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Mobility-Aware Analysis of 5G and B5G Cellular Networks: A Tutorial Hina Tabassum, Mohammad Salehi, and Ekram Hossain

Abstract—Providing network connectivity to mobile users is latency communication (URLLC), enhanced Mobile Broad- a key requirement for cellular wireless networks. User mobility Band (eMBB) communication and massive machine type com- impacts network performance as well as user perceived service munications (mMTC) for a wide variety of applications such quality. For efficient network dimensioning and optimization, it is therefore required to characterize the mobility-aware network as augmented/virtual reality, ultra-high-definition video, cloud performance metrics such as the handoff rate, handoff proba- storage, Internet of Things (IoT), Internet of Vehicles (IoV), bility, sojourn time, direction switch rate, and users’ throughput smart home, and smart cities. In the sequel, 5G networks or coverage. This characterization is particularly challenging for will utilize ultra-dense deployment of access points, higher heterogeneous, dense/ultra-dense, and random cellular networks frequency bands (e.g., mm-wave, free-space optics [FSO], such as the emerging 5G and beyond 5G (B5G) networks. In this article, we provide a tutorial on mobility-aware performance visible light, and Tera Hertz) via carrier aggregation or dual analysis of both the spatially random and non-random, single- connectivity, and massive antennas to overcome higher path tier and multi-tier cellular networks. We first provide a summary loss and blocking associated with such high frequencies. Fur- of the different mobility models which include purely random ther, technologies enabling device-to-device communications models (e.g., random walk, random way point, random direction), (D2D), cognitive radios, inter-vehicular (V2V), vehicle-to- spatially correlated (e.g., pursue mobility, column mobility), and temporally correlated models (e.g., Gauss-Markov, Levy flight). pedestrian (V2X), vehicle-to-infrastructure (V2I), drone-to- The differences among various mobility models, their statistical infrastructure (D2I), and drone-to-user (D2X) communications properties, and their pros and cons are presented. We then are expected to be integral parts of future 5G/B5G wireless describe two main analytical approaches (referred to as trajectory- networks. The key features of 5G/B5G cellular networks in- based and association/handoff based approaches) for mobility- clude spatial randomness of network tessellation, heterogene- aware performance analysis of both random and non-random cellular networks. For the first approach (which is more general ity of base-stations (BSs), dense/ultra-dense nature of network but less tractable than the other approach), we describe a general deployment, and diversified mobility patterns of users/devices methodology and present several case studies for different cellular and network nodes. network tessellations such as square lattice, hexagon lattice, Modeling and analysis of user mobility plays a vital role single-tier and multi-tier models in which base-stations (BSs) in optimizing the design and performance of cellular wireless follow a homogeneous Poisson Point Process (PPP). For the second approach, we also outline the general methodology. In networks. User mobility directly impacts the following: addition, we discuss some limitations/imperfections of the existing • Resource management aspects such as channel allocation techniques and provide corrections to these imperfections. For schemes, multiple access mechanisms, estimate of net- both the approaches, we present selected numerical and simula- work capacity, call blocking rate, traffic volume per cell, tion results to calibrate the achievable handoff rate and coverage probability in various network settings. Finally, we point out users’ quality of service (QoS), signaling and traffic load specific 5G application scenarios where the impact of mobility estimation, etc. would be significant and outline the challenges associated with • Radio propagation aspects such as signal strength vari- mobility-aware analysis of those scenarios. ation, interference level, call dropping rate, handoff1 Index Terms—Fifth generation (5G) and beyond fifth genera- algorithms (typically based on signal strengths). arXiv:1805.02719v1 [cs.NI] 7 May 2018 tion (B5G) cellular, individual mobility, group mobility, handoff • Location management aspects that include location area analysis, stochastic geometry, hexagon lattice, square lattice, planning, multiple-step paging strategies, data location spatial correlation, temporal correlation. strategies, database query load. The significance of mobility-aware network performance anal- I.INTRODUCTION ysis is thus evident in optimizing the interference and network- A. 5G/B5G Networks and User/Device Mobility wide resource management and accordingly user QoS pro- The fifth-generation (5G) mobile communication networks visioning through network dimensioning, optimizing hand- are envisioned to support massive connectivity (millions of off thresholds, and handoff methods. Since mobility directly devices per sq. km), higher data rates, lower transmission affects the availability of network resources, mobility-aware delays (around 5 ms) in user plane and (around 10 ms) for performance modeling and optimization of systems such as control plane, and devices with very high mobility speeds (∼ device-to-device (D2D) communications, cognitive radio net- 500 kmph) [1], [2]. 5G networks will support ultra-reliable low works, unmanned aerial vehicles (UAV) or drone networks, and vehicle communications is of immediate relevance. The authors are with the Department of Electrical and Computer Engi- 1 neering at the University of Manitoba, Canada (emails: {Hina.Tabassum, An event where a mobile user connected to one BS switches to another Ekram.Hossain}@umanitoba.ca, [email protected]). BS in order to maintain its ongoing transmission and/or network connectivity. 2

