A multi-queue-based ECN marking strategy for multi-class QoS guarantee in programmable networks

Virtual queue and queue scheduling

This article utilizes BMv2 switches for programmable data plane simulation. By default, BMv2 switches employ Strict Priority (SP) queues, where packets are assigned to different queues based on their priority, enabling multi-queue emulation. However, SP queues neglect fairness among queues. In the event of congestion, if there are continuously packets in the high-priority queue, packets in the low-priority queue will not receive service. Additionally, due to the developmental stage of BMv2 switches, some functionalities are incomplete, and obtaining queue parameters for individual subqueues is not possible (Harkous et al., 2021). To address these limitations, this article proposes a virtual queue-based Weighted Round-Robin (WRR) scheduling mechanism, which is based on priority queues, to ensure fairness among queues. This approach aims to alleviate the fairness issues associated with SP queues, while also overcoming the incomplete functionality of BMv2 switches in obtaining subqueue parameters.

In our P4 pipeline, we utilize virtual queues, which are mechanisms used to model the length of queues. Unlike regular queues, virtual queues do not contain any actual packet data. Instead, they are numeric values that increment as packets arrive and decrement based on a predefined model. In our implementation, we utilize the data structure register available in the P4 language to implement virtual queues and monitor their states. The register allows us to store and manipulate the values associated with each virtual queue, providing a way to track and manage their state within the P4 pipeline.

We employ a matching table to divide each incoming packet into different virtual queues based on their source and destination addresses. Furthermore, we assign weights to these virtual queues and utilize the register to track the utilization of the priority queues within each virtual queue. As depicted in Fig. 4, if the utilization of a priority queue within a specific virtual queue exceeds the weight associated with that virtual queue, we enforce the usage of a lower priority queue. In the algorithm designed in this article, the queue weights are controlled by the control plane.

In Fig. 4, the sequence number on the packets represents the order in which they arrive at the switch. With a queue weight set to 3, when a packet arrives at a virtual queue, the first-arrived packet in that virtual queue is assigned the highest priority. If, for a particular virtual queue, the length of its packets in a priority queue reaches 3, the priority of that packet is downgraded, and it enters a lower-priority queue. This process continues, enabling packet forwarding according to the WRR scheduling method.

To validate that simulating WRR with virtual queues can mitigate the impact of SP queues on traffic in BMv2 switches, this experiment ran both the default SP scheduler and a WRR scheduler based on virtual queues in the switch. High, medium, and low priority traffic were simultaneously sent to the switch with equal weights for the three types of traffic. The bandwidth performance of each traffic type under the two scheduling schemes is shown in Table 1. It can be observed that in SP scheduling, low-priority packets have fewer scheduling opportunities, resulting in lower bandwidth. In contrast, with WRR scheduling, this issue is addressed, and all three types of traffic have opportunities to transmit data. Therefore, in the programmable data plane, WRR scheduling based on virtual queues can effectively mitigate the problem of flow starvation compared to the default SP scheduling, ensuring fairness among traffic flows.

Model establishment

In this chapter, according to reference (Wu, Qiao & Chen, 2018), the data flows in a network can be broadly classified into the following three categories to meet the QoS requirements of different types of data streams:

Category A data flows: These are bandwidth-sensitive and delay-sensitive data streams. This category of data flows has higher requirements for network performance, necessitating sufficient bandwidth and low transmission latency. Typically, these data flows include applications such as audio, video, and real-time gaming that have high demands for real-time transmission. Ensuring priority transmission for these data flows ensures their immediate and seamless delivery in the network, providing a good user experience and service quality.

Category B data flows: These are delay-sensitive data streams. This category of data flows is sensitive to transmission latency, and the network should provide low-latency transmission for them.

Category C data flows: These are best-effort data flows, which do not have specific requirements for latency and bandwidth. A common example is file transfer protocol (FTP) traffic. For these data flows, the main objective of the network is to deliver the data to the best of its ability.

By classifying data flows into different categories, networks can employ appropriate strategies and mechanisms to provide corresponding quality of service guarantees for each category of data flows, meeting the requirements and performance needs of diverse applications. The symbols and meanings used in this article are shown in Table 2.

