Coordinated load balancing, handoff/cell-site selection ... - CiteSeerX

Wireless Netw DOI 10.1007/s11276-006-8533-7

Coordinated load balancing, handoff/cell-site selection, and scheduling in multi-cell packet data systems Aimin Sang · Xiaodong Wang · Mohammad Madihian · Richard D. Gitlin

Published online: 9 June 2006 C Springer Science + Business Media, LLC 2006 

Abstract We investigate a wireless system of multiple cells, each having a downlink shared channel in support of highspeed packet data services. In practice, such a system consists of hierarchically organized entities including a central server, Base Stations (BSs), and Mobile Stations (MSs). Our goal is to improve global resource utilization and reduce regional congestion given asymmetric arrivals and departures of mobile users, a goal requiring load balancing among multiple cells. For this purpose, we propose a scalable cross-layer framework to coordinate packet-level scheduling, call-level cell-site selection and handoff, and system-level cell coverage based on load, throughput, and channel measurements. In this framework, an opportunistic scheduling algorithm—the weighted Alpha-Rule—exploits the gain of multiuser diversity in each cell independently, trading aggregate (mean) downlink throughput for fairness and minimum rate guarantees among MSs. Each MS adapts to its channel dynamics and the load fluctuations in neighboring cells, in accordance with MSs’ mobility or their arrival and departure, by initiating load-aware handoff and cell-site selection. The central server adjusts schedulers of all cells to coordinate their coverage by prompting cell breathing or distributed MS handoffs. Across the whole system, BSs and MSs constantly monitor their load, throughput, or channel quality in order to facilitate the overall system coordination. Our specific contributions in such a framework are highlighted by the minimum-rate guaranteed weighted Alpha-Rule scheduling, the load-aware MS handoff/cell-site selection, and the Media Access Control (MAC)-layer cell breathing. Our evaluations show that the proposed framework A. Sang () · X. Wang · M. Madihian · R.D. Gitlin NEC Laboratories America, 4 Independence Way, Princeton, NJ 08540, USA e-mail: [email protected]

can improve global resource utilization and load balancing, resulting in a smaller blocking rate of MS arrivals without extra resources while the aggregate throughput remains roughly the same or improved at the hot-spots. Our simulation tests also show that the coordinated system is robust to dynamic load fluctuations and is scalable to both the system dimension and the size of MS population. Keywords Cellular · Scheduling · Load balancing · Handoff · Cell-site selection

1. Introduction 1.1. Motivation Recently much attention has been devoted to opportunistic downlink scheduling algorithms [1, 2, 3, 4, 5, 6, 7] that exploit the asynchronous peaks of fading channels of multiple Mobile Stations (MSs) in a single cell. A time-slotted downlink shared data channel, together with the associated signaling and control channels, supports those MSs for the highspeed downlink packet access. Two major commercial systems employ such a channel architecture. One is Qualcomm’s High Data Rate (HDR) system [8] which is based on the techniques of cdma2000 [9]. The other is the High Speed Data Packet Access (HSDPA) which is based on the WCDMA systems [10]. In those systems, the proposed scheduling algorithms work independently in individual cells given certain constraints on long-term intra-cell resource sharing [2, 3, 5, 7] or minimum rate (minRate) requirements [4, 6] of MSs. However, to our best knowledge, few studies (see [11] and references therein) are devoted to such systems in a multi-cell environment, where inter-cell interference and asymmetric Springer