Due to the irregular deployment of BSs in emerging time/frequency selectivity of the propagation channel. The 5G/B5G cellular networks, mobility-aware performance anal- condition for handoff can be written as: ysis must capture the location uncertainty of the BSs [3], [4]. S − S ≥ O − O + H + H (1) One of the common and analytically tractable approaches to neighboring serving s n s off incorporate spatial randomness in cellular networks is to model where Os and On represent offsets of serving and neighboring BSs with the homogeneous Poisson point process (PPP) where BSs configured by the network operator, respectively. Hs is the number of nodes in area |A| is a Poisson random variable the handoff hysteresis parameter which corresponds to the and the nodes are uniformly distributed. The accuracy of PPP- traffic load of different BSs and Hoff is a parameter specific based model for a two-tier cellular network was examined in for each pair of network BSs. handoff occurs when the [5] and it was shown that the signal-to-interference-plus-noise condition in (27) has been met for a specific duration, i.e., time ratio (SINR) coverage probability (i.e., the probability that the equal or longer than value of the Time-To-Trigger (TTT)2. instantaneous SINR is above a given target threshold) of a Later, mobility enhancements for co-channel heterogeneous user in a 4G network lies between the PPP model (pessimistic networks are considered in LTE Rel-11 [14]. Specifically, lower bound) and the hexagonal grid model (optimistic upper handoff procedures are optimized by dynamically adapting bound). Since then there have been various follow-up research handoff parameters for different cell sizes and user velocities. studies where PPP-based modeling has been used to assess The LTE network architecture is composed of BSs (pro- the rate and coverage probability of users [6], [7], [8]. Taking viding both user plane and control plane to users), mobility into account the spatial randomness of cellular networks using management entity (MME) and system architecture evolution stochastic geometry tools, some of the pioneering research gateway (S-GW) [15]. BSs are connected to MME/S-GW studies in which mobility-aware performance analysis has been by the S1 interface and connects to each other through carried out are [9], [10], [11], [12]. X2 interface. The S-GW controls inter-3GPP mobility while Due to inherent heterogeneity of 5G/B5G cellular networks, routing and forwarding the user data packets. Note that the user a given user may traverse among extremely diverse networks mobility support is needed whether the user is in idle mode and cells with diverse transmission frequencies, e.g., radio or in connected mode [16]. When a user turns on Public Land frequency cells and mm-wave cells. This will result in frequent Mobile Network (PLMN) is selected and the user searches handoffs that create heavy signaling overhead and deteriorate for a suitable cell of selected PLMN and tunes to its control user’s experience even at low to moderate velocities. Mobility channel. This procedure is referred as “camping on the cell”. modeling will therefore be more important compared to homo- In connected mode, LTE utilizes a network controlled and geneous scenarios where users move among the same type of user-assisted handoff procedure. The LTE handoff procedure is cells. Note that compared to horizontal handoffs (where a user shown in Fig. 1 and the steps are summarized as follows [17]: switches to another BS with similar transmission features), • Each user continues to measure the received signal vertical handoffs (where a user switches to another BS having strength S from the serving and neighboring BSs. diverse transmission characteristics such as transmit power and • To initiate handoff, the user reports the measurements frequency) may impact the overall system more adversely. The (e.g., reference signal received power (RSRP) and refer- reasons include extra control signaling, possible call drops ence signal received quality (RSRQ)) taken from neigh- due to channel unavailability, and varying channel attenuation boring BSs to their respective serving BS. factors due to different transmission frequencies. Note that a • Handoff preparation: The serving BS makes the handoff mobile user may improve data rate by performing a vertical decision based on the measurement reports and radio handoff to a more dense tier, but this may also result in resource management information of the target BS. frequent handoffs/delays, which potentially deteriorates the • The serving BS then sends the handoff request to the tar- service quality. Balancing the trade-offs among handoff rate, get BS. Based on the admission control of the target BS, service delay, and achievable coverage/data rate in hetero- the serving BS gets the acknowledgment from the target geneous, dense, and random 5G/B5G cellular networks is BS. Once the serving BS receives the acknowledgment, therefore an open challenge. it transfers all information to the user. • Handoff execution: The user then sends a confirmation B. Mobility and Handoff Management signal to the target BS. After that the target BS sends the Mobility of users/devices results in handoff. The number of path switch command to MME/S-GW. handoffs are proportional to the intensity of BSs and velocity • Handoff completion: After path switch completion, user of users. The handoff process requires a smooth transfer of a releases the serving BS resources. and access the target connected user when moving from one cell to another with the BS using the random access channel (RACH). Upon guaranteed QoS. The objective of efficient handoff/mobility synchronization with the target BS, the user sends the management is to reduce radio link failures during handoff, confirmation message to notify the network that the handoff failures, and ping pong events. Mobility management handoff has been completed. was included in the first release of Long-Term Evolution (LTE) It can be observed that the signaling overhead (due to the standard (Rel-8) for homogeneous networks [13] where the searching process and handoff related signaling between the handoffs are generally based on the measurement of signal 2 strengths from the neighboring BSs and are affected by the This is the minimum time for which the handoff criterion needs to hold. 3 user, serving BS, target BS, and core network) can increase of the joint event that the user is in coverage and handoff the handoff delay3 significantly. occurs penalized by the cost of handoff. • Mobility-aware throughput [19]: is defined as the tradi- C. Mobility-Aware Performance Measures tional spatially averaged throughput of a user multiplied by a factor (1 − Hd) where H is the handoff rate and d Network performance metrics such as coverage or through- is the delay per handoff. This allows to incorporate the put need to incorporate the impact of user/device/node mo- impact of handoff on the users’ achievable throughput. bility and network performance analysis methodologies need to be tractable. Some relevant mobility-aware network perfor- mance metrics include [9], [11], [10], [18]: D. Scope of the Tutorial • Handoff rate [9], [10]: This is given by the expected This tutorial provides a comprehensive review and compar- number of handoffs divided by the average transition time ative analysis of tractable analytical methodologies presented taken by a user to move from one way point to another. in [9], [10], [11], [12] for mobility-aware performance analysis • Sojourn time (or dwell time) [9]: This refers to the time a (in layer 2) of emerging 5G/B5G cellular networks. The mobile node resides in a typical cell. In other words, this issues related to handoff management (e.g., optimization of the is the time for which a BS provides service to a node. handoff parameters, resource allocation for handoff) and the • Direction switch rate [9]: This is the reciprocal of the analysis of aspects related to radio propagation (e.g., signal sum of transition time and pause time. strength variation, time dispersion of signals) are not within • Handoff probability [11]: This is the probability that the the scope of this tutorial. user crosses over to the neighboring cell in one movement We will first review different mobility models that can period (i.e., the probability that the serving BS does not potentially mimic the movement patterns of users/devices and remain the best candidate in one movement period). wireless nodes such as air crafts, high speed trains, vehicles, By definition, the handoff rate is the average number of wearables, drones, unmanned air vehicles (UAVs) etc. These handoffs per unit time, i.e., models include purely random models (e.g., random walk, ran- dom way point, random direction), spatially correlated (e.g., H = E [Number of handoffs per unit time] pursue mobility, column mobility), and temporally correlated ∞ X models (e.g., Gauss-Markov, Levy flight). The distinctive fea- = kP (Number of handoffs per unit time = k) . tures of the aforementioned mobility models, their statistical k=1 properties, and their benefits and drawbacks will be presented. For low velocities, the handoff rate is equal to the proba- Then we will provide a summary of the existing state-of- bility of the handoff since the number of handoffs in a unit the-art of mobility and handoff analysis (sheer majority of time is one with probability P(H) and zero with probability which are for spatially non-random cellular networks) based P(H¯ ) = 1 − P(H), i.e., H ∼ P(H), where P(H) denotes on simulation and theoretical approaches. the probability of handoff. Also, when the BS density is low, We will then provide a systematic introduction to the exist- the handoff rate can be approximated by the probability of ing analytical methodologies for mobility-aware performance handoff for larger range of velocities. Note that handoff rate is analysis in spatially random cellular networks. These method- inversely proportional to the expected sojourn time; however, ologies are general to accommodate a variety of mobility mod- their distributions can be quite different [9]. els to conduct mobility-aware performance analysis. In this Generally, it is difficult to incorporate the impact of handoff tutorial, two major approaches, namely, the trajectory-based rate and sojourn time on the rate or coverage probability and the association-based approaches, are described. For the of a typical mobile user. This is why the coverage or rate trajectory-based approach, which is more general (however expressions are typically derived for stationary (but randomly less tractable), we highlight a general methodology to perform located) users and spatial averaging is then performed. Nev- mobility-aware performance analysis for both random and ertheless, due to heterogeneous and ultra-dense nature of non-random cellular networks. Case studies are presented for 5G/B5G networks, it is not sufficient to compute the coverage different cellular network topologies such as square lattice, and rate metrics only for stationary users. The reason is that the hexagon lattice, single-tier and multi-tier models in which optimal association of a user (from the perspective of data rate BSs follow a homogeneous PPP. For the association-based maximization) may not remain optimal due to higher handoff approach, we will also outline the general methodology to rates. As such, the trade-off between handoff rate and data rate calculate the handoff probability and the mobility-aware cov- needs to be captured and the performance measures should erage probability. In addition, some limitations/imperfections be designed accordingly. In this regard, the relevant mobility- of the existing techniques in this approach will be pointed aware network performance metrics include: out and corrections to these will be also provided. Also, for • Mobility-aware coverage probability [11]: can be defined both the approaches, we will present selected numerical and as a sum of (i) probability of the joint event that the user simulation results to calibrate the achievable handoff rate and is in coverage and no handoff occurs and (ii) probability coverage probability by a user in various network settings. Finally, we will outline some research directions and potential 3The handoff delay is measured from the beginning of initiation phase to approaches for mobility-aware analysis of 5G/B5G networks. the end of execution phase. The organization of the article is shown in Fig. 2. 4

User Equipment (UE) Source BS Target BS MME/S-GW

User Data Packets 1. Measurement Control

2. Measurement Reports Handoff PreparationHandoff 3. Handover Decision

4. Handover Request 5. Admission Control 6. Handover Request ACK 7. Handover Command

8. Detach from Source BS 9. Deliver buffered and synchronize with

packets to Target BS ExecutionHandoff Target BS User Data Forward

10. Buffer Packets from Source BS 11. Synchronization 12. Resource Allocation 13. Handover Confirm 14. Path Switch Request

15. Path Switch CompletionHandoff Request ACK 16. Path Switch

17. Release Resource

User Data Packets

Fig. 1. Procedure for handoff in 3GPP LTE [17].

II.CLASSIFICATION OF MOBILITY MODELS precision may result in huge computational cost or reduced The handoff delay and signaling overhead may become mathematical tractability. The mobility models to characterize significant in ultra-dense networks given that each small cell the movement patterns of mobile nodes in wireless networks may receive a large number of handoff requests, followed are typically classified as follows [21]: by the execution of the admission control algorithm for • Trace-Based Mobility Models: are obtained by measure- each accepted request. Some of these handoff requests may ments of deployed systems (e.g., from logs of connec- even be unnecessary, especially for truly mobile users who tivity or location information of mobile users) [22], [23], are expected to enter and leave the cells swiftly. Therefore, [24]. These models are realistic in terms of the movement sophisticated mobility-aware handoff procedures (based on and topology of the area, e.g., CRAWDAD project [25]. the information of users such as their location, speed, and These traces are valuable for the performance assessment direction) will be required. Subsequently, characterizing the and optimization of handoff protocols but may not serve statistics of the location, speed, and direction of users is as benchmarks for the scientific community. The reason of prime relevance since it will enable us understanding is that the available real traces may not be applicable and the mobility pattern4 of users, deriving sophisticated handoff generalized for a variety of scenarios. criteria, and mobility-aware performance analysis of cellular • Random Synthetic Models: are mathematical models to networks. We will review various mobility models and their characterize the movement of the devices. The models are potential applications in emerging 5G/B5G cellular networks. generally simple and analytically tractable, but may not The precision of mobility models can be measured in terms reflect realistic mobility patterns [26]. Examples include of how close they can model the real mobility patterns of users Bayesian models that are capable of mimicking random and/or different kind of wireless nodes. However, attaining this behavior of a node (or group of nodes), Brownian motion [27] that characterizes the diffusion of tiny particles with 4Often, the mobility models and mobility patterns are used synonymously. a mean flight time and a mean pause time between flights However, one must carefully distinguish between them since the mobility patterns can be obtained by tracking real moving objects (e.g., pedestrians, and the Levy pattern [28] which is more diffusive than vehicles, aerial, robot, and outer space motion [20]), while mobility models Brownian motion and is a good approximation of human offer mathematical formulations for different mobility patterns. walk in outdoor environments. 5