We define I = {1, 2, …, k} to represent the set of traffic types present in the network, where traffic i, i ∈ I represents a specific type of flow. When traffic arrives at the switch, the classification module will allocate traffic i to the corresponding queue, and the ECN marking module will set the appropriate ECN marking threshold in accordance with the business requirements of traffic i. Let the optimized service rate be used as the threshold K_i. Assuming that each switch has the same capacity limit and can accommodate a queue length of N, the arrival rate of traffic i is λ_i, and the service rate is μ_i. Let Λ represent the total arrival rate of packets at the switch, and Γ represent the total service rate of packets leaving the switch through the same port. All packets, after passing through the classifier, are stored in different queues, and only one scheduler serves multiple queues. Let ω_i represent the weight of traffic i’s queue in the virtual queue, and ${\sum }_{i=1}^k{\omega }_i=1$. The weight determines how many packets from that queue are served by the scheduler in one unit of time. If the scheduler serves a total of Γ packets in one unit of time, then ω_iΓ packets are served in queue i, i.e., μ_i = ω_iΓ. Therefore, the weighted round-robin scheduling queue model can be viewed as k parallel M/M/1/N queuing models.

In the multiple parallel queues of M/M/1/N, it is sufficient to consider only one of them because their only difference lies in the input rate and service rate. In the following discussion, we will focus on the queue associated with traffic i.

P_m represents the probability that there are m packets in the queue where traffic i resides at time t. We can use the method of discrete-time Markov chains to establish the probability distribution of queue length. For the M/M/1/N queuing model, assuming the steady-state distribution of queue length is P_m, based on the principles of queuing theory, we can derive the following equations: (1)${\displaystyle P_0=\frac{1-{\rho }_i}{1-{\rho }_i^{N+1}},\rho \ne 1}$ (2)${\displaystyle P_m=\frac{1-{\rho }^i}{1-{\rho }_i^{N+1}}{\rho }_i^m,1\le m\le N}$

where ρ_i = λ_i/μ_i. In the system with a capacity of N, when the queue length reaches N, any additional arriving packets beyond the capacity will be discarded. Consequently, for queue i, its effective arrival rate can be determined using the following equation, as indicated in Eq Eq. (3), where P_N represents the probability of the queue length reaching the upper limit N. (3)${\displaystyle {\lambda }_e={\lambda }_i\left(1-P_N\right).}$

Through the decomposition of parallel queues, we can determine the relationship between the arrival rate λ_i and service rate μ_i of flow i with the parameters Λ and Γ of the overall parallel queue system. (4)${\displaystyle \sum _{i=1}^k{\lambda }_i\le \Lambda ,\sum _{i=1}^k{\mu }_i=\Gamma .}$

So, as to the stability of the network, there should be: (5)${\displaystyle {\lambda }_i\le {\mu }_i,\sum _{i=1}^k{\lambda }_i\le \Gamma .}$

When ρ_i = λ_i/μ_i ≠ 1, the calculated metric results are as follows:

(1) Queue length: The average length $L_s^i$ of queue i is equal to the sum of the expected value $L_q^i$ of the number of packets waiting to queue in the system and the expected value $L_c^i$ of the number of packets being served. (6)${\displaystyle L_q^i=\sum _{k=0}^{N-1}k{P}_{k+1}=\frac{{\rho }_i}{1-{\rho }_i}-\frac{N{\rho }_i^{N+1}+{\rho }_i}{1-{\rho }_i^{N+1}}{L}_c^i=1-P_0=\frac{{\rho }_i-{\rho }_i^{N+1}}{1-{\rho }_i^{N+1}}{L}_s^i=L_q^i+L_c^i=\frac{{\lambda }_i}{{\mu }_i-{\lambda }_i}-\frac{\left(N+1\right){\lambda }_i^{N+1}}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}.}$

(2) Queueing delay: The waiting time $W_s^i$ of packets in queue i is equal to the sum of the queuing time $W_q^i$ and the service time $W_c^i$. (7)${\displaystyle W_s^i=W_q^i+W_c^i=\frac{L_q^i}{{\lambda }_e}+\frac{L_c^i}{{\lambda }_e}{W}_s^i=\frac{1}{{\mu }_i-{\lambda }_i}-\frac{N{\lambda }_i^N}{{\mu }_i\left({\mu }_i^N-{\lambda }_i^N\right)}.}$

(3) Packet loss count: When the queue capacity of a switch is reached (N packets), any new incoming packets will be dropped. Therefore, the packet loss count in the system per unit of time is determined. (8)${\displaystyle N_{loss}={\lambda }_i{P}_N=\frac{{\lambda }_i^{N+1}\left({\mu }_i-{\lambda }_i\right)}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}.}$

(4) Queueing delay jitter: We define jitter as the difference between the actual delay experienced by a packet in the switch and the expected delay. Let W_i denote the actual queueing time for traffic flow i in the switch. The jitter of the queueing delay, compared to the expected queueing delay, can be represented by the following equation: (9)${\displaystyle △T=|W_i-W_s^i|.}$