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traffic arrival may be the major hinderance to good resource utilization and high system scalability. Take such a multi-cell system for example, where a TimeDivision-Multiplex (TDM)-based channel is shared by users (i.e., MSs) in each cell. At each time slot the Base Station (BS) in a cell may exclusively select only one user for data transmission according to certain intra-cell opportunistic scheduling rule. All of the transmission power left by dedicated-channel handling is devoted to the selected user. Each user can only be served by at most one BS at any time.1 In doing so the system avoids intra-cell interference to a very large extent, but it precludes the commonly used loadbalancing techniques, such as power control and soft handoff, as in circuit-switched cellular systems [12, 13, 15] (see Section 1.2). Thus the current packet data cellular systems rely heavily on isolated intra-cell schedulers to provide user satisfaction, i.e., Quality of Service (QoS) guarantee for MSs, as well as high throughput. The isolation creates high local congestion and low global resource utilization across multiple cells. Therefore, it is not clear how existing multi-cell systems perform given asymmetric load oscillation in practice. In this paper, we characterize the global system performance using several major metrics. The first and the most important metric is the maximum number of satisfied users the system can accommodate, i.e., the blocking rate of MS arrivals under long-term minRate guarantee for each; The second metric is the downlink throughput of the whole system or around the cells at hot-spots. Yet another metric, the load symmetry across multiple cells given asymmetric input, characterizes load balancing and resource utilization efficiency. Based on those performance metrics we propose a crosslayer coordination framework incorporating entities such as MSs, BSs, and a central server, e.g., the Radio Network Controller (RNC) in WCDMA systems. This framework involves packet-level scheduling, call-level MS handoff or cell-site selection, and system-level cell coverage tuning. We can formulate the global system performance into a utility maximization problem that requires iterative (channel/slot) assignments for the optimal solution. In our solution, the system entities actively interact with each other to increase resource utilization and reduce congestion in the system. Each entity adapts to its real-time dynamics measured at different time scales: MSs react to the channel states and throughput, BSs to the multiuser diversity and load fluctuations, and the central server to the load imbalance across neighboring cells. Our ultimate goal with this framework is to meet the user-centric service expectations for intra-cell resource fairness and minRate guarantee, and to maximize the service 1

This does not prohibit an MS from communicating with multiple BSs simultaneously through dedicated signaling or common pilot control channels.

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provider’s revenue by accommodating more “satisfied” users into the system. In particular, we propose an opportunistic downlink scheduling algorithm, named the weighted Alpha-Rule, to provide high aggregate throughput and tunable resource fairness among users within each cell. To leverage the asymmetric traffic loading across the whole system, we propose a Medium Access Control (MAC)-layer “cell breathing” to coordinate the scheduling or the coverage of MSs in neighboring cells. We also propose a load-aware handoff and cellsite selection scheme for individual MSs to proactively avoid hot-spots and locate a good service sites. Note that the traditional schemes only consider the physical-layer radio closeness, and cause local congestion and asymmetric blocking of MSs across multiple cells. Extensive experiments show the advantages of our schemes over the legacy schemes: our schemes enable the multi-cell system to accommodate more satisfied users, to reduce regional congestions, and to leverage asymmetric load dynamics among neighboring cells.

1.2. Background There is not much work focusing on multi-cell issues in cellular systems of high-speed downlink shared channels. In earlier CDMA systems of dedicated (voice) channels only, intercell interference mitigation and load balancing resorts to the coupled power-control and cell site selection (e.g., [12, 13]), which may not be directly applicable in high-speed shared channel systems, where fast power control is replaced by rate adaption. As mentioned in [11, 12], another approach manipulates the power level of the common pilot channel: The level is advertised as lower than the actual in congested cells. Thus MSs will switch to other cells in search for “stronger” channels, and therefore the load becomes more balanced. This approach is adopted in Qualcomm’s systems [14] and is applicable in our case too. However, such a manipulation conflicts with the desire by MSs for an accurate and stable pilot power, e.g., to accurately estimate the channel states and to support adaptive modulation and coding. In contrast, our load-aware handoff/cell-site selection scheme and our MAC-layer cell breathing, which originated from the physical-layer cell breathing in [12], both achieve load balancing effect without power control. Other related work in this field focuses on (dedicated) channels borrowing from lightly-loaded cells, or retrying of admission requests by newly arrived MSs [15, 16, 17, 18], which are either inapplicable here or orthogonal to our efforts. This paper is organized as follows. Section 2 introduces the multi-cell packet data system and its performance metrics. Section 3 introduces the key networking entities in the framework of our coordinated system. Section 4 describes in detail the intra- and inter-cell mechanisms in such a

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system. Section 5 evaluates the performance under stationary or dynamic traffic loading. Section 6 summarizes related work and considers certain practical issues including parameter setup. Section 7 concludes the paper.

guarantee over certain time scale, i.e., the exponential life time of MSs (with a mean of 20s) in our simulations. From the customers’ point of view, the QoS (minRate) guarantee over certain period is expected in exchange for a flat-rate charging. On the other hand, from the service providers’ point of view, the more satisfied users the system can accommodate, the more revenue it may generate. Therefore, the users’ blocking rate or the maximum number of satisfied users reflects how good resource utilization and revenue can be. The second important metric is the aggregate (mean) downlink throughput. Later we will see that limited to geographic distributions of MSs and their received signal strength, more satisfied users may not always mean a higher aggregate throughput in such systems. Finally, the third metric is characterized by the load (a)symmetry across multiple cells given asymmetric load inputs, which shows to what extent a load balancing scheme may mitigate regional congestions.