to sudden stops, sudden acceleration, and sharp turns. Typically, the velocity of vehicles and pedestrians accel- erate incrementally rather than randomly and the direction Mobility-Aware Cellular Network Analysis changes are also smooth leading to temporal correlation or temporal dependency among the mobility parameters. • Individual Mobility - With Memory: In the individual Performance Metrics (Section I.C) mobility models with memory, a mobile user moves in- dependent of other nodes. Different from the memoryless Mobility Models (Section II) models, a node’s next location is a function of its past locations and velocities. These models are also referred Individual Models to as mobility models with temporal dependency. • Group Mobility: The group-mobility models are generally Memoryless Models an extension of the individual mobility models. These models either utilize a mathematical function to describe Memory-based Models the mobility behavior of a group (e.g., exponential cor- (Temporal Correlation) related random mobility model [26], community model, and column mobility model [31]). These models are also Group Models (Spatial Correlation) referred to as mobility models with spatial dependency. Individual Models (Section III) The set of mobile nodes in column mobility model form a line and move forward in a particular direction. A Existing State-of-the-Art (Section IV) community mobility model is the one where a set of mobile nodes move together from one location to another. Mobility-Aware Analysis (Section V) Another type of group mobility models tends to mimic the behavior of mobile nodes that associate with a group Trajectory-based Approach leader (e.g., pursue mobility model [31], reference point group mobility model [32]). The pursue model allows Association-based Approach the users in a group to follow a target node moving over the simulation area. The reference point group mobility model considers the group movement based upon the path Fig. 2. Organization of the tutorial. traveled by a logical center according to an individual mobility model described before [32]. A classification of the useful mobility models is provided in Due to the differences in the trace acquiring methods, sizes Fig. 3 and a more extensive description of some of these mod- of trace data, and data filtration techniques, a trace-based els can be found in [26] and [33]. The mobility models with mobility model for one network data set may not be applicable spatial and temporal dependencies have not been exploited to other network scenarios. The traces may not be publicly fully in the context of cellular networks. To date, most of the available. The available traces may not be sufficient to analyze mobility-aware performance analysis is based on memoryless the network performance as the parameters such as speed or models such as random walk or RWP models. Note that group- the density of the nodes cannot be varied. Nevertheless, such based mobility models can also be very relevant for vehicular models are precise and realistic for a specific scenario. On the applications since high-speed trains, aircrafts, or vehicles will other hand, random mobility models are generic and math- require group handoffs since a group of people will be transi- ematically tractable. Subsequently, random mobility models tioning from one BS to another BS. Moreover, incorporating can be used for rapid assessment, mathematical analysis, and the impact of temporal correlations due to human walking optimization of a variety of network scenarios [29]. tendency and human clustering behaviors is another important The random synthetic models can be further classified as: direction to be considered. • Individual Mobility - Memoryless: In the individual mem- oryless mobility models, a mobile user moves indepen- III.RANDOM SYNTHETIC MOBILITY MODELS dent of other nodes. The location, speed, and movement direction of a given mobile node are neither affected by In this section, we provide an overview and taxonomy other nodes in its vicinity nor a function of its previous of random synthetic individual mobility models as they are velocities and locations. These models are mathematically relatively tractable, and hence, beneficial for rapid perfor- tractable but may not be close to reality. For example, mance modeling and assessment of mobile users in various 5G to avoid collision on a road, the speed of a vehicle cellular network scenarios. The goal is to provide readers with cannot exceed the speed of the vehicle ahead of it. a fundamental background to easily understand and compare Therefore, it is evident that the mobility of users could be different statistical models and eventually identify the one influenced by other neighboring nodes which results in according to their requirements. spatial correlation or spatial dependency among mobile nodes [30]. Furthermore, these models are vulnerable 6

Mobility Models

Synthetic Mobility Trace-based Models Mobility Models

Random Individual Random Group Memory less Mobility Models Mobility Models

 Random Walk Mobility  Exponential Correlated Random Mobility  Random Way Point With Memory  Column Mobility Mobility  Nomadic Community Mobility  Random Direction  Levy Flight Mobility  Pursue Mobility Mobility  Markovian Waypoint  Reference Point Group Mobility Gauss Markov Mobility  Fluid Flow Mobility

Fig. 3. Classification of various mobility models potentially applicable to cellular network modeling, analysis, and optimization.

Consider mobile users move randomly in a two-dimensional The pause time of the mobile node Tp = 0. For every spatial region. The random movement conducted by each new interval, mobile node randomly and uniformly chooses mobile user can be expressed by stochastic sequence S as: direction in the range Θ ∈ [0 2π]. The speed follows a uniform distribution or a Gaussian distribution and is in the S = (L, Θ,T,Tp) (2) range V ∈ [vmin vmax]. The PDF of L can be given as: where a mobile user covers a distance of length L (the distance   1 φ l−T E[v] is generally referred to as flight length in the literature) and T σv T σv fL(l) = (3) flight duration T followed by a pause of duration Tp. Θ Φ( vmax−E(v) ) − Φ( vmin−E(v) ) represents the direction change from the previous flight. Before σv σv taking another flight, a mobile user chooses the variables where φ and Φ denote, respectively, the probability density (L, Θ,T,Tp) according to their respective distributions. The function (PDF) and the cumulative distribution function (CDF) mobile velocity can then be expressed as V = L/T . The of standard Gaussian random variables. During the flight, beginning of each transition is referred to as a way point, the node moves with velocity vector [V cosΘ V sinΘ]. At whereas the trajectory of a mobile node can be expressed as boundaries, the user can either reflect back from the boundary, a set of way points and lines generated by S. or wrap around resulting in sharp directional changes termed as Border Effect [30]. A. Memoryless Individual Mobility Models Random walk was used in various research studies [36], [37]. For example, [36] used the random movement to derive The memoryless mobility models retain no knowledge about the mean cell sojourn time and [37] conducted a systematic the previous locations and velocities of the mobile nodes. tracking of the random movement of a mobile node. At each This characteristic limits the practicality of the memoryless instant, the area is partitioned into several regions according to models to some extent because mobile nodes typically have previous, current, and next direction of the mobile node [37]. a predefined destination and speed which may affect future Explicit mathematical conditions for movements from the destinations and speeds. Some of the popular memoryless current region into the next region were derived. Based on individual mobility models are reviewed in the following [21]. these conditions, channel holding time, cell residence time, 1) Random Walk (Brownian) Model [34], [27]: The and the number of handoffs were derived. Although this is concept of random walk was first invented by Pearson in one of the most popular mobility models, it fails to capture 1905 [34]. In this model, a user randomly chooses a direction realistic human/vehicle movement patterns. Θ and speed V from a given range and then travels for a fixed duration T or, equivalently, a distance L = VT . 7

TABLE I FEATURES OF INDIVIDUAL MEMORYLESS RANDOM MOBILITY MODELS

Mobility Flight Length (L) Direction (Θ) PDF Flight Time Pause Time (Tp) Limitations Benefits Model (T ) 1 Random Eq. (3) 2π , 0 ≤ Θ ≤ 2π T = constant Tp = 0 Border effect, Far Tractable Walk [34] from human mobil- ity Random PDF: Eq. (4) - rectan- [30, Eq. 13], Eq. (8) PDF: Eq. (7) Tp = constant Non-uniform Tractable, Way gular, Eq. (6) - circular Θ and node Available in point [35] distribution network simulators NS-2 and NS-3

λπl2 1 Modified PDF: 2πλle 2π , 0 ≤ Θ ≤ 2π PDF: Eq. (9) Tp = constant Way points are not Tractable, Uniform Random and Eq. (10) i.i.d and form a node distribution, Direc- Markov process Close to Levy tion [9] Flight

1 R ∞ −ixl−|cl|α 1 1−ρ 1 R ∞ −ixt−|ct|β Truncated 2π −∞ e dx 2π , 0 ≤ Θ ≤ 2π kL 2π −∞ e dx Accuracy (within Close to human Levy [28] 10 km) mobility

2) Random Way point (RWP) Model [35], [38]: The RWP The PDF of flight time can then be derived as follows: model was first introduced in 1996 [35] to model the move- Z vmax ment of mobile users. RWP is an extension of random walk fT (T ) = vfL(vt)fV (v)dv. (7) mobility model with pause time between changes in direction vmin or speed. RWP has a simple implementation and is available It was observed in [40], [41], [39] that the spatial node dis- in typical network simulators such as in NS-2 and NS-3. In tribution becomes non-uniform with the increasing simulation this model, each node picks a random destination (referred runs. As such, the node density becomes maximum in the to as way point) uniformly distributed within a finite space center and nearly zero at the boundary of the simulation and travels with a speed uniformly chosen from an interval space [42]. This phenomenon happens since the nodes are V ∈ [0 Vmax]. Then the user moves along the line (whose likely to either move towards the center of simulation field length is called transition length L) connecting its current way or choose a destination that requires movement through the point to the newly selected way point at a chosen velocity middle [30]. [40] showed that the underlying reason is the non- V . Upon reaching the destination, the process repeats itself uniform distribution of the direction angle at the beginning of Θ (possibly after a random pause time Tp). each flight. Based on the PDF of direction angle , [39] described RWP as a discrete-time stochastic process. Z 2π Z a r It was shown that the average flight length in a single epoch fΘ(Θ) = fΘ(Θ|r) 2 drdφ, (8) 0 0 πa over all mobile nodes (i.e., spatial average) is equal to the average flight length of a specific node over time (i.e., time it was shown that the probability of moving in a direction towards the boundary within interval [ π 3π ] is only 12.5%. average). As such, RWP has mean-ergodic property according 2 2 to the theory of random processes. Once RWP is ergodic, the However, the node moves toward the center within interval [− π π ] with a probability of 61.4% [40]. PDF of flight length L can be described by considering the 4 4 Euclidean distance between two independent random points in 3) Random Direction Model [43]: This model was con- the simulation space. Consequently, by applying the standard structed mainly to address the tractability issues arising due geometrical probability theory, the PDF of transition (or flight) to non-uniform node distribution of RWP [43]. In this model, length fL(l) in a rectangular region (of length a and width b) at each way point the mobile node chooses a random direction can be given as follows [39]: Θ uniformly distributed on [0, 2π] and a velocity V from 4l some distribution. Then the node moves to the next way point f (l) = f (l) (4) L a2b2 0 (determined by transition length and direction) at the chosen velocity. After the node reaches the boundary of the simulation where area and stops for duration Tp, the node then randomly and  2 π ab − al − bl + l 0 ≤ l ≤ b uniformly chooses another direction to travel. As such, the  2 2 f (l) = G(l) b < l < a (5) nodes remain uniformly distributed with in the simulation area. 0 √ G(l) − H(l) a < l < a2 + b2 Nevertheless, the transition lengths may deviate significantly from those in human walks. √ 2 in which G(l) = ab sin−1 b +a l2 − b2 − b −al and H(l) = √ l 2 4) Modified Random Direction Model [9] : Lin et al. −1 a 2 2 l2+a2 ab cos l + b l − a − 2 . The PDF of L for a circular updated the classical random direction model by providing the region of radius a can be derived as follows [39]: transition length distributions directly as a Rayleigh distributed s They refer their model as modified  2 random variable in [9]. 8l −1 l l l random way point in [9]. Through simulations, it was shown fL(l) = cos − 1 − . (6) 2πa2 2a 2a 2a that, the modified model is close to Levy walk model which 8 is close to human mobility patterns. The distribution of flight change, a new target speed is chosen according to (11). Then, time was derived for constant velocity V as follows [9]: the speed changes incrementally from the current speed to the