(5) Link remaining bandwidth: Assuming C is the bandwidth of every link and n represents the number of links connected to the switch, the available remaining bandwidth of the link per unit of time can be expressed as the difference between the total bandwidth and the amount of data transmitted to the switch per unit of time (bandwidth occupied by existing traffic). (10)${\displaystyle C_{rest}=nC-\sum _{i=1}^k{L}_s^i=nC-\sum _{i=1}^k\left[\frac{{\lambda }_i}{{\mu }_i-{\lambda }_i}-\frac{\left(N+1\right){\lambda }_i^{N+1}}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}\right].}$

We assume the presence of three types of traffic services in the network: voice, video, and email. Real-time data, such as voice, imposes high demands on both delay and bandwidth. Streaming applications also have certain requirements on latency as they employ buffering mechanisms and can tolerate reduced bandwidth to some extent compared to real-time applications. File transfer services, such as email, generally have lower bandwidth and latency requirements.

Taking voice traffic as an example, based on the QoS requirements for voice flows, we develop an optimization model that jointly adjusts the arrival rate and service rate of flows. The objective is to minimize delay and residual bandwidth by optimizing the service rate and target sending rate. (11)${\displaystyle min\left(C_{rest}\right)=min\left(nC\right)-\sum _{i=1}^k\left[\frac{{\lambda }_i}{{\mu }_i-{\lambda }_i}-\frac{\left(N+1\right){\lambda }_i^{N+1}}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}\right]min\left(W_s^i\right)=min\left(\frac{1}{{\mu }_i-{\lambda }_i}-\frac{N{\lambda }_i^N}{{\mu }_i\left({\mu }_i^N-{\lambda }_i^N\right)}\right)s.t.C1:\sum _{i=1}^k{\omega }_i=1,{\mu }_i={\omega }_i\Gamma ,{\omega }_i>0C2:\sum _{i=1}^k{L}_s^i=\sum _{i=1}^k\left(\frac{{\lambda }_i}{{\mu }_i-{\lambda }_i}-\frac{\left(N+1\right){\lambda }_i^{N+1}}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}\right)\le NC3:\sum _{i=1}^k{\lambda }_i\le \Lambda C4:0<{\lambda }_i<{\mu }_{i}C5:\sum _{i=1}^k{\mu }_i=\Gamma C6:C_{rest}=nC-\sum _{i=1}^k\left[\frac{{\lambda }_i}{{\mu }_i-{\lambda }_i}-\frac{\left(N+1\right){\lambda }_i^{N+1}}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}\right]\ge 0.}$ C1 represents the relationship between μ_i, ω_i, and Γ. C2 states that the sum of average queue lengths in all queues should not exceed the storage capacity of the switch. C3 states that the number of packet arrivals for all traffic flows within a unit of time should not exceed the number of packet arrivals at the port within the same unit of time. C4 states that in order to maintain network stability, the arrival rate of traffic should not exceed the service rate. C5 states that the number of packets processed for all traffic flows within a unit of time should be equal to the number of packets processed at the port within the same unit of time. C6 states that the available remaining bandwidth of a link should be greater than zero.

Video streams are sensitive to both delay and jitter, so their optimization objective is to minimize latency and jitter. (12)${\displaystyle min\left(W_s^i\right)=min\left(\frac{1}{{\mu }_i-{\lambda }_i}-\frac{N{\lambda }_i^N}{{\mu }_i\left({\mu }_i^N-{\lambda }_i^N\right)}\right)min\left(△T\right)=min\left(|W_i-W_s^i|\right).}$

File transfers are sensitive to both delay and packet loss, so their optimization objective is to minimize latency and packet loss rate. (13)${\displaystyle min\left(W_s^i\right)=min\left(\frac{1}{{\mu }_i-{\lambda }_i}-\frac{N{\lambda }_i^N}{{\mu }_i\left({\mu }_i^N-{\lambda }_i^N\right)}\right)min\left(N_{loss}\right)=min\left(\frac{{\lambda }_i^{N+1}\left({\mu }_i-{\lambda }_i\right)}{{\mu }_i^{N+1}-{\lambda }_i^{N+1}}\right).}$

The constraints of the above optimization target models are the same.

The optimal arrival rate, service rate, and virtual queue weights

In the aforementioned mathematical model, this study aims to determine the optimal arrival rate, ${\lambda }_i^{\ast }$, and optimal service rate, ${\mu }_i^{\ast }$, given the optimization objective. To achieve this, a two-layered solving approach is devised. Firstly, the actual arrival rate, λ_i, is inputted into the model to solve for the optimal service rate, ${\mu }_i^{\ast }$, thereby completing the first optimization layer. Subsequently, the optimal service rate, ${\mu }_i^{\ast }$, is fed back into the model to solve for the optimal arrival rate, ${\lambda }_i^{\ast }$, thereby completing the second layer of optimization. It is worth noting that both layers of the solving model are multi-objective non-linear models, necessitating consistency in the solving method for each layer.

