End-to-End Latency Evaluation of the Sat5G Network Based on Stochastic Network Calculus

: Simultaneous use of heterogeneous radio access technologies to increase the performance of real-time, reliability and capacity is an inherent feature of satellite-5G integrated network (Sat5G). However, there is still a lack of theoretical characterization of whether the network can satisfy the end-to-end transmission performance for latency-sensitive service. To this end, we build a tandem model considering the connection relationship between the various components in Sat5G network architecture, and give an end-to-end latency calculation function based on this model. By introducing stochastic network calculus, we derive the relationship between the end-to-end latency bound and the violation probability considering the traffic characteristics of multimedia. Numerical results demonstrate the impact of different burst states and different service rates on this relationship, which means the higher the burst of arrival traffic and the higher the average rate of arrival traffic, the greater the probability of end-to-end latency violation. The results will provide valuable guidelines for the traffic control and cache management in Sat5G network.


Introduction
Benefiting from the rapid development of satellite link technologies and the on-board processing, there will be more than one hundred high-throughput satellite systems using geostationary earth orbit (GEO) and mega-constellations of low earth orbit (LEO) satellites by 2020-2025 [Giambene, Kota and Pillai (2018)]. These evolving satellite systems are expected to provide radio access networks (RANs), which will be integrated into 5G systems along with other wireless technologies [3GPP TR22.822 (2018)]. Seamless handover between heterogeneous radio access technologies will be an inherit characteristic of 5G, while different radio access technologies will be used to improve reliability, availability, capacity and security [Liu, Zeng, Shi et al. (2019)]. Moreover, due to the pressing demand for communication and connection quality, the amount of data produced [Burchard, Liebeherr and Patek (2012)]. Based on these concepts, the data departures of a network element can be calculated by convolving the arrival curve with the system service curve [Chang (2000)]. This form of convolution is important because it provides a general framework for the analysis of the entire network. The systems along the network path can easily be connected through the convolution of their service curves to produce network service curves that specify the end-to-end availability of services. However, with the continuous evolution of communication systems, especially considering the many random factors in wireless network communication, deterministic network calculus is greatly limited in its use [Wang, Di, Jiang et al. (2017)]. Therefore, many scholars worldwide are actively conducting research into stochastic network calculus theory, constantly improving the relevant theories of the theory and applying it to the performance analysis of actual communication systems. One of the methods of performance analysis is to build a traffic model which is able to accurately describe the traffic characteristics [Cheng, Zhuang and Ling (2007)]. Markov chain model and associated queueing analysis are widely and deeply studied as tools to evaluate the performance of multimedia applications. However, a large number of network traffic measurement studies show that network traffic is self-similar or long-range dependent (LRD) [Izabella, Zhong and Cees (2020)], which cannot be captured by the short-range dependent (SRD) Markovian model. The FBM process is a self-similar Gaussian process, which is therefore a model suitable for capturing the long-range dependence within traffic. At the same time, a variety of applications of stochastic network calculus have emerged, including the evaluation of network end-to-end latency. In Zheng et al. [Zheng, Liu, Lei et al. (2013)], The performance of finite state Markov channel is analysed. The latency bound is derived based on the MGFs. Ma et al. [Ma, Chen, Li et al. (2019)] considering the characteristics of 5G architecture and used SNC to analyse the latency in URLLC. For latency-sensitive traffic, Wang et al. [Wang, Di, Jiang et al. (2017)] compared two different arrival models, the Poisson process and self-similar process, and applied the traditional scheduling strategy to MEO nodes while considering link impairment between a pair of satellites. In addition, Fidler et al. [Fidler and Rizk (2015)] used a stochastic service process to analyse the latency performance of TCP. They used using stochastic network calculus considering both backlog and latency [Lübben and Fidler (2016)].

Network architecture
Both the International Telecommunication Union (ITU) and 3GPP have conducted research on the convergence of satellite and terrestrial 5G networks. On the one hand, for the problem of satellite and terrestrial 5G convergence, the ITU proposed four application scenarios for satellite 5G convergence, including relay-to-station, community-backhaul, mobile-to-communication, and hybrid broadcast scenarios. On the other hand, 3GPP space-ground integrated communication related standards research is mainly carried out in two projects, TR38.811 and TR22.822. TR38.811 mainly studies the 5G new air interface standard for non-terrestrial networks, and TR22.822 mainly studies the access of 5G satellites. The architecture of Sat5G is shown in Fig. 1. From a technical point of view, the architecture of Sat5G has both a bentpipe forwarding mode and an on-board processing mode. The two modes are different in implementation complexity and application scenarios, as illustrated in Fig. 2  In the long run, some or all of the ground base stations will be used. The gradual migration of functions to the satellite is a trend that can effectively reduce processing latency and improve the quality of experience (QoE) of users. Therefore, we will take mode 2-a as an example to perform end-to-end latency performance analysis.

Latency of Sat5G
Based on mode 2-a, the connection relationship between the various components in Sat5G is shown in Fig. 3. Here we consider the packet transmission latency from User Equipment (UE) to Data Network (DN).

Figure 3: Connection relationship between the various components in Sat5G network
(1) Radio Access Network (RAN): RAN consists of User Equipment (UE) and Active Antenna Unit (AAU), AAU is part of the base-station, and UEs first accesses AAU.
(2) Fronthaul: the communication process between AAU and Centralized Unit (CU) is called Fronthaul. AAU forwards the traffic to Distributed Unit (DU), when the traffic gets to DU, there are two scenarios. If both CU and DU are deployed, the traffic can reach CU immediately. Otherwise, the traffic will be sent from DU to CU. (3) Backhaul: the communication process between CU and Next Generation Core (NGC) is called Backhaul. The traffic leaves CU and goes to NGC, NGC will take some time to deal with the traffic. Finally, NGC transmits the data to Data Network (DN). The unidirectional transmission is thus completed. Consequently, the whole latency in the Sat5G system will be associated with the transmission latency in RAN, Fronthaul, Backhaul, DN, and the processing latency in NGC. We have used the calculation method in Fidler et al. [Fidler and Rizk (2015); Ma, Chen, Li et al. (2019)], which is expressed as Eq. (1).
(1) In order to satisfy the QoS requirements of massive services, especially latency-sensitive services, it is essential to study ETE T .