2 −λπV 2T 2 new speed by acceleration speed or deceleration speed a(t) fT (T ) = 2πλV T e (9) whose PDF is uniformly distributed. When V is uniformly distributed in the range [vmin vmax], 2) Gauss Markov Model [45]: This model was introduced then fT (T ) can be derived as follows [9]: in [45] as an improvement over the Smooth Random mobility

g(vmin) − g(vmax) model [44]. In this model, a node’s velocity at any time slot fT (T ) = (10) is a function of its previous velocity, and thus, a temporal t(vmax − vmin) √ dependency exists. The degree of temporal dependency is −λπt2x2 Q(tx 2πλ) where g(x) = xe + λt in which Q(·) is the determined by the parameter α which shows the memory complimentary CDF (CCDF) of a Gaussian random variable. level and randomness of the Gauss-Markov process. When As in the classical RWP mobility model, the users can have a α = 0, the Gauss Markov process has strong memory and random pause time Tp at each way point. the velocity is determined by the fixed drift velocity and the Gaussian random variable. When α = 1, the Gauss Markov 5) Synthetic Truncated Levy Walk Model [28]: This model process becomes equivalent to fluid flow model where the is constructed from real mobility trajectories. In the model, the velocity of the mobile node becomes equivalent to the previous transitions lengths and the pause time have an inverse power velocity. For 0 ≤ α ≤ 1, the current velocity depends on law distribution (Levy distribution as shown in Table I). Flight both previous velocity and the Gaussian random variable. The times and lengths are found to be highly correlated, therefore degree of randomness is adjusted by α. As α increases, the [28] modeled the relation as T = kL1−ρ. When ρ = 0, T current velocity gets more influenced by the previous velocity; becomes proportional to L thus modeling constant velocity otherwise, the current velocity becomes more biased with the movement; whereas, when ρ = 1 flight time T becomes a Gaussian random variable. At given intervals of time, the new constant and flight velocity is proportional to L. Although speed and direction are calculated which is followed until Levy walk model is constructed from real mobility trajectories, the next time epoch. The dynamics of the model are greatly human walks are not Levy walks since human walks have influenced by α and the mean and standard deviation chosen complex temporal and spatial correlations and its nature has for the Gaussian random variable. Near the boundaries, the not yet been fully understood. direction of movement is forced to flip 180 degree.

B. Memory-Based Mobility Models 3) Markovian Way Point Model [46]: This model is a gen- eralized mobility model where the node moves along a straight Due to the memoryless nature of the aforementioned mobil- line segment from the current way point to the next way point ity models, it is difficult to capture the temporal dependency. (chosen from a discrete time Markov process). The way points For example, the current velocity or direction of a mobile constitute a Markov chain with finite transition probabilities. node may depend on the previous velocity and direction. As As such, the way points enable us to create popular routes such, the velocities at different time epochs may be correlated. a user walks or drives through, i.e., the consecutive legs In the following, few mobility models are discussed that are may be correlated. The velocity distribution can be designed somewhat close to human mobility patterns and/or consider based on the traveled distance, i.e., the longer transitions with spatial and temporal correlations. vehicular speeds and shorter transitions with speeds typical to 1) Smooth Random Mobility Model [44]: As has been a pedestrian user [47]. The node can have a random pause noted before, the speed and direction of a node should vary time at each way-point as well as during the transitions. incrementally and smoothly rather than randomly. In this context, an extension of random walk model, referred to as C. Lessons Learned the smooth random mobility model, was proposed in [44]. In Having examined the aforementioned mobility models, we this model, the PDF of velocity in the range [0 Vm] can be observe that a trade-off exists between the analytical tractabil- explained by noting that the preferred speed values of mobile ity and closeness to realistic mobility patterns. Moreover, node has a higher probability, whereas a uniform velocity dis- among the memoryless mobility models, the modified random tribution is considered on the remaining interval. For example, direction and Levy flight models are the most recommended if the node has the preferred speed set {0.25Vm 0.5Vm}, then models due to their analytical tractability and closeness to fV (v) can be derived as follows: human mobility patterns. Note that the remaining memoryless  models demonstrate a slow convergence towards the stationary Pr(v = 0.5V )δ(v − 0.5V ) v = 0.5V  m m m distribution [48]. Intuitively, once the mobile node chooses a fV (v) = Pr(v = 0.25Vm)δ(v − 0.25Vm) v = 0.25Vm far away destination with a slow speed, the node will get stuck  1−Pr(v=0.25Vm)−Pr(v=0.5Vm)  0 < Vm < 1 in finishing this trip (due to low speed and far distance). Even Vm (11) with the increase in simulation runs, on average, more and where Pr(v = 0.5Vm)+Pr(v = 0.25Vm) < 1. In particular, at more nodes can get stuck with long journeys and low speeds. each way point, the new speeds (or directions) are chosen from A such, the average nodal speed keeps decreasing over time. a weighted distribution of preferred speeds. The frequency of Interested readers can refer to [49], [50] for more details. A speed change is a Poisson process, i.e., in an event of speed summary of the memoryless models is provided in Table I. 9

While the memoryless individual models are relatively classify a given user as fast if it remains connected to the tractable for performance analysis, they may not precisely upper tier regardless of any changes in its speed [67]. Another capture the realistic movement patterns of wireless nodes such alternative is to introduce a dwell-time threshold to take into as high-speed trains, different variety of UAVs and drones, air account the history of the user (in terms of speed) before any crafts, vehicles, and human pedestrians. It is therefore impor- handoff decision [65]. Due to unnecessary or frequent handoffs tant to incorporate temporal correlation along with obstacle between the tiers or among the BSs within one tier, the handoff restrictions in the mobility models and then utilize them for schemes should be designed to reduce the handoff delay. 5G/B5G wireless network applications. Finally, individual mo- Other handoff criteria include degradation of the desired signal bility models need to be generalized for group mobility models strengths, available resources/bandwidth at different BSs, and that are more suitable for high-speed vehicular applications. velocity of mobile users. A detailed overview of such studies Later in the article, we will describe how memoryless indi- can be found in [68], [33], [69], [70], [71]. vidual mobility models are useful in the analysis of wireless cellular networks with hexagonal grids, square grids, and B. Theoretical Studies single/multi-tier networks with BSs following a homogeneous Despite aforementioned research on mobility management, PPP. For example, [9] considered a random way point mobility there are limited research works that provide tractable mobility model for a node and then conducted a mobility-aware per- models and characterize network or users’ performance mathe- formance analysis while [10] considered an arbitrary mobility matically with mobility. Performance characterization of a cel- pattern for handoff analysis. lular network enables network operators to qualitatively assess and optimize the performance beforehand without expensive IV. CURRENT STATE-OF-THE-ART:MOBILITYAND field trials or time-consuming simulations. Approximations HANDOFF ANALYSIS may also be developed that can potentially simplify the A. Simulation-Based Studies optimization procedures and may provide closed-form optimal To date, a plethora of research studies analyzed the mobility- solutions for important network performance metrics. In this based handoff performance in cellular networks via either context, some of the classical mobility-aware performance computer simulations or numerical optimization algorithms. models employed queuing, i.e., the cells are generally modeled For instance, [51] investigated the handoff performance of LTE as queues, active users are modeled as units in the queues, networks. Self-organizing handoff management techniques and handoffs correspond to unit transfers among queues. For were proposed in [52] to autonomously configure the mobility example, [72] studied the single-cell set-up using an M/G/∞ management parameters. In heterogeneous networks, handoff queue and [73] proposed a two-queue model considering a parameters (e.g., time-to-trigger (TTT), hysteresis threshold5, wireless local-area network (WLAN) cell overlaying one 3G etc.) were optimized to achieve seamless mobility of users cell. For multi-cell networks, queuing was employed in [74], in [53]. [54] presented multiple vertical handoff decision [75], [76], [77], [78], [79]. The impact of cellular network algorithms for heterogeneous networks, while [55] investigated geometry was however not considered. the handoff management in multi-tier networks by proposing a A few of the research works incorporated spatial features of theoretical model to characterize the performance of a mobile cellular networks by analyzing single-tier [80] and multi-tier user in heterogeneous networks. In [56], the significance of networks [81] with BSs deployed on regular grids. In [80], inter-cell interference coordination was shown to improve a mathematical formulation was developed for the random the handoff performance for both low and high speed users. movement of a user in a single-tier hexagonal cellular network. Mobility state estimation was performed in [57] to estimate the The proposed model characterized the distribution of the velocity of users and managing their associations accordingly, cell residence time (sojourn time), the channel holding time thereby enhancing the handoff performance. In [58], mobility (defined as the time during which a call occupies a channel performance was analyzed with and without inter-site carrier in the given cell), and the average number of handoffs per aggregation for macrocells and picocells deployed on a differ- user. Results showed that the generalized gamma distribution ent carrier frequencies. is adequate to describe the cell residence time distribution. It The delays caused due to handoffs [11], [59] in multi-tier was also shown that the negative exponential distribution is a cellular networks were studied in various research works [60], good approximation for the channel holding time distribution. [61], [62], where macrocells are overlaid by microcells [63], In this work, no specific user mobility model was considered. [64]. The classic handoff algorithms typically assign users [81] studied a two-tier cellular network including one circular to the tier with maximum received signal power [65]. In macrocell and a predetermined number of circular microcells. some research works, the users are classified as slow or fast A mobility model was proposed to calculate the user transition according to a sojourn time threshold, and based on this, the probabilities from different cells assuming that the sojourn users will be assigned to a specific tier [66]. Some velocity- time distribution is given. based handoff algorithms utilize the estimated velocity and the direction of the user to perform handoff [61]. Nevertheless, to C. Lesson Learned avoid the unnecessary ping-pong effect, some handoff schemes The aforementioned studies considered non-random spatial 5It corresponds to the traffic load of BSs. tessellation of cellular BSs and therefore may not be suitable for dense, heterogeneous, and random 5G/B5G networks. 10