First, we can apply the method of linear weighted sum in multi-objective optimization. Assuming the weight coefficients for the three traffic flows are ω₁, ω₂, and ω₃, respectively, with ω_i = μ_i/∑μ_i, the above multi-objective optimization problem can be transformed into a single-objective optimization problem by linearly weighting the objectives. Let f(x) represent the overall optimization objective for traffic: (14)${\displaystyle f\left(x\right)=min\left({\omega }_{1}Eq\left(11\right)+{\omega }_{2}Eq\left(12\right)+{\omega }_{3}Eq\left(13\right)\right).}$

Therefore, the current focus is to solve a single-objective multi-variable nonlinear programming problem.

Differential evolution (DE) is a stochastic search algorithm designed specifically for global optimization problems. It originated from the early development of genetic algorithms (GA). Differential evolution employs a unique evolutionary mechanism that utilizes the individual differences within the existing population to construct mutant individuals. Compared to other intelligent algorithms such as genetic algorithms, particle swarm optimization, ant colony optimization, and artificial bee colony algorithms, DE requires fewer parameters and exhibits strong optimization capability. DE belongs to the category of evolutionary algorithms and inherits all the advantages of evolutionary algorithms. The DE algorithm selects a more optimal next generation through processes such as population initialization, individual fitness evaluation, differential mutation operation, crossover operation, and selection operation. In summary, the DE algorithm is suitable for solving large-scale, nonlinear, and combinatorial optimization problems that are challenging for traditional search methods. It does not rely on gradient information, nor does it require the objective function to be continuous or differentiable.

In this study, the DE/best/1/L (Opara & Arabas, 2019) algorithm is adopted. The population is classified and described, and the target-to-best strategy is used to select the base individuals for differential mutation from the current population. Differential mutation is applied to the current population to generate mutant individuals. Then, the current population is combined with the mutant individuals to obtain an experimental population using the exponential exchange method. A one-to-one survivor selection is performed between the current population and the experimental population to generate a new population. The algorithm for determining the optimal packet arrival rate ${\lambda }_i^{\ast }$, service rate ${\mu }_i^{\ast }$, and virtual queue weight ω_i is as follows ( Algorithm 2 ):

 
__________________________________________________________________________________________ 
Algorithm 2 The optimal arrival rate, service rate, and virtual queue weight 
algorithm___________________________________________________________________________________________ 
 Input: N,Λ,Γ,C,n,λi,Wi and other model parameters; 
 Output: λ∗i,μ∗i,ωi; 
  Step 1: Initialize; 
  Step  2:  The  multi-objective  optimization  problem  is  transformed  into  a 
   single-objective  optimization  problem  by  linear  weighted  sum  method,Let 
   fi(x) represent the optimization objective for traffic flow i: 
  min(μ1 
 Γ f1(μ1) + μ2 
 Γ f2(μ2) + μ3 
 Γ f3(μ3)) 
  s.t. 
  C1 : ∑k 
    i=1 Li 
s ≤ N 
  C2 : 0 < λi < μi 
    C3 : ∑k 
    i=1 μi = Γ 
  C4 : Crest = nC −∑k 
    i=1 [ 
λi ___ 
μi−λi − (N+1)λN+1 
i _____ 
μN+1 
i    −λN+1 
i     ] 
                  ≥ 0 
  Step 3:  Find the optimal solution μ∗i  by differential evolution algorithm, 
   the virtual queue weight is      μ∗ 
i _____ 
μ1+μ2+μ3 Γ,  and the queue marking threshold 
   Ki =      μ∗ 
i _____ 
μ1+μ2+μ3 N; 
  Step 4: Construct the second layer single objective optimization problem: 
  min(μ∗ 
1 
 Γ f1(λ1) + μ∗ 
2 
 Γ f2(λ2) + μ∗ 
3 
 Γ f3(λ3)) 
  s.t. 
  C1 : ∑k  
    i=1 Li 
s ≤ N 
  C2 : ∑k 
    i=1 λi ≤ Λ 
  C3 : 0 < λi < μ∗i 
    C4 : Crest = nC −∑k 
    i=1 [ 
λi ___ 
μi−λi − (N+1)λN+1 
i _____ 
μN+1 
i    −λN+1 
i     ] 
                  ≥ 0 
  Step 5: Input model parameters such as N,Λ,Γ,C,n,λi,Wi and the optimal 
   solution μ∗i 
    Step 6: Find the optimal solution λ∗i by differential evolution algorithm.____