2. A Multi-cell system for high-speed packet data services 2.1. System model Refer to Fig. 1(a) for a 3-tier hexagonal cellular system, where ρt = λμt denotes the traffic intensity at tier t, while the central cell (of ID 0) is defined as tier 0. λt is the Poisson arrival rate of MSs in any cell at tier t. μ1 is the exponential lifetime of each arrived MS. There is a unique BS within each cell. So we may use the term “cell” and “BS” interchangeably. In each cell, the initial positions of MS arrivals are uniformly distributed in the hexagonal domain. All MSs remain static after arrival. However, given the arrival (ON) and departure (OFF) of MSs, we create similar scenarios as in a mobile system. Note this static setup is only for the simplicity of study, while our proposed schemes work the same in more practical mobile scenarios. Each MS after arrival will be associated to exactly one serving cell at any time, while each cell has only one BS at the center. At each time slot, the BS can schedule only one associated MS to access the high-speed downlink shared channel, e.g., the HS-DSCH channel in WCDMA systems. Assume cells have identical resources but possibly different control parameters and asymmetric MS arrivals. Thus certain cells may become congested while others remain underloaded, naturally causing high blocking in some cells and low resource utilization in others. Three metrics decide the performance of such a system. Firstly, the number of “satisfied” users, or users’ blocking rate from another point of view, should be the most important metric. The users’ satisfaction is defined by the minRate

Fig. 1 A multi-cell system model: (a) three-tier of hexagonal cells: MS arrival intensity is ρi for a cell at tier i, i = 0, 1, 2, (b) inter-cell channel interference with path loss model

ρ0

2.2. Link model Take a look at Fig. 1(b). Each cell is a hexagon which can be circumscribed by a circle of radius D, i.e., the distance from the central BS to the apex of the hexagon is D. Assume there are N cells and the complete active MS set is K(t) = {1, . . . , K } at time t. Each cell i, ∀i ∈ {1, . . . , N }, serves a non-overlapping set of active MSs at time t, denoted Ki (t) = {1, . . . , K i (t)}. We take into account the path loss factor, the fast Rayleigh fading, and the slow log-normal shadow fading in modelling the received downlink signal and the path gain. Then the received signal at user k is:  yk (t) = +

N  j=1, j=i

D di,k 

γ si,k (t)h i,k (t)xi,k (t)

P j,k c



D d j,k

γ

s j,k (t)h j,k (t)x j,k (t) + n(t),

MS k

9 8

10 3 12

1 0

4 13

d jk 7

2

11

d ik

18 6

Cell j

D

17

5 14

ρ1

 Pi,k c

16 15

(a)

ρ2

Cell i (b)

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where

r xi,k (t) is the desired signal from the serving cell (or BS) i r

with transmission power Pi,k ; x j,k (t) is the interfering signal from non-serving cells with transmission power P j,k . n(t) is the complex additive Gaussian white noise (AGWN) 2 with  0 and variance σn .  mean

rc

r

r

γ

D d j,k

denotes the propagation loss of the transmission power, where d j,k is the line-of-sight (LOS) distance from BS j to user k, γ is the path loss exponent and ranges from 2 to 6 for most indoor and outdoor environment, c is the constant median of the mean path gain at d j,k = D. h j,k (t) is the fast Rayleigh fading, characterizing the multipath scattering from BS j to user k. It is represented by (the amplitude of) a zero-mean unit-variance complex Gaussian random variable. s j,k (t) corresponds to the large time-scale log-normal fads (t) ing. 10 log10j,k is a zero-mean Gaussian random variable with variance  σs2 in dB. The large time-scale autocorrelation function s j,k (t) as defined in [20] usually depends on the user mobility [21].