Also, performance metrics such as mobility-aware SINR cov- averaging over the distribution of X1 and the distribution erage and mobility-aware throughput were not considered. of Poisson-Voronoi tessellation. • Derive the spatial node distribution f(r, θ) which is V. MOBILITY-AWARE PERFORMANCE ANALYSIS OF defined as the probability that the node resides in some RANDOM CELLULAR NETWORKS measurable set A while transitioning from X0 to X1. Recently, in a handful of studies, mobility has been con- The distribution is needed for sojourn time computation. sidered for random cellular networks. The approaches for Step 2: Handoff Rate Using Buffon’s Needle Problem mobility-aware analysis of random cellular networks can be classified as follows: To derive the handoff rate for a user that moves with velocity • Approach 1 (Trajectory-Based Approach) [9], [10]: This v in a time period of ∆t in area A, we need to calculate the approach assumes that the handoff event occurs when the probability that this user crosses the cell boundaries. That is, moving user travels across cell boundaries of different find the probability that a needle with length ` = v∆t crosses BSs along its trajectory (which can be defined according a line, where the lines are the cell boundaries. This problem to a mobility pattern described in Section II). Then the is referred to as the Buffon’s needle problem. analysis of handoff rate involves the evaluation of the Definition 1 (Buffon’s Needle Problem [82]). A needle of number of intersections between the user trajectory and length ` is dropped onto a floor with equally spaced parallel the set of cell boundaries. This approach requires the lines. What is the probability that needle crosses a line? derivation of the statistical distribution of cell boundaries which is relatively complex. This approach leads to Using the generalized argument for Buffon’s needle prob- 6 handoff rate and sojourn time evaluation. lem , for a user that moves in direction θ, the handoff rate • Approach 2 (Association-Based Approach) [11], [12]: (conditioned on the θ and velocity) can be obtained as [9] This approach assumes that the handoff event occurs |BA| E[T ] when there is a neighboring BS that provides a stronger H = v| sin θ| lim . (12) |A|→∞ |A| E[T ] + E[S] signal quality than the serving BS. That is, this approach leads to the evaluation of the probability of handoff In the modified random direction model, θ is uniformly distributed on [0, 2π]. Therefore, E [| sin θ|] = 2/π which during one movement period using the user association 7 criterion and association probability. yields In the following, we review some of the pioneering research 2 |BA| E[T ] H = E[V ] lim (13) works where the aforementioned mobility-aware performance π |A|→∞ |A| E[T ] + E[S] analysis techniques were considered. where T denotes the transition time and S denotes the pause time, i.e., E[T ]/ (E[T ] + E[S]) is the expected proportion of A. Trajectory-Based Approach transition time. |A| is the size of area A and |BA| is the |BA| [9] utilized the modified random direction model to mimic length of cell boundaries in A. Note that lim|A|→∞ |A| is the movement of users in a single-tier cellular network with the average length of the cell boundaries in a unit area which BSs deployed regularly as hexagonal lattices and randomly in [10] is called length intensity of cell boundaries, denoted (1) following a homogeneous PPP. Analytical expressions were by µ1(T ). Therefore, derived for the handoff rate (i.e., the average number of cells a 2 (1) E[T ] mobile user traverses to the average transition time (including H = [V ]µ1(T ) , (14) π E [T ] + [S] the pause time)) and sojourn time. The transition length was E E considered to be i.i.d. Rayleigh distributed which is contrary where T(1) represents set of cell boundaries. The length to classical RWP model where the transition lengths are not intensity of cell boundaries can then be defined as follows. i.i.d. and the random way points are i.i.d. Definition 2 (Length Intensity of Cell Boundaries [10]). The general approach for mobility-aware performance anal- Length intensity of the cell boundaries, denoted by µ (T(1)), ysis in this approach can be summarized as follows: 1 is the average length of T(1) in a unit square. Step 1: Characterize Mobility-Related Parameters Remark: The handoff rate for hexagonal lattice can be • Derive the expected transition length E[L]. obtained by using the generalized argument of the Buffon’s • Derive the expected velocity E[V ]. needle problem. However, for single-tier PPP, the handoff rate • Derive the distribution and expected value of the flight was derived using an alternative approach in [9]. In [10], the time T = L/V . authors provided a general approach to model the handoff rate • Derive the mean of the pause time S. by deriving the length intensity of cell boundaries considering • Derive the distribution of the target way point X1 which single-tier as well as multi-tier PPP. The approach is applicable is required for the evaluation of handoff rate. Conditioned 6 on the position of X , the number of handoffs equals Buffon’s needle problem was studied for both short (i.e., length of the 1 needle is less than the distance between two lines) and long needles. In this the number of intersections of the segment [X0,X1] and article, since we are considering short time period of ∆t, we need the result the boundary of the Poisson-Voronoi tessellation. The derived for short needle. expected number of handoffs can therefore be derived by 7 (13) can be used for any mobility model where θ is uniformly distributed. 11 for random multi-tier BSs, arbitrary user movement trajectory, and flexible user-BS association. A connection between the network performance metrics such as coverage probability and network ergodic capacity was not established in [9], [10]. Nevertheless, [83], [18], [19] incorporated the handoff rate calculations from [10] to derive mobility-aware throughput. Step 3: Length Intensity of Cell Boundaries Evidently, to derive the handoff rate, we need to calculate (1) the length intensity of cell boundaries µ1(T ). In the follow- (1) ing, the steps to derive µ1(T ) are discussed [10]. • First, we need to derive area intensity of ∆d-extended (2) cell boundaries, µ2(T (∆d)), which is the average area of T(2)(∆d) in a unit square, where T(2)(∆d) denotes Fig. 4. Square lattice with spacing d. The orange dots represent the BS locations, the black dashed lines represent the cell boundaries T(1), and the the ∆d-extended cell boundaries and is defined as the set shaded red area represents T(2)(∆d). of points that are located within (perpendicular) distance ∆d from T(1), i.e., n o cell and we call this user the typical user. Then µ (T(2)(∆d)) (2)(∆d) = x ∈ 2 : ∃y ∈ (1), |x − y| < ∆d . 2 T R T s.t. is the probability that the typical user is in the shaded area, (15) i.e., µ (T(2)(∆d)) can be interpreted as the probability that a (d − 2∆d)2 4∆d 2 µ (T(2)(∆d)) = 1 − = + O(∆d2). (18) randomly located point in a unit square is in T(2)(∆d). 2 d2 d In a cellular network, BSs locations are fixed and users are randomly distributed. However, from the perspective As we have mentioned earlier, we can assume that the of each user, the BS realization is different. Instead of typical user is always at the origin and the BSs are randomly considering a fixed realization of the BSs and a randomly distributed, i.e., one BS (the reference BS) is located uniformly located user, we assume that the user is always located in the square [−d/2, d/2]2 and the other BSs are located with at the origin and the BSs are randomly distributed. spacing d. Let us denote the location of the reference BS by (2) Therefore, µ2(T (∆d)) is the probability that the origin (x, y). Therefore, the BSs in the neighboring cells are located (0) is in T(2)(∆d), i.e., at (x, y + d), (x, y − d), (x + d, y), (x − d, y) and the cell boundaries are y + d/2, y − d/2, x + d/2, and x − d/2. These (2)  (2)  µ2(T (∆d)) = P 0 ∈ T (∆d) . (16) boundaries are shown in Fig. 5(a). The blue area in Fig. 5(a) shows ∆d-extended region of the cell boundaries T(2)(∆d). Cell boundaries are given by the BS locations. Thus, (2) (2) According to (16), µ2(T (∆d)) is the probability that the event that the origin is in T (∆d) is equal to the (2) (2) event that the BSs are located such that the set of cell 0 ∈ T (∆d). 0 ∈ T (∆d) means that the origin is boundaries T(1) is within distance ∆d from the origin. within distance ∆d from one of the cell boundaries, i.e., |y +d/2−0| < ∆d, |y −d/2−0| < ∆d, |x+d/2−0| < ∆d, • Then the length intensity is obtained by or |x − d/2 − 0| < ∆d. Simplifying these four inequalities (2) (1) µ2(T (∆d)) and considering −d/2 < x, y < d/2, yields −d/2 < y < µ1(T ) = lim . (17) ∆d→0 2∆d −d/2+∆d, d/2−∆d < y < d/2, −d/2 < x < −d/2+∆d, or d/2 − ∆d < x < d/2. The shaded area in Fig. 5(b) illustrates these four inequalities for −d/2 < x, y < d/2. Consequently, B. Case Studies and a Recommended Methodology 0 ∈ T(2)(∆d) is equal to the event that the reference BS Here we provide three case studies in which we derive located at (x, y) falls within the shaded area in Fig. 5(b). It is handoff rates for square lattices, hexagonal grids, and three worth mentioning that the shaded area in Fig. 5(b) is exactly dimensional (3-D) single-tier PPP networks (e.g., for drone the same as the shaded area in the typical cell in Fig. 4. applications) by combining Buffon’s needle approach from [9] (1) From (17), the length intensity is µ1(T ) = 2/d, and using with length intensity of cell boundaries from [10] as it can be (14) we can derive the handoff rate as extended to multi-tier cellular networks. Also, we show that 4 E[V ] E[T ] (a) 4 √ E[T ] this approach can be easily applied to both random and non- H = = E[V ] λ , (19) random cellular networks. π d E[T ] + E[S] π E[T ] + E[S] 1) Case Study 1 (Square Lattice): Assume that the BS where λ in (a) denotes the BS density (average number of BSs locations are modeled by a square lattice with spacing d8 in a unit area), which can be obtained by λ = 1/d2. (1) as shown in Fig. 4. The set of cell boundaries T and 2) Case Study 2 (Hexagonal Grid):√ For the hexagonal ∆d-extended cell boundaries T(2)(∆d) are also illustrated in lattice with side length of d, i.e., (3 3/2)d2 = 1/λ, the area Fig. 4. Assume that a user is randomly located in the typical intensity of the ∆d-extended cell boundaries is equal to the

