropping functions already discussed earlier.
This analysis is observed in MATLAB for numerical and graphical simulations. The input values of the RED parameters,
The
 In
 In
 In
To detect the best possible operation from the power of a function
 In
 In
 The graphical and numerical outcomes visibly illustrate that out of the two operations, exponential function,
Finally, to draw a general conclusion, a tentative analysis is carried out using different parameter values of a, about the exponential function, a^{x}.

 These parameter settings may be utilized for various applications of data service. Whereas, for realtime applications that need minimum delay such a setting should be utilized where the parameter should be reaching 1.
 All the results are compatible with a typical system. The exponential operation depends on the input values and setting of the parameter for AQM method. Therefore, this analysis is a handout for the performance modeling.
This paper presents an analytical model to investigate the best possible packet dropping operation that utilizes virtual mathematical approaches. The performance modeling of the proposed model has also been discussed. The proposed modeling technique is derived from Random Early Detection techniques of AQM methods. The discretetime queuing system, single threshold, departures and independently distributed packets arrivals maintain the process of Markov chain state transition and are based on the Bernoulli process. Performance metrics such as throughput, the average length of the queue, average delay of queuing, the possibility of packet loss and threshold are derived for divergent functions. These metrics are analyzed for the precision of the model by performing a wide variety of simulation experiments. The preset input values for packets arrival and departure, when the variable threshold values are used to compare the parameters at the stable state. Finally, it is concluded by analyzing the results that the exponential operation is the best possible operation which attained the lowest probability of losing packet, maximum throughput and minimum delay in comparison to other operations when the threshold value is increased.
The authors would like to thank Dr. M. Amin and Dr. Waqar assistant professors whose constructive comments helped in the improvement of the presentation of this project.