Stochastic network calculus
The queuing system is analysed by means of minimum plus algebra in stochastic network calculus. Let F denote the set of nonnegative nondecreasing functions and F denote the set of nonnegative nonincreasing functions. A traffic flow is representing by a cumulative process. Arrival process is denoted as ( ) A t , departure process is denoted as ( ) D t and service process is denoted as ( ) ( ) A t is the cumulative arrival traffic. The same applies for ( ) D t and ( ) S t . Referring to Fidler et al. [Fidler and Rizk (2015)], we give the following definition. Definition 1 (Stochastic Arrival Curve). A traffic flow has a stochastic arrival curve (2) where ( ) α τ is the arrival curve, which denotes the maximum traffic, ( ) f x denotes the violation probability. Definition 2 (Stochastic Service Curve). A system S provides a stochastic service curve F β ∈ with bounding function g F ∈ , denoted by ~< , > S g β , if for all The symbol ⊗ represents the operation of cumulative min-plus convolution. where is the stochastic service curve which is similar to the stochastic arrival curve, The probability of generating excess traffic is constrained by the bound function ( ) g x . Similar to Eq. (3), the departure process and is described as (2)-(5), we can now discuss the definition of the latency process and latency bound.

Definition 3 (Latency process) Arrival process is denoted as ( )
A t , departure process is denoted as ( ) D t . The latency process ( ) L t at time 0 t ≥ can be describled as L t is the minimum value of d , and d must satisfy the constraint that the amount of traffic arriving at time t is not more than the traffic leaving at time t d + .

Lemma 1 (Latency Bound). ( )
A t is a stochastic arrival process with a curve F α ∈ , which is bounded by function f F ∈ (i.e., ~< , > A f α ). ( ) S t is a stochastic service process with a curve F β ∈ , which is bounded by function g F ∈ (i.e., ~< , > S g β ). Then, for all 0 t ≥ and 0 x ≥ , the latency bound ( ) L t can be described as is the maximum value of horizontal distance between x α + and β ; the expression

Traffic model
The traffic model is an important factor in network queuing performance analysis. A large number of WAN, LAN, MANET, Internet switches, and video and VBR traffic data were collected and analysed in detail. Finally, possible self-similarity of service flows was assumed to exist at any time and in any network environment. Here, we can give the definitions of the self-similarity of traffic and the mathematical expression of self-similarity. Definition 4 (Self-similarity of Traffic) The self-similarity of network traffic means that the network flow exhibits the same burst mode at different observation time scales, that is, the burstiness of the aggregated service is maintained regardless of whether the time scale is increased or decreased.

; then, ( )
A t is called the fractal Brownian motion traffic model.

End to end latency calculation 4.1 Problem description
As shown in Fig. 3, the data in Sat5G are transferred from UE to the data network. To satisfy the requirement of Sat5G, the end-to-end latency can be described as Eq. (10).
is the whole latency in the Sat5G system and ε is defined as a violation probability. Eq. (10) shows that Sat5G network transfers traffic successfully and satisfies the latency requirements.

Model building
Sat5G network characteristics can be regarded as dynamic servers using the stochastic processes described in Section 3.3. Traffic from UE can be depicted as the arrival process ( ) A t . Accordingly, the service capacity of the network server node can be represented by the service process ( ) S t . Therefore, if the Sat5G is considered as a tandem system, the end-to-end latency of Sat5G should fall into the tandem characterization in stochastic network calculus. Considering that a traffic flow from UE passes through the gNB, NGC and DN. Each network node k provides a stochastic service curve ~< , >

Derivation of all g
We adopt latency-rate (LR) server to analyse scheduling algorithms in Sat5G. The feature of node service is described as ( ) ( ) , where T is the maximum processing delay and R is the minimum service rate. For a work-conserving server with constant rate, , where L is the maximum value of packet size, and the bound function , C is the service rate and m is the average arrival rate.

Experimental results and performance evaluation
we will evaluate the determinants of end-to-end latency of Sat5G in this section. The packet arrival process satisfies the FBM model. More simulation parameters can be found in Tab. 1.  . As shown in the figure, on the one hand, under the same latency bound, the larger the H value, the higher the violation probability. On the other hand, under the same H value, the greater the latency bound, the lower the violation probability. H . As shown in the figure, on the one hand, under the same service rate, the greater the latency bound, the lower the violation probability is. On the other hand, under the same latency bound, the larger the service rate, the higher the violation probability is.

Conclusion
In this paper, the Sat5G network is modelled as a tandem system by analysing the architecture characteristics. Through the application of SNC, the traffic model is proposed, and the performance analysis is carried out in combination with the characteristics of Sat5G network. The relationships among latency bound, service rate, Hurst parameters, violation probability and arrival rate in Sat5G network are studied. The satellite link propagation latency is considered when the simulation parameters are setting. Numerical results verify that the Hurst parameter, corresponding to the burstiness of traffic, will affect the violation probability to some extent. This also means that we need to adopt an adaptive strategy in the traffic scheduling process. The service rate is also a factor affecting latency. In the future, different scheduling strategies will be taking into account for self-similar traffic.