8  2 In 2-D space, square lattice with spacing d is defined as Ld = dZ [84]. 12

Fig. 5. Graphical illustration for the length intensity T(1) and area intensity T(2)(∆d) of the cell boundaries in square and hexagonal spatial cellular networks. probability that the reference BS (randomly distributed in the a ground user). Therefore, we can study the handoff rate of hexagon) falls in the shaded area in Fig. 5(c), i.e., the drone by projecting its trajectory onto R2 plane, i.e., the √ handoff rate of the drone is the same as the handoff rate of 3 3 (d − √2 ∆d)2 (2) 2 3 4∆d 2 a ground user that moves with velocity v(t) sin(ϕ(t)) in the µ2(T (∆d)) = 1 − √ = √ + O(∆d ). 3 3 2 3d direction θ(t) in time interval [t, t+1). If we assume no pause 2 d time, from (12), we have The handoff rate can then be obtained as follows [9]: √ (1) (a) 4 E[V ] E[T ] H = E[v]E[sin ϕ]E [| sin θ|] µ1(T ) =v ¯ λ (22) H = √ . (20) √ d [T ] + [S] (1) 3π E E where (a) is obtained from (i) µ1(T ) = 2 λ for the single- 3) Case Study 3 (3-D Single-tier PPP): Consider a single- tier PPP network [10], (ii) E[sin ϕ] = π/4 for the mentioned tier cellular network, where the BS locations are modeled by distribution, and (iii) E [| sin θ|] = 2/π since θ is uniformly a homogeneous PPP of intensity λ. We assume that all the distributed in [0, 2π]. BS antennas are installed at the same height from the ground. 4) Results: Fig. 7 compares the handoff rates observed in We want to derive the handoff rate for a mobile drone which various cellular network settings such as square lattice (19), is associated to these BSs. The location of the drone at time hexagonal grid lattice (20), and single-tier PPP [9], [10] for t+1, t ∈ N, is denoted by x(t+1) and assume that x(t+1) is various user velocities when λ = 0.0004. The handoff rate uniformly distributed within the sphere of radius (4/3)¯v (the for multi-tier PPP [10] is also shown in this figure (for two- term (4/3) is used to normalize the average velocity) centered tier networks). Based on the analysis, the handoff rates for at x(t), i.e., for t ∈ N, square lattice and single-tier PPP are the same since the length intensities of the cell boundaries are the same and equal to v(t) sin(ϕ(t)) cos(θ(t)) √ 2 λ. This is also verified from the simulations in Fig. 7. v(t) sin(ϕ(t)) sin(θ(t)) x(t + 1) = x(t) +   (21) Moreover, the hexagonal lattice shows a slightly reduced v(t) cos(ϕ(t)) handoff rate compared to the square lattice and single-tier PPP. where v(t) is the velocity of the drone during t-th movement period; ϕ(t) and θ(t) also determine the moving direction C. Association-Based Approach during the t-th movement period. Since x(t + 1) is uniformly In [11], the authors considered K-tier (orthogonal spectrum distributed within the 3-D ball of radius (4/3)¯v centered at allocated to different tiers) PPP network model for handoff x(t), v(t) is i.i.d. over t and its distribution is given by 2 3 and coverage analysis of a mobile user moving at speed v fv(v) = 81v /(64¯v ), where v ∈ [0, (4/3)¯v]; therefore, from one point to another. The handoff probabilities provided [v] =v ¯. ϕ(t) is also i.i.d. over time and f (ϕ) = 1 sin ϕ, E ϕ 2 in [11] are not precise. In the following, first we will provide where ϕ ∈ [0, π]. Moreover, at time t, θ(t) is uniformly a brief overview of their methodology and then provide the distributed in [0, 2π]. We assume that all the BSs transmit exact expression for handoff probability. with the same power; therefore, we consider the nearest BS Consider a single-tier Poisson cellular network where BSs association. Since the BS antennas are installed at the same follow a homogeneous PPP Φ of intensity λ and each user height from the ground, the set of cell boundaries consists of connects to its nearest BS. Assume a user located at u0 is planes that are orthogonal to the 2 plane so that the set of R connected to a BS located at x0 as shown in Fig. 6. Let us cell boundaries can be fully defined by its intersection with denote the distance between the BS and the user by r, i.e., r = 2 plane (which is the same as the set of cell boundaries for R ku0 − x0k. Since the user is connected to its nearest BS, there 13

between 0 and π/2 or v cos(π − θ) ≤ r. When θ is between −1  v sin(θ)  π/2 and π and v cos(π −θ) > r, sin R in (24) must −1  v sin(θ)  be replace by π −sin R since ϕ is between π/2 and π. Therefore, the exact expression for the handoff probability h −1  v sin(θ) i is given by (26), where A = π − θ + sin R . 2) Mobility-Aware Coverage Probability: The coverage probability (or transmission success) of a typical user, con- ditioned on r and θ, can then be defined as follows: ¯ Ck =P(γk ≥ τk, Hk) + (1 − β)P(γk ≥ τk,Hk) (27) where β is the probability of handoff failure due to dropped Fig. 6. System model in [11]. connections even though the user is in coverage from SIR point of view. The coefficient β represents the system sensitivity to handoffs and its value depends on the radio access technology, is no BS in the ball of radius r centred at u0. Now assume that this user moves with velocity v at angle θ (with respect to the the mobility protocol, and the speed of the link. When β = 1, every handoff leads to an outage irrespective of SIR coverage, direction of connection) and its new location is u1. Using the p 2 2 whereas for β = 0, the coverage of a user is not sensitive law of cosines, u1 is at distance R = r + v + 2rv cos(θ) to handoffs and becomes equal to the traditional coverage from the BS located at x0. probability of a user. 1) Handoff Probability: Clearly, handoff occurs when a For multi-tier networks, the coverage probability of a user different BS is closer to u1 than the BS located at x0, i.e., who is initially associated to tier k was defined as follows: when there is at least one BS in the shaded green area in K Fig. 6. Therefore, given r and θ the probability of handoff is X Ck = (1 − β)P(γk ≥ τk, n = k) P(H | r, θ) = P (Φ (b (u1,R) \ b (u0, r)) > 0 | r, θ) k=1 (a) + β (γ ≥ τ , n = k, H¯ ) (28) = 1 − exp (−λ|b (u1,R) \ b (u0, r) |) P k k k which can be equivalent written as follows: where b (u1,R) denotes the ball with radius R centred at u1 and b (u0, r) is excluded from b (u1,R) since we know the BS K located at x is the nearest BS to u . Note that (a) is obtained X ¯ 0 0 Ck = P(γk ≥ τk, n = k, Hk)+ from the void probability of the PPPs and |b (u1,R)\b (u0, r) | k=1 denotes the area of b (u ,R) \ b (u , r). Finally, the handoff 1 0 (1 − β)P(γk ≥ τk, n = k, Hk). (29) probability is obtained by averaging over r and θ, where θ is Correction: The formulation in (28) or (29) considers the uniformly distributed between 0 and π (due to the symmetry),√ and r is a Rayleigh random variable with mean 1/(2 λ), i.e., SIR of the user with tier k even after handoff occurs which −λπr2 cannot precisely capture the inter-tier handoff as the user is fr(r) = 2λπre . Following these steps, P(H) for single- tier PPP can be derived as follows [11]: now connected to the j-th tier. For multi-tier networks, the Z π Z ∞ coverage probability of a user initially associated to tier k 1 −λπr2 P(H) = P(H | r, θ)2λπre drdθ (23) should be defined as follows: π 0 0 K where (H | r, θ) is given as [11]: X P Ck = (1 − β) P(γj ≥ τj, n = k, Hk,j) −λ R2 π−θ+sin−1 v sin θ −r2(π−θ)+rv sin θ j=1 1 − [e ( [ ( R )] )]. (24) ¯ + P(γk ≥ τk, n = k, Hk) (30) Correction: For θ = π, the above handoff probability cal- where P(n = k) is given by the association probability to tier culation is precise when v ≤ r. This can easily be understood k. Another limitation is that the closest BS to the user after by setting θ = π in (24) which gives P(H | r, θ) = 0. For handoff is always identified as the new serving BS, which may θ = π, P(H | r, θ) = 0 is only true when v ≤ r. Therefore, not be true in the downlink of multi-tier cellular networks (due for v > r we must use the following equation: to distinct transmission powers and received signal powers). As such, the results are limited to nearest BS association −λ(R2[2π−θ−sin−1( v sin θ )]−r2(π−θ)+rv sin θ) P(H | r, θ) = 1 − e R (which is valid in case of single-tier downlink networks). (25) These results precisely elaborate horizontal handoff probability while ignoring the essence of multi-tier networks. The biased which is not zero for θ = π. Since θ is between 0 and π,   received powers are considered only in the evaluation of the ϕ = sin−1 v sin(θ) in (24) is always between 0 and π/2. R association probability metric P(n = k). ϕ = ∠u0x0u1, i.e., ϕ is the angle of the vertex x0 in 4u0x0u1 [12] provided the horizontal and vertical handoff probability as illustrated in Fig. 6. ϕ is between 0 and π/2 when θ is expressions for a mobile user in K-tier cellular network. 14