Assume that all BSs have the same transmission power and consider both inter- and intra-cell interference in the system. We can write the instantaneous signal-to-interference-andnoise-ratio (SINR) for user k given its desired signals from BS i as:  

Si,k (t) =

D di,k

γ

si,k (t)|h i,k (t)|2 N (t)

,

where  N (t) = φ +

D di,k

Central controller Li(t)

αi

αj

Lj(t)

Active BSj

Serving BSi

rik(t)

E[Ki(t)] MSk

Central controller

E[Kj(t)]

~ Tik (t)

Handoff for: • mobility • load balancing

Active BSi

Serving BSj

rjk(t) E[Kj(t)]

E[Ki(t)] MSk

~ Tjk (t)

~ T (t) : mean throughput. L(t): current load in the cell.

r(t) : supportable rate α : scheduling parameter. E[K(t)]: mean num. of MSs.

Fig. 2 Coordinated system entities in a hierarchy: load-aware handoff and signaling/measurement parameters

serving BS (or cell) i to a new cell j in its active set. By our definition, each MS, once admitted and thus presumably “satisfiable,” remains active or ON all through its lifetime. For each MS we assume an infinite data backlog at the serving cell. To improve the system performance we propose measurement-based distributed coordination schemes among those entities. In our design, newly arrived MSs are aided by system-level loading information to avoid selecting the closest-radio BS which may actually be a hot-spot. Later they may proactively switch over to “better” cells based on online service measurement and load fluctuations. Furthermore, the central controller coordinates cells’ coverage across the whole system based on periodically collected loading reports from BSs or cells. Please refer to Fig. 2 (the bottom part) for a definition list of important parameters. 3.1. Mobile stations

γ si,k (t)|h i,k (t)|2

  N  D γ s j,k (t)|h j,k (t)|2 + σn2 . d j,k j=1, j=i

φ is the orthogonality factor characterizing intra-cell interference. Correspondingly, the instantaneous supportable channel rate is: ri,k (t) = B log (1 + Si,k (t)), ∀k and ∀i,

(1)

where B is the bandwidth in Hertz.

Through initial signaling and the measurement of pilot signal strength, a newly arrived MS k learns from each BS not only its channel strength but also the number of active users in the corresponding cell. Based on the information MS k may select an optimal serving BS i from its active set of BSs, denoted Bk . Once admitted into the cell i, MS k remains active for an exponential lifetime during which it constantly measures its mean throughput Ti,k (t). A measured degradation of throughput may trigger the MS to make load-aware handoff. The mean throughput is measured as follows:   1 ˜ 1  ˜ Ti,k (t) = 1 − Ti,k (t − 1) + ri,k (t)Ii,k (t), tc tc

(2)

3. Measurement-based system coordination Figure 2 illustrates the logical modules and key networking entities in the multi-cell system of a hierarchical architecture, where an active MS k is switching over from its original Springer

where tc might be set as 1000 time slots, say, to get both a stable estimation and an acceptable delay; ri,k (t) as defined in (1) refers to the instantaneous channel rate measured by MS k based on the pilot signal from BS i; Ii,k (t) = 1

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indicates actual data transmission from k to i at time t, and 0 otherwise. MS k constantly measures the strength of signals from each BSs in Bk , but it feeds back ri,k (t) only to the serving BS i. This reduces the signaling overhead and facilitates the opportunistic scheduling at i with downlink channel information.

k ∈ K = {1, . . . , K }. An MS can not be assigned to two cells simultaneously, i.e., it can receive services from at most one BS at any moment. The optimal assignment proceeds with time, aiming to maximize the long-term revenue R(t) =

At each time slot, the BS in each cell schedules one and only one associated MS for data transmission. Refer to Fig. 2, where k can only be scheduled by its serving BS (either i or j) exclusively. In our scheme, each BS (i, say) maintains a complete list of MSs, Ki (t) = {1, . . . , K i (t)}, which are receiving services from this BS. Each BS i broadcasts E[K i (t)], the mean number of its associated MSs, to all MSs through a control channel, which notifies the MSs about the loading situation in this cell. Each BS i periodically reports its mean load E[L i (t)] to the central controller, which is defined [11] and measured as follows: E[L i (t)] =

 k∈Ki (t)

 mk mk ≈ , E[ri,k (t)] k∈K (t) r˜i,k (t)

