User and Content Dynamics of Edge-Aided Immersive Reality Services

This letter presents a practice-inspired methodology for characterizing the user and content dynamics of extended reality (XR) services over wireless networks. The proposed approach is based on a fluid approximation to capture the time and space dynamics of XR content exchange during its transient phase while considering both radio communication and edge computing resources. Hence, our methodology provides an effective tool to support resource assignment for radio and computing in 5G and beyond networks, especially under non-stationary processes with time-varying traffic arrivals, such as those with a periodic arrival rate function.

User and Content Dynamics of Edge-Aided Immersive Reality Services Olga Chukhno , Graduate Student Member, IEEE, Olga Galinina , Member, IEEE, Sergey Andreev , Senior Member, IEEE, Antonella Molinaro , and Antonio Iera , Senior Member, IEEE Abstract-This letter presents a practice-inspired methodology for characterizing the user and content dynamics of extended reality (XR) services over wireless networks.The proposed approach is based on a fluid approximation to capture the time and space dynamics of XR content exchange during its transient phase while considering both radio communication and edge computing resources.Hence, our methodology provides an effective tool to support resource assignment for radio and computing in 5G and beyond networks, especially under non-stationary processes with time-varying traffic arrivals, such as those with a periodic arrival rate function.
Index Terms-5G+ connectivity, wireless communications, edge computing, immersive reality, user and content dynamics.

I. INTRODUCTION
W ITH the increasing consumer interest in immersive applications, extended reality (XR) technology is rapidly advancing toward its mass adoption.Compared to traditional technologies, XR services offer higher user mobility and interaction freedom.The incorporation of wireless network solutions in XR services, e.g., [1], has further facilitated user motion and introduced new challenges, such as user/content dynamics and performance evolution, thereby requiring careful consideration and innovative solutions.
In the literature, XR systems are usually assessed in steadystate operating conditions [2], [3].However, due to the recent developments in the context of XR interaction, state-of-the-art modeling solutions may have limited applicability to practical XR deployments.A major challenge is to accurately model the dynamic and non-stationary [4] aspects inherent to the operating behavior of modern immersive reality systems in the presence of periodic arrival processes [5].Addressing that is crucial to provide network engineers with an effective means to plan and optimize radio and computing resources by taking into account the specific features of XR.
To capture the time and space dynamics and the system effects in a transient phase of XR operation, the actual discrete numbers of users engaged in XR content exchange can be approximated with an equivalent continuous process.For example, in [6], a fluid approximation is used to model the evolution of vehicles along a highway.Further, in [7] and [8], the numbers of users retrieving the content and those who have already received it are represented as continuous flows.In wireless sensor networks, the volume of traffic is also modeled using macroscopic fluid dynamic models [9].
By their design, XR systems have a unique set of features, including form factor constraints, which impose strict requirements on power consumption and heat dissipation of user equipment.Therefore, content processing may not always be conducted on the XR head-mounted displays (HMDs), thus requiring task offloading to an edge server over a wireless network.As a result, analyzing XR content exchange dynamics requires the consideration of both radio communication and edge computing resources.This letter addresses the challenge of modeling the dynamics and non-stationarity of emerging XR systems by bridging the gap between traditional steady-state assessments and practical XR technology deployments.
We thereby offer a practice-inspired methodology to characterize the evolution of users utilizing XR services in radio networks as a continuous fluid, thus providing insights into XR content dynamics.Specifically, we model the dynamic behavior of XR services with periodic arrivals and consider the departure rate that is determined by the communication and computing characteristics of the 5G New Radio (NR) and edge technologies.We then apply our fluid approximationbased methodology to assess the XR system performance under characteristic deployment setups.