π/2 ∞ π v cos(π−θ) " Z Z Z Z −λ(R2A+r2θ+rv sin(θ)) −λ(R2[2π−θ−sin−1( v sin(θ) )]+r2θ+rv sin(θ)) P(H) = 1 − 2λ re drdθ + re R drdθ 0 0 π/2 0 π ∞ # Z Z 2 2 + re−λ(R A+r θ+rv sin(θ))drdθ . (26)

π/2 v cos(π−θ)

TABLE II COMPARISON OF APPROACHESFOR MOBILITY-AWARE PERFORMANCE ANALYSIS IN RANDOM SINGLE-TIERAND MULTI-TIER CELLULAR NETWORKS

Ref Number BS Deployment Mobility model Approach Metrics Association of Tiers [9] Single- Hexagonal, PPP Modified Approach-1 Handoff rate, Sojourn Nearest BS tier Random time Direction [10] K-tier PPP Arbitrary Approach-1 Handoff rate Biased received and direction power θ ∈ {0, 2π} [11] One-tier PPP Arbitrary Approach-2 Handoff probability, Nearest BS and direction Mobility-aware coverage θ ∈ {0, 2π} probability [12] K-tier PPP Arbitrary Approach-2 Handoff probability, Biased received and direction Mobility-aware coverage power θ ∈ {0, 2π} probability [18], K-tier PPP Arbitrary Approach-1 Mobility-aware Biased received [19] and direction throughput power θ ∈ {0, 2π}

The distance-based equivalence has been established between 3) Results: When the network parameters are the same as in multiple tiers to incorporate biased received power-based as- Fig. 7, the handoff rate and handoff probability for single-tier sociation. Similar to [11], the coverage probability expressions PPP derived in [9] and [11], and for multi-tier PPP derived consider the fixed handoff cost and same mobility model. The in [10] and [12] are compared for low velocities in Fig. 8. general methodology for mobility-aware coverage analysis can Also, the handoff probability for single-tier PPP [11] and for then be summarized as follows [12]: multi-tier PPP [12] are compared for various user velocities in 1) Derive the zero handoff probability from tier k to tier j Fig. 9. The analytical handoff probabilities are obtained after using the distance-based equivalence as: applying the mentioned correction to the results in [11], [12].

¯ 0 0 0 P(Hk,j|rk, θ) = P[N(B \B ∩ A ) = 0|Tk 6= Tj] D. Lessons Learned + P[N(B\B ∩ A) = 0|Tk = Tj] (31) Both the trajectory-based (Approach 1) and the association- 0 where B denotes the circular area centred at l2 with based (Approach 2) approaches are feasible for mobility 0 −αˆj 0 modeling in advanced cellular networks and can accommodate equivalent radius of tier j as Rj = wjRk , A denotes the circular area centred at l1 with equivalent radius of a variety of mobility models discussed in Section II. The first 0 −αˆj 0 approach can incorporate a variety of user mobility patterns tier j as rj = wjrk , and rj denotes the equivalent with different statistics of flight length, velocity, and flight distance of rj. time. However, analyzing the intersections of user trajectories 2) After de-conditioning H¯k,j, the total handoff probability of a mobile user from tier k can be given as: and the cell-boundaries may become more complicated in ultra-dense cellular networks with hot spots modeled as cluster K Y processes. On the other hand, incorporating the impact of (H ) = 1 − (H¯ ) (32) P k P k,j handoff rate on the users’ coverage probability is not straight- j=1 forward. The second approach is more tractable since it Subsequently, the total handoff probability can be given characterizes handoff probability to directly evaluate coverage PK as H0 = k=1 AkP(Hk) where Ak is given by the probability. However, the essence of user mobility models standard association probability to tier k. with spatial and temporal correlation may not be easy to 3) The coverage probability of a user associated to tier k incorporate. Sojourn time analysis was presented only in [9] can then be derived using (30). using Approach 1. In the following, we provide an alternative Remark: The correction in (26) must also be applied to the method for sojourn time analysis and relate it to the handoff results derived in [12] for multi-tier PPPs. probability analysis considering a mobile user that moves with velocity v during time T in a single-tier PPP cellular network. 15

10 1

Square lattice − simulation Handover rate − simulation 9 0.9 Square lattice − analysis Handover rate − analysis Hexagonal grid − simulation Handover rate − simulation 8 0.8 Hexagonal grid − analysis Handover rate − analysis Single−tier PPP − simulation Handover probability − simulation 7 0.7 Single−tier PPP − analysis Handover probability − analysis Multi−tier PPP − simulation Handover probability − simulation 6 0.6 Multi−tier PPP − analysis Handover probability − analysis

5 0.5

4 Handover 0.4

Handover rate Multi−tier PPP

3 0.3 Single−tier PPP 2 0.2

1 0.1

0 0 0 20 40 60 80 100 120 140 160 180 200 0 2 4 6 8 10 12 14 16 18 20 Velocity Velocity

Fig. 7. Handoff rate for square lattice, hexagonal grid, single-tier PPP, and Fig. 8. Handoff rate and handoff probability for low velocities. Network multi-tier PPP with no pause time. For square lattice, hexagonal grid, and parameters are same as in Fig. 7. single-tier PPP networks, λ = 0.0004. For the two-tier PPP, λ1 = 0.0004, λ2 = 0.001, P2/P1 = 1/5, B2/B1 = 4, and path-loss exponent α = 4. 1

0.9 E. Sojourn Time Analysis - Recommended Approach 0.8 We focus on sojourn time in the cell where the connection 0.7 Single−tier PPP − simulation is initiated. Moreover, we only consider one movement period Single−tier PPP − analysis and no pause time. Let us denote the duration that a mobile 0.6 Multi−tier PPP − simulation Multi−tier PPP − analysis node stays within a particular serving cell by S. Then P(S > t) 0.5 is the probability that the mobile user resides in the serving cell more than time t and the sojourn time is 0.4