Uk (Tk (t)) ,

(4)

k=1

3.2. Base stations and the central controller



K 

where Uk (·) is a concave non-decreasing utility function of the mean throughput Tk (t) of MS k up to time t. Note that the utility function has been widely used to represent system revenue, being a concave non-decreasing function of userreceived services [22]. Therefore, in consideration of HDR systems’ causality, i.e., only past scheduling decisions and throughput are known, and one-step channel prediction, i.e., ri,k (t)’s are assumed known as constants at the beginning of time slot t, our goal is to find optimal MS-BS matchings that maximize R(t) at current time t. Define an assignment indicator variable Ii,k (t) =

(3)

1, k-th MS is assigned to BS i at time t, 0, otherwise.

i

where the user set Ki (t) denotes the active MSs being covered by cell i; m k kbps is the average minRate requirement  of MS k; r˜i,k (t) = (1 − t1c )˜ri,k (t − 1) + t1c ri,k (t) is the measurement of E[ri,k (t)], i.e., the mean channel rate between MS k and BS i. Under proper admission control, the accommodated load within each cell should not exceed the full capacity 1. For scalability of our scheme, the central controller controls only BSs instead of each specific MSs. It balances the loads among neighboring cells by tuning the coverage of neighboring cells based on the reports of loads from all cells: heavily loaded cells should shrink while neighboring cells expand, which is controlled through a scheduling parameter αi within each cell i (described later). A shrinking cell i impacts the throughput Ti,k (t) of each MS k under its coverage, and thus triggers k’s load-aware handoff indirectly. This procedure is later named MAC-layer cell breathing.

4. Coordinated handoff/cell-site selection, load balancing, and scheduling

At any time t, the non-zero decision set is a vector of indicator: I(t) = {Ii,k (t), i = 1, . . . , N , k = 1, . . . , K }, which denotes a one-to-one matching between a BS i and an MS k. Note I(t) is only one of the whole solution set I = {1, 2, . . . , K } N . At the beginning of t-th time slot, the optimization problem is thus formulated as an assignment problem 2 : max R(t) = I (t) s.t.

N 

K 

Uk (Tk (I(t))) ,

(5)

Ii,k (t) ≤ 1, ∀k = 1, . . . , K ,

(6)

Ii,k (t) ≤ 1, ∀i = 1, . . . , N .

(7)

k=1

i=1 K  k=1

With ergodic assumption, the long-term mean throughput of MS k by the end of t-th slot is 

Tk (I(t)) = Tk (t) =

N t  1 ri,k (τ )Ii,k (τ ). t τ =1 i=1

(8)

4.1. A utility-based system optimization Now let us describe the multi-cell system from the point of view of network economy. Given N base stations and K mobile stations, ideally at each time slot the system would assign to each BS i only one MS k, where i ∈ N = {1, . . . , N },

2

Note: Our formulation is pursuing a myopic optimization on a slotby-slot basis. It reflects practical requirement of causality and realtime decision making given one-step channel prediction. Whether such an optimization necessarily reaches the optimal long-run throughputs requires more profound studies [27, 28, 29, 30, 31].

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In this formulation, (6) as an inter-cell constraint says that at any time t, each user k can be associated (usually over a sustained period) with at most one BS i, i.e., no soft handoff or macro-diversity. Another constraint (7) as an intra-cell constraint says that at any time t, each BS i, if associated with a non-empty user set, can pick one and only one associated user k due to TDM-based channel access within each cell; otherwise i has to stay idle. Finally, by the system causality and one-step channel prediction, the mean throughput Tk (t) defined in (8) depends only on the past and current decision factor Ii,k (τ ) (∀τ ≤ t). Assume the size of each time slot t is small. For a concave and non-decreasing utility function, the optimal assignment I ∗ (t) at time t may proceed slot-by-slot along the steepest gradient ascent, as in the domain of continuous time. This assignment problem requires a maximum-weight 0-1 perfect matching between the BS set and the MS set: I ∗ (t) = arg max I (t)∈I

N K   ∂Uk (Tk (t)) k=1 i=1

∂ Tk

ri,k (t)Ii,k (t).

