Swarm intelligence-based packet scheduling for future intelligent networks

An analysis of LSTM

Long short-term memory (LSTM) (Houdt, Mosquera & Nápoles, 2020) is a special RNN cell that addresses the issues faced with traditional RNNs, such as loss of the long-term dependencies due to vanishing gradient issues, as discussed in Bengio, Simard & Frasconi (1994).

Figure 4 shows that an LSTM employs three gates to control adding or removing information from the cell state. The forget gate (f_t) defines what information needs to be removed from the cell state. It analyses the previous state (y_p) and current input sequence (x_t).

The f_t is defined in Eq. (1), and its output is always between 0 and 1 for each state in the c_p where zero means discarding it. (1)${\displaystyle {\mathrm{f}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{f}}.\left[{\mathrm{y}}_{\mathrm{p}},{\mathrm{x}}_{\mathrm{t}}\right]+b_f\right)}$

The information that needs to be retained in the current state of the cell is determined in two steps. First, the input gate (i_t) function, as defined in Eq. (2), determines the parameters that need to be updated. Then, the candidate parameter values (${\tilde{\mathrm{c}}}_{\mathrm{t}}$) are generated by the tanh function as per Eq. (3). Next, these are combined to update the values of c_t as per Eq. (4).

(2)${\displaystyle {\mathrm{i}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{f}}.\left[{\mathrm{y}}_{\mathrm{p}},{\mathrm{x}}_{\mathrm{t}}\right]+b_i\right)}$ (3)${\displaystyle {\tilde{\mathrm{c}}}_{\mathrm{t}}=tanh\left({\mathrm{W}}_{\mathrm{c}}.\left[{\mathrm{y}}_{\mathrm{p}},{\mathrm{x}}_{\mathrm{t}}\right]+b_c\right)}$ (4)${\displaystyle {\mathrm{c}}_{\mathrm{t}}={\mathrm{f}}_{\mathrm{t}}\mathrm{\ast }{\mathrm{c}}_{\mathrm{p}}+{\mathrm{i}}_{\mathrm{t}}\mathrm{\ast }{\tilde{\mathrm{c}}}_{\mathrm{t}}}$

The output of the LSTM is based on the current state, and the sigmoid function is applied to select the values to be output. The final output of the cell is obtained by applying the tanh function to the above values and multiplied by the output gate. The output gate function is defined in Eq. (5), and the current output state is defined in Eq. (6).

(5)${\displaystyle {\mathrm{o}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{o}}.\left[{\mathrm{y}}_{\mathrm{p}},{\mathrm{x}}_{\mathrm{t}}\right]+b_o\right)}$ (6)${\displaystyle {\mathrm{y}}_{\mathrm{t}}={\mathrm{o}}_{\mathrm{t}}\mathrm{\ast }tanh\left({\mathrm{c}}_{\mathrm{t}}\right)}$

TAOC learning model (TLM)

TIPS scheduling algorithm requires five different values, including the time, node function, number of downstream nodes, and rank and weight of the erlang values. Therefore, the objective of the TLM is to characterize each access node and provide the above mentioned information to the upstream node. To cope with the above requirements, an LSTM-based encoder–decoder model is adopted, as shown in Fig. 5.

The above model is replicated for each physical interface on the downstream side. In addition to the unit model for each interface, an aggregate model combines the input and output values. The model takes the ts number of sample values of x and predicts the m number of values for t + 1, T + 2, …, t + m.

In the unit model, C_ei represents the LSTM cells for the encoder where i falls in $\left(\mathrm{t},\mathrm{t}+\mathrm{n}\right)$ and C_dj represents the LSTM cells for the decoder part. The j ranges from t + 1 to t + m. The $\mathrm{D}\left({\mathrm{L}}_{\mathrm{d}}\right)$ forms the dense layer, which receives the state information from all the cells and transforms it into the output of L_d dimension. On the other hand, $\mathrm{D}\left(1\right)$ is a dense layer (Helen Josephine, Nirmala & Alluri, 2021) that receives the m inputs and connects the F layer to connect a single dimension stream. The F flattening layer (Chen et al., 2023) that receives the inputs equals the hidden layers ( L_e) multiplied by the ts units.

The TLM is installed on each network node with the downstream nodes, such as the aggregation layer (DAL) and core nodes (CAL). The core nodes receive the swarm of g inputs fed to TLM(c) nodes. The TLM(g) nodes provide the data to TIPS instances running on G nodes, and TLM(c) provides the data for the TIPS instances running on C nodes, as shown in Fig. 6.