Z ∞ Handover probability 0.3 S¯ = E[S] = P(S > t)dt. (33) 0 0.2

0.1 Since we are only considering one movement period, P(S > t) = 0 for t > T . Let us denote the location of the mobile 0 0 10 20 30 40 50 60 70 80 90 100 user at time t by ut where 0 ≤ t ≤ T . Then P(S > t) Velocity can be interpreted as the probability that the mobile user is always connected to the same BS during movement from u0 Fig. 9. Handoff probability for single-tier and multi-tier PPPs. Network parameters are same as in Fig. 7. to ut. Since, in single-tier PPPs with nearest BS association, the Voronoi cells are convex, when the mobile user is served by the same BS at both locations u0 and ut we can conclude that aiming to provide high data-rates anytime and anywhere with S > t. Therefore, for 0 ≤ t ≤ T , P(S > t) = 1 − P(H | v, t), users/devices moving with very high-speeds (such as up to where P(H | v, t) is obtained by replacing v with vt in (26). 500 km/h). Mobility management can be very challenging ¯ R T Finally, the sojourn time is obtained by S = 0 P(S > t)dt = due to frequent handoffs, higher penetration losses, heavy R T T − 0 P(H | v, t)dt. signaling overheads, and sub-optimal cell selection mecha- It is worth mentioning that we can derive sojourn time for nisms. Furthermore, with the emerging new wireless frequen- mobility models with random velocity and random flight time cies, software-defined resource management solutions, aerial by averaging S¯ over the distribution of v and T . Moreover, and underwater communication, the existing mobility models (26) is derived for mobility models with uniform θ. When and handoff trigger mechanisms need to be customized for the distribution of the movement direction is not uniform, specific applications. In the following, we discuss some of we first need to modify (26) to derive the sojourn time. It the challenges related to mobility-aware analysis and handoff is not straightforward to apply the same approach to derive management in more detail. the sojourn time for multi-tier PPP cellular networks because, in multi-tier PPP cellular networks with biased nearest BS A. Mobility-Aware Analysis of Advanced Cellular Networks association, the Voronoi cells are not convex. Coverage and rate analysis for multi-tier networks assuming VI.OPEN CHALLENGESAND RESEARCH DIRECTIONS homogeneous PPP deployments may not capture the correla- In this section, we will highlight the impact of mobility in tion between BSs and users (e.g., hot spots where more BSs or emerging applications of 5G/B5G wireless cellular networks user devices tend to be installed) as well as other BSs belong- 16 ing to different tiers. It is therefore desirable to develop and C. Mobility-Aware Analysis of Wireless Energy Trans- analyze the user mobility considering advanced 3GPP-inspired fer/Harvesting Networks cellular network models [85] where different tiers of BSs Compared to wireless information transfer, wireless energy follow Poisson cluster processes (PCP) or some tiers follow transfer is relatively more vulnerable to the mobility of a PCP and some tiers follow PPP. In addition, flexible scaling user [90]. The reason is that the desired receiver sensitivity of cell sizes should be incorporated to consider advanced user for wireless energy harvesting (reported to be -10 dBm) is association mechanisms such as biased user association, chan- higher than the desired receiver sensitivity for data receptions nel access aware user association, backhaul aware association, (which is around -60 dBm). Due to different sensitivity levels, decoupled uplink-downlink association, etc. Clearly, for such the successful energy harvesting distance can be noticeably scenarios, the expressions for handoff rates experienced by an low. Consequently, depending on the level of mobility of active mobile user with arbitrary movement trajectory will be users, the number of handoffs for wireless charging can be novel and may even be complicated. Mobility-aware handoff, significantly higher. As such, sophisticated analytical models coverage and rate analysis for aforementioned models may would be required that can model the velocity of mobile energy also choose to incorporate higher frequencies such as optical harvesting devices and characterize a precise mobility-aware frequencies. In addition, three dimensional mobility models handoff criteria for efficient energy transfer. In a multi-operator based on stochastic geometry taking into account the antenna environment, different operators will likely have different height, azimuth, and beam-forming for drone applications are energy levels, spectrum, traffic load, and operational cost. For of immediate relevance. instance, given the strong energy transfer capabilities of a spe- cific operator, other operators may achieve higher incentives B. Mobility in Millimeter-Wave and Nanometer-Wave Net- by off-loading their associated energy harvesting devices to the works strong operator. In return, the strong operators (i.e., in terms A fundamental challenge in high frequency (e.g., of energy transfer capability) can either demand incentives or millimeter-wave [mm-wave] frequency, nanometer-wave offload their users to other nearby operators which are stronger [nm-wave] or optical frequency) transmission is intermittent from the perspective of wireless resources and information connectivity due to blocking, channel attenuation, and transfer. New analytical/optimization frameworks should thus availability of only line-of-sight (LoS) propagation. The be developed to model and evaluate the energy trading process signal strength degradation as a function of distance results in wireless energy harvesting networks. in a small coverage area, thereby causing frequent handoffs. Contrary to traditional radio frequencies, small movements D. Mobility in UAV networks of obstacles, reflectors, and changes in the orientation of a Compared to terrestrial networks, UAV/drone networks have handset relative to the body or a hand, can vary the channel their unique attributes such as the mobility of both transmitter rapidly. Thus a channel handoff may even be required while and receivers, altitude of the drones, frequent network topol- associated to the same BS and with very low mobility. It is ogy changes, mechanical and aerodynamic constraints, strict thus crucial to exploit macro-diversity, i.e., alternate channels safety requirements, and harsh communication in the discon- should be available for rapid reconnection. For example, due nected, intermittent, limited bandwidth (DIL) environments. to higher isotropic path-loss, mm-wave transmissions are Moreover, field tests in air and emulations might be very always supported with phased arrays or massive antennas; costly and scenario-specific to assess the handoff performance. thus signals are transmitted in narrow beams. As such, To cope with this, simulations using random mobility models frequent handoffs (even for users with low mobility levels) are generally a low-cost, systematic and robust alternative. are a big concern. Mobility-aware analysis of such networks However, the traditional random mobility models may not as well as efficient mobility management in these networks correctly emulate aerial networks. A redesign is therefore are open research problems. necessary in order to develop reliable simulation environ- To overcome the higher handoff rates and handoff cost in ment and subsequent design/evaluation of the drone networks. these networks (due to small cell coverage areas), intelligent Compared to air-to-air (AtA), an air-to-ground (AtG) handoff handoff skipping techniques would be essential to maintain a procedure may also be vital in ensuring efficient network trade-off between handoff rate and throughput. For example, resource consumption while attaining QoS requirements of the the decision of a user to skip the BS may be based on the users. Since drones in near future may likely deploy WiFi due coverage area of the cell, the velocity of the user, trajectory to lighter payload compared to LTE [91], it may be difficult to distance or dwell time within the cell, and the interference and perform seamless handoff because a traditional WiFi network transmission frequency offered by the BS. Also, the handoff not only has a narrow communication coverage but also gives a skipping decisions can be based on the traffic load conditions relatively long handoff time [92]. Traditional handoff decision of various consecutive BSs on the user’s trajectory as well as algorithms typically assume that the coverage of each BS the velocity patterns of nearby users. It was shown that handoff is the same, which does not apply to drone networks with skipping strategies are an effective way to minimize handoff different size, weight, and power (SWAP) constraints and rates while improving the QoS requirements of the users and altitudes in the three-dimensional (3-D) space [93]. Based on this way achieving a balance between the two [86], [87], [18]. the information of the received signal strength (RSS), drones 17 can potentially adjust their speed and height as well as distance G. Mobility-Aware Caching from other drones. With the increase in mobile traffic and repeated content requests, caching at the BSs becomes important to reduce E. Mobility in Software-Defined Cellular Networks the excessive backhaul load and delay, particularly for on- Mobility management has evolved significantly from man- demand video-streaming applications. Generally, it is assumed aging single-RAT to multi-RAT networks. Nevertheless, net- that the user can download the entire requested content through work slicing in 5G will bring mobility related challenges due the connected BSs. However, it is noteworthy that the user to heterogeneity in the characteristics, latency, and reliability mobility in such a scenario makes the contact duration between requirements of various slices. Ultra-reliable and low latency user and BSs random which directly impacts the cache hit and communication (uRLLC) slice, Internet-of-things (IoT) slice miss probabilities. Subsequently, the content placement and and enhanced mobile broadband (eMBB) slices are three the content delivery strategy should take mobility into account. main categories of network slicing in 5G. For example, in A few recent works have has addressed this issue [94]. uRLLC slicing, communication devices are more sensitive to time delay and require lower transmission rate than those in H. Data-Driven Learning Models for Mobility-Aware Analysis other slices. Communication requirements in air planes or high-speed trains are expected to trigger significant handoffs For a dense, multi-tier, and heterogeneous 5G/B5G network, compared to IoT slices with static or nearly static devices. in some scenarios, it may not be possible to accurately model Therefore, the handoff procedure may change significantly the mobility of users/devices to analyze system metrics such among various network slices. Note that, traditionally handoffs as the handoff rate, cell sojourn time, mobility-aware coverage are event-triggered. However, in network slicing-based 5G net- and rate. In these scenarios, data-driven machine learning mod- works, flexible handoff criteria and adaptive handoff thresholds els [88], [89] such as the deep neural networks (DNNs) may are needed to support mobility management in SDN. Multi- serve as an important tool to predict the system parameters RAT coordination may also be exploited among different and network performance. The essence of data-driven machine RATs to share location information of their respective mobile learning is, a pattern exists in the system behavior which can- devices. [83] analyzed the negative impact of user mobility in not be pinned down mathematically. However, data is available dense multi-tier cellular networks and the concept of Phantom and the system behavior can be learnt (or predicted) from the small BSs (split control and data plane architecture) has been input data set by analyzing the data. Deep learning (DL) is a advocated to mitigate such negative impact. Furthermore, the branch of machine learning and a DNN is a neural network handoff delay due to handoff related signaling can be tackled (NN)-based DL architecture consisting of the input and output using SDN paradigm. For example, a mobile node that exists layers and many hidden layers of neurons, which can perform in one of the BSs may have a number of neighboring BSs non-linear functions. The neurons in a hidden layer are fully- and thus have finite transition probability associated with each connected and weights are assigned to various neurons. The neighboring BS. The controller can utilize the automatic neigh- auto-encoder NN, convolutional NN, and recurrent NN are bor relation (ANR) function of the BSs. With the neighbor most common types of DNNs. A DNN is trained by a subset removal and detection functions of the ANR, the neighbor of available data called the training set and then tested by relation tables and transition probabilities can be constructed. using another set of data called the test data. A DNN can be used to learn the mobility patterns of network nodes, and F. Mobility-Aware C/U Plane Splitting based on this, network performance metrics can be predicted. 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