II. SYSTEM MODEL
We consider an outdoor environment where multiple homogeneous users engage in an interactive XR experience through HMDs.As XR devices have limited computing performance due to constraints on their size, power consumption, and heat dissipation, we assume that an HMD acts as a thin client by receiving personalized video streams from a proximate edge computing server.The server is co-located with a 5G base station (BS), as illustrated in Fig. 1, and connects to HMDs over a wireless link using, for example, millimeter-wave radio technology.
Assumption 1 (User State): The XR services involve users sending location and motion information to the BS, which is then used to process the corresponding video on an edge server.Hence, a user can be in one of the three states: (i) an active communicating user sending the location and  motion information to the server, (ii) an active computing user processing XR 360 • video on the server, or (iii) an idle user.
Active users transition to the idle state only after completing their uplink transmission and processing the required content at the edge, i.e., after passing through both communication (transmission) and processing (computing) states.In turn, idle users switch to the active communicating state based on their content demand, thus resulting in a transition rate μ a , which corresponds to the average value commonly employed to model systems with homogeneous user behavior.While we assume that μ a does not vary over time, our methodology can also incorporate time-varying dependencies if needed.
Assumption 2 (User Motion): We consider one-way motion around a semi-infinite pedestrian area.For example, users may traverse from one XR-ready area to another or follow a straight path along the street.We note that such one-way motion can readily be generalized to a two-way traffic scenario.The pedestrian area is divided into K zones, each served by a 5G BS.Both active and idle users move within pedestrian zone k ∈ K = {1, . . ., K } with an average velocity v.
Assumption 3 (System Dynamics): We consider the following arrivals of active and idle users into the system: 1) zone 1: external active communicating or idle users; 2) zone k: active communicating or active computing or idle users from zone k − 1 arriving with rate β; 3) zone k: transition from idle to active communication due to an initiated transmission with rate μ a ; 4) zone k: transition from active communication to active computing due to a completed transmission; 5) zone k: transition from active computing to idle due to a completed content processing at the edge node.As an example, we assume a periodic external arrival rate typical for XR services [5], which varies between the minimum and the maximum values as a sine function.To control arrivals in time, we additionally parameterize such processes using phase shifts w a 0 and w d 0 and angular frequencies w a and w d for active and idle users, correspondingly.Angular frequency is thus related to the period T as w = 2πT .We limit the maximum and minimum values of the external arrival rate by λ a 1 , λ d 1 and λ a 2 , λ d 2 , respectively.Therefore, the external arrival rate for actively communicating and idle users at time t may be expressed as (2) Assumption 4 (Communication (Transmission) State): Each 5G BS serving a given zone k provides wireless connectivity to the users within it.We require that the available radio resources at each BS are sufficient and are equally shared in time and frequency among N at k (t) active users during the transmission phase at time t.
Further, we assume that B t is the average uplink packet size and R t 0 is the total uplink capacity (in bits per second).In the case of N at k (t) participants, we may express the transition rate of users from their status of active in the communication phase (i.e., transmitting) to that of active in the processing phase (i.e., their content is being processed) as Assumption 5 (Processing (Computing) State): The BS that serves zone k is associated with an edge node, wherein multiple virtual machines (VMs) are utilized to implement parallel processing of content.To take into account the input/output interference among VMs of the same node, we introduce a degradation factor d [10], so that the individual share of the available resources in the case of N ac k (t) active computing users in zone k is estimated as [11].If B c is the average size of the uploaded content (in bits), C c is the computational intensity (in CPU cycles per bit) required to process the content, and R c 0 is the processing capacity (in CPU cycles per second) of the edge node, then the actual transition rate from the user status of active in the processing phase (i.e., content is being processed) to that of idle (i.e., content processing completed) can be determined as and 1/C c 0 represents the time for processing the received content at the edge node.For the sake of analytical tractability, we modify the shape of (4) as where α is a fitting parameter obtained numerically to approximate (4).We note that specific distributions of file size, channel conditions, and data/computing rates can be readily incorporated into the considered average parameters.As a result, our system model offers a general but accurate representation of XR user and content dynamics, which is validated in Section IV below.

III. FLUID APPROXIMATION
In this section, we detail the proposed methodology to evaluate the performance of a dynamic XR system.We employ a fluid approximation, which allows replacing integer-valued processes with deterministic real-valued alternatives and is particularly well-suited for analyzing non-stationary systems.
We denote the total numbers of idle and active users in the communication and processing states within zone k at time t as N   (9) The evolution of the numbers of active and idle users in zone k is governed by a system of ordinary differential equations (ODEs) for where variables C d/a +/− k are collected in Table I.We assume that the content requests start at t = 0, where the number of idle users in zone k equals M k , which defines the initial conditions for (9).Expanding (9), we arrive at the Cauchy problem in (6), which determines the numbers of active users during the communication and computing phases and idle users, N at k , N ac k , and N d k .We solve the system in ( 6) by substituting N k = N at k + N ac k + N d k and obtain the following: Based on the first ODE in (10), we may obtain the number of users in zone 1 as where constant C 1 is defined by the initial conditions, while H and C 1 are given by expressions ( 7) and ( 8), correspondingly.
Further, using (11), we may obtain the total number N k for k = i + 4m, where i = 1, 2, 3, 4 and m ≥ 0, as follows: where parameters Z 0 , Z a 1/2 , and Z d 1/2 are given by , . (13) Knowing the total number of users, N k , we may derive N at k , N ac k , and N d k separately as 16) where C at k and C ac k can be established for any zone k by substituting ( 14)-( 16) into the initial conditions of ( 6).This straightforward technical work is left out of scope here.
In summary, this section details the fluid approximation method to characterize the non-stationary evolution process of the numbers of users engaged in XR content exchange under periodic user arrivals.We derive (12) to express the total number of users, while the numbers of idle and active users in the communication and processing states can be obtained with ( 14)- (16).