(9)

For each matching (i, k), the nonnegative weight is ∂Uk (Tk (t)) ri,k (t). Note that each feasible matching I(t) follows ∂ Tk the constraints (6) and (7). The optimal matching I ∗ (t) can be approximated by the Hungarian Method [23] in a polynomial time, while an exhaustive search takes O(K N ) steps in the worst case.3 The formulation (5) logically considers all the feasible assignments I(t) ∈ I. Therefore, the optimal assignment I ∗ (t) reflects the most efficient assignment, or resource allocation, of the whole system. Hence, it has an inherent load balancing effect. However, to find I ∗ (t) requires the global knowledge of the system: the instantaneous channel ri,k (t) between any BS-MS pairs (i, k) at time t; and the past mean throughput Tk (t − 1) of all MS k. In addition, the optimization is centrally computed at each time slot, which is not practical in multi-cell systems. Therefore, in spite of being ideal, this formulation (5) is too complicated, if feasible at all, to realize in practice. 4.2. A localized, distributed approximation

individual MS, or BS, or the central controller. All the three stages aim to maximize the system utility from a specific perspective, controlled by different system entities, and they jointly approximate the global optimization. In practice, each user k sojourns at a unique cell i for certain stable period during which the association or longterm matching of BS-MS (i, k) is known as fixed, i.e., k stays with i rather than switches over to another cell. Suppose during the most recent sojourn period, MS k is associated to cell i for downlink services.

r Stage 1: Every th period, say, th = 1 s or 600 slots in HDR, all MSs periodically check their long-term matching relationship asynchronously and independently. Suppose at time t, MS k is scheduled to check whether switch-over from cell i to j ∗ (t) increases the system utility. If yes, k’s long-term matching partner is changed to j ∗ (t); otherwise, k continues to sojourn in cell i. From BSs’ perspective, at any moment the user set K is partitioned into N nonoverlapping subsets, each associated to a different BS i: Ki (t) = {0, 1, . . . , K i (t)}, i = 1, . . . , N . r Stage 2: At any time t, given Ki (t) from Stage 1, each cell i optimizes its utility locally and independently, i.e., the (5) is optimized with k ∈ Ki (t), N = 1, and without intercell constraint (6). Essentially at this time slot, each BS i schedules a unique MS out of Ki (t) for data transmission. r Stage 3: Every tl period, say tl = 10 s, the central controller periodically adjusts the long-term partitioning of K into Ki (t), i.e., it adjusts each cell’s coverage of MSs based on global loading information. This iteratively impacts Stages 1 and 2, and thus the global utility. Stage 1 is periodically triggered by individual MSs over a small timescale th and in a distributed manner. It relates to the handoff and cell-site selection upon MS arrival/departure (ON/OFF) or when MS crosses cell “boundaries”. Stage 2 is the real-time intra-cell scheduling in each cell. Stage 3 refers to a centralized system optimization periodically triggered by the central controller over a large timescale tl . 4.3. Load-aware handoff/cell-site selection: a distributed load balancing algorithm

To overcome the problem, we divide the global centralized optimization issue into a 3-stage distributed and/or localized optimization issue. Each optimization stage is done by either

First let us focus on Stage 1. The most popular method of cell-site selection and handoff is based on the shortest radio distance or the strongest channel. For example, a newly arrived MS k selects the serving BS as follows:

3

i ∗ (t) = arg max{E[Si,k (t)]},

The above formulation omits the minRate requirement or the constraint of Tk ≥ m k that can be reliably checked only by the end of k’s lifetime. Thus it would transform the problem of step-by-step, 0-1 assignment into a problem of dynamic programming. For simplicity and feasibility, we drop this constraint from the assignment, and count on admission control and weight design schemes instead. Please refer to [32] for further studies.

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i∈Bk

(10)

 where E[Si,k (t)] is estimated by S˜i,k (t) = (1 − t1c ) S˜i,k (t − 1) + t1c Si,k (t). We refer to this SINR based Cell-Site Selection (CSS) scheme as SINR-CSS, a distributed but purely