There are two approaches available for implementing TLM on the DAL layer. The first approach is to install TLM on the egress interface of the access nodes, which predicts the $d_i\left(m+1\right)$ used by the TLM instances running on DAL. This approach is efficient for large-scale networks and allows the distributed learning model. The other approach is to implement TLM on the ingress interfaces of aggregation nodes, i.e., DAL nodes. In this case, it serves two purposes; the TLM provides the base learning as well as $d_i\left(m+1\right)$ in addition to $g_i\left(m+1\right)$.

Network topology

Figure 7 shows the experimental network setup following the state-of-the-art hierarchical topology. The hierarchal network topologies offer several benefits in scalability, redundancy, performance, security, manageability, and maintenance (Cisco, 2022; Zhang & Liang, 2008). The access nodes represent a serving area with a distinct traffic profile. The access nodes to aggregation nodes connectivity is achieved with dedicated physical links with different data rates according to the requirements of the serving area. Furthermore, the access node to aggregation nodes connectivity follows the rule of proximity, i.e., the access nodes from co-locating areas are connected to the same aggregation node.

For the experimental setup, traffic sources are configured to generate the traffic with Gaussian distribution, a well-known internet traffic distribution discussed in Bothe, Qureshi & Imran (2019) and Meent, Mandjes & Pras (2006). Although all the access nodes will follow a Gaussian distribution, their mean values and shapes are different for different types of demographics of the serving area, as discussed in a study conducted by Husen et al. (2021).

The specifications of different links are given in Table 3. The access to aggregation links follows random allocation for each experiment instance and uses a FIFO scheduler. The TIPS is not used on access links as it represents a single traffic profile. On access to aggregation nodes, the link’s capacity is set to 4 Mbps, and aggregation to the core link has a 6 Mbps capacity. Both of the above links use the TIPS packet scheduler. The edge links connecting the destination nodes use the FIFO scheduler as there is only a single type of traffic profile.

Traffic Intensity based Packet Scheduling

The Traffic Intensity based Packet Scheduling (TIPS) is a packet scheduler that schedules packets according to the traffic profile of the downstream links. Packets are enqueued to different queues with dynamic dequeue order following the ranks of the traffic profile, and the size of the dequeue is dependent on the weights of traffic profiles. The control traffic is separated and handled with different policies different from TIPS. The TIPS was initially developed for NS2 (Husen et al., 2021); however, since the NS2 development has stopped, it was ported to Network Simulator 3 (NS3) (Riley & Henderson, 2010). The implementation of TIPS for NS3 is available in the supplementary material of this paper.

Access traffic profiles

The TLM performance’s primary expectation is traffic profile diversity. Several experiments were conducted with different traffic profiles. Distinct traffic profiles were generated for each experiment iteration with separate distribution parameters such as mean and standard deviation. A set of randomly selected traffic profiles generated according to Gaussian distribution are shown in Figs. 8, 9 and 10 for different aggregation nodes to demonstrate the effects of Gaussian parameters. The lower and upper parts of the graphs of the figures above show the cumulative density and histogram of the data rates generated by the respective node. The histogram on the top part of the graphs shows that an access node’s traffic follows a Gaussian distribution (Yamanaka & Usuba, 2020). This implies that for a given mean value, there are equal chances of traffic generated below or above.

Prediction accuracy of TLMs

This section analyses the performance of the TLM models on different nodes. The TLM learners are used on G1, G2, G3, and C1 as per the selected links. The prediction accuracy of different TLMs is shown in Figs. 11, 12, 13 and 14. The figures present the histograms of the actual data rates and those predicted by the respective TLM. A summary of the mean absolute error (MAE) and mean squared error (MSE) is given in Table 4, which shows the MAE values between 8.41 to 6.38 for TLM on nodes G1, G2, G3, and C1. Since the TLMs coordinate with each other to realize swarm learning, the latency of the inter TLMs may pose a limitation. In practice, to address it, low-latency dedicated communication links can be used to address it. The latency issues between inter-TLM communications can also be minimized by implementing the TLMs on the same location as the nodes of the network. The location of TLMs for different network nodes is an essential factor to ensure optimal performance. In this work, the TLMs were implemented in the same location as the respective network nodes to eliminate the effects of the latency. If the TLMs are implemented in a centralized location to avail benefits of the cloud computing paradigm, low latency dedicated networks would be required.