IV. NUMERICAL RESULTS
Our simulation setup models a large social/public XR event, e.g., a concert or an outdoor exhibition, where user HMDs offload their extensive computations to the edge.We study the time and space dynamics of users engaged in XR content exchange captured by our deterministic fluid model in Section III and Monte Carlo simulations.The simulation data (see "S" curves) agree with the analytical results (marked as "A") for all of the considered metrics of interest.
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TABLE II MODELING PARAMETERS
In simulations, the transition rate to the idle state is set as per (4), while when applying our analytical model, we employ the approximation in (5).Our additional results confirm that (5) with α = 0.12 closely matches (4).We examine the XR system performance in terms of the number of users, transmission rate 1 /processing speed, 2 and latency.To evaluate the performance of a dynamic XR system, we consider three scenarios with varying levels of radio and computing resources.Scenario 1 illustrates the case of limited radio and computing resources and is characterized by parameters B t = 15 MB [16], R t 0 = 100 Mbps [16], B c = 30 MB [17], R c 0 = 20 GHz, [19].Scenario 2 corresponds to limited computing resources and abundant radio resources as given by R t 0 = 3000 Mbps.Further, we focus on the case of abundant radio and computing resources that is illustrated by R t 0 = 3000 Mbps, R c 0 = 175 GHz [20], which is Scenario 3. Table II summarizes the main system parameters.
In Fig. 2, we assess the performance of our XR system under Scenario 1.The numbers of active users involved in the communication and processing phases increase with a cyclic trend governed by our periodic arrival rate function.The uplink transmission rate and processing speed decrease, which triggers the rising delays.Here, the availability of 100 Mbps of the total uplink capacity and 20 GHz of the total edge node processing capacity is insufficient for the uplink packet size of 15 MB and downloaded content size of 30 MB.
For Scenario 1, the bottleneck manifests during both the communication and the processing phases.Conventional system configurations may fail to support seamless low-latency XR experience, thereby calling for improved network capacities.System designers may thus consider distributed computing to reduce the computation times for video processing at the edge server.In addition, beyond-5G cellular networks with multi-RAT, multi-connectivity functionalities, and contentaware edge-node deployments may become promising for the emerging XR-ready systems.
In Fig. 3, we consider Scenario 2. Our results demonstrate that the availability of 3000 Mbps of the total uplink capacity ensures low-latency uplink transmissions.However, the processing procedure for the XR video remains demanding.At time instant t = 221 s, no further content requests Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.arrive in the system, thus leading to its gradual unloading, a decrease in the number of computing users, and, hence, a decline in latency.As per our additional results, a scenario with limited communication and abundant computation resources yields qualitatively similar observations but with an opposite trend between the communication and the computing resources.
Further, as shown in Fig. 4, our findings demonstrate that the availability of 3000 Mbps of the total uplink capacity and 175 GHz of the edge node processing capacity can support low-latency communications assuming typical uplink packet size, B t , of 15 MB and content size, B c , of 30 MB.Based on the reported evaluation, we may conclude that today's 5G NR deployments may encounter challenges in supporting the required latency for seamless XR user experience in the case of large social/public events.

V. CONCLUSION
In this letter, we presented our methodology to characterize user and content dynamics of immersive reality services in wireless networks with non-stationary arrival processes, i.e., a periodic arrival rate function.This approach considered both communication and computing resources to capture the time and space dynamics of users engaged in XR content exchange.We validated our analytical method to assess the system operation under various network configurations.The uplink transmission for XR is highly demanding in terms of radio resources, as it requires a minimum of 3000 Mbps for the packet size of 15 MB.The computation procedure for XR video processing appears to also be demanding in terms of computational resources by requiring more than 175 GHz to process the model of 30 MB.To provide effective support for XR experience, future research may explore artificial intelligence-based resource optimization as well as consider mobility patterns specific to XR applications.
c 2023 The Authors.This work is licensed under a Creative Commons Attribution 4.0 License.
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TABLE I EXPRESSIONS
FOR ARRIVING/DEPARTING FLOWS IN