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physical-layer scheme. Note that E[Si,k (t)] can be replaced by E[ri,k (t)] due to Shannon rate (10). Obviously, Ti,k (t) differs from E[ri,k (t)]: E[ri,k (t)] is the throughput assuming i is the only user in cell i; Ti,k (t) is the throughput of MS k achieved/predicted by competing against other MSs in the subset Ki (t) for channel access. Therefore, SINR-CSS does not necessarily optimize utility (5) or the measured/predicted throughput Ti,k (t) because the strongestchannel cell might be the most crowded cell too. In contrast, Ti,k (t) reflects not only the physical-layer channel strength, as E[Si,k (t)] does, but also the MAC-layer scheduling rule as well as the time-varying Ki (t) due to MS ON/OFF or mobility. In light of the above, we derive a cross-layer distributed scheme based on utility maximization: a new MS k selects the serving site i in order to maximize the net increment of utility in a long run, estimated by this MS as follows: i ∗ (t) = arg max{ R(t)}, i

where R(t) = Uk (Ti,k (t))  − [Ul (Ti,l (t − 1)) − Ul (Ti,l (t))].

(11)

l∈Ki (t)

Note that MS k is competing for the shared channel resources against existing MSs in Ki (t), resulting in a smaller Ul (Ti,l (t)) because Ti,l (t) becomes smaller than Ti,l (t − 1). 4 Considering the decreasing margin of a concave U (·) and especially a usually large population K i (t) in cell i, we may omit the second term in (11), i.e., neglect the impact of k on the aggregate utility, and thus get i ∗ (t) = arg maxi {Uk (Ti,k (t))}. However, Ti,k (t) is unknown because k is a new user to i. Thus by estimation k may adopt a distributed Load-Aware Cell-Site Selection (LA-CSS): i ∗ (t) = arg max i∈Bk



 E[ri,k (t)] , E[K i (t)] + 1

(12)

where Bk is the active set of cells; E[K i (t)] is the mean population size in cell i, constantly measured by BS i and advertised to k through a signaling channel; E[ri,k (t)] is measured E[ri,k (t)] is the by k from pilot signals as illustrated in Fig. 2; E[K i (t)]+1 throughput Ti,k (t) predicted by MS k. Thus, LA-CSS allows new MSs to avoid “hot-spot” cells, and implicitly balances asymmetric load across neighboring cells in a distributed manner.

4

The addition of a new MS k has a long-term impact on resource sharing and Ti,l (t), which potentially persists for a whole remaining life of active MSs. So the timescale of (11) is actually much larger than a single time slot.

Following the same logic, each active MS k may adopt the following scheme named as Load-Aware Handoff (LA-HO):

∗

E[r j,k (t)] | ∀ j ∈ Bk , E[K j (t)] + 1

 E[ri,k (t)] ˜ T j,k (t) > max , Ti,k (t) , (13) E[K i (t)]

j (t) = arg max T j,k (t) ≈ j∈Bk

where E[K i (t)] and E[K j (t)] are broadcast to k by BS i and j, respectively, according to Section 3.2; T˜i,k (t) is measured by k in (8). This scheme says that a switch-over from serving BS i to j ∗ (t) is triggered by load changes, i.e., when MS k measures a significant throughput T˜i,k (t) reduction in cell i, E[r (t)] or when k predicts a higher throughput E[K jj,k(t)]+1 by joining another cell j. Both scenarios may arise when k crosses cell boundaries, when cell i experiences a MAC-layer scheduling disruptions, or when i (its neighbor j) sees population variations in E[K i (t)] (E[K j (t)]) due to MS mobility or MS arrival and departure. Both LA-CSS and LA-HO consider physical-layer channel fluctuations and throughput changes due to user mobility or random ON/OFF within the system. Thus both achieve an inE[ri,k (t)] herent load balancing effect. In (12) and (13), E[K and i (t)]+1 E[ri,k (t)] estimate per-user throughput under the assumption E[K i (t)] of equal sharing of time slots among all users. 5 Note that this estimation tends to be conservative for lack of multiuser diversity gain. Therefore, the actually measured throughput T˜i,k (t) acts as a calibration of the estimation. 6 On the other E[r (t)] hand, E[K jj,k(t)]+1 is the throughput T j,k (t) in cell j predicted by k before the actual handoff. The factor E[K j (t)] + 1 considers the addition of the new MS (k) into cell j. In LA-HO, MS k’s handoff requests may be rejected by the target cell j ∗ (t) due to j ∗ (t)’s heavy load or local policy. If it is only a “soft” request for k to pursue higher throughput, the rejected k may try other cells sorted in a decreasing order of T˜ j,k (t), or may stay with i. In this case, LA-HO does not incur any performance penalty. Clearly, just like SINR-HO, LAHO also has the same functionality of handling forced handoffs when user’s physical channel deteriorates below certain level. This happens with MSs passing through cell boundaries, where the degraded throughput of k from its serving cell i, as found by k’s LA-HO mechanism,is mainly due to mobility-incurred channel weakening.

5 The weighted Alpha-Rule introduced later was studied in detail in [24]. It achieves resource fairness when α = 1, when it is identical to the weighted version of Proportional Fairness [2, 5]. 6 According to weighted Alpha-Rule scheduling, T˜i,k (t) may be smaller i,k (t)] (when α  1) or larger (when α ≈ 1) than E[r for users at cell E[K i (t)] E[ri,k (t)] ˜ boundary. max{ E[K i (t)] , Ti,k (t)} as in (13) raises the handoff threshold, and thus avoids the Ping-Pong phenomenon, i.e., frequent handoffs back and forth.

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4.4. Call (MS) admission control In Stage 1, an admission control algorithm is necessary in order to check minRate requests against resource availability. It is done by each BS independently to decide whether a new MS arrival or an MS handoff can be accepted into the cell. For simplicity, we only consider the case when call (i.e., MS) admission control (CAC) algorithm treats handoff requests and new arrivals equally. For simplicity we adopt the same measurement-based CAC scheme as in [11]. More refined algorithms on admission control (e.g., [17, 16]) may be used. In [11], a cell i accepts a newly arrived or a switched-over MS l if and only if:  ∀k∈Ki (t)

mk ml + < 1, E[ri,k (t)] E[ri,l (t)]

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where m k and m l denote the long-term minRate requirement in kbps by MS k and l, respectively; E[ri,k (t)] and E[ri,l (t)] are measured by BS i based on channel feedback. The CAC says that the aggregated per-user load after accepting l should not exceed the “full” capacity. This scheme is conservative for lack of multiuser diversity in the definition of per-user load E[rmi,kk(t)] , and it does not provide fair admissions for location-dependent users. In our study, if l is a newly arrived MS and is rejected, the rejection will be counted into the blocking rate of cell i and the whole system, respectively. For aforementioned reason, a rejected LA-HO “soft” request is not part of the blocking rate. 4.5. Weighted alpha-rule: an opportunistic downlink scheduling algorithm Now refer to Stage 2 in Section 4.2. In each cell, an opportunistic downlink scheduler runs independently to pick an associated MS for each time slot. In our scheme, schedulers in different cells are correlated only through central controller in Stage 3. As stated before, each scheduler is solving the intra-cell assignment problem (5) with N = 1 and given the non-overlapping per-cell coverage Ki (t) = {0, 1, . . . , K i (t)}, i = 1, . . . , N . The algorithm depends on the concrete form of the utility function, which by definition should be a concave and non-decreasing function of per-user mean throughput, and which integrates the long-term fairness requirement. Inspired by [26], we adopt a generic form of utility function for best effort services as follows: Uk (Tk (t)) = wk

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which represents the (w, α)-proportional fairness criterion [26] in the terminology of Internet bandwidth sharing Springer

over fixed-capacity links. For multiple users accessing a shared radio link, as we will see below, such a utility function enables a flexible tradeoff between resource fairness and aggregate throughput. In other words, the value of α controls the resource allocation among MSs far or close to the cell site. Given α(≥0), per-user weight wk (>0), and cell coverage Ki (t), and under the causality constraint, the total utility of any cell i, which is defined by Ri (t) =



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i,k (t) 1, if k = arg maxk∈{Ki (t)} wk Tkr(t−1) α ,

0, otherwise.

Please refer to [24, 25] for a simple, gradient-ascent based justification. Note Tk (t) by default refers to Ti,k (t) when MS k is associated to cell i. By weighted Alpha-Rule, each BS i schedules the following MS at the t th slot: ki∗ (t)

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where Ti,k (t − 1) is estimated as T˜i,k (t − 1) in (8). In this paper, α is limited to [0, 1]. By [24], α is a flexible control knob for location-dependent resource allocation, featuring the flexible tradeoff between per-user fairness and aggregate throughput in each cell: When α goes to 0, the scheduler favors central MSs with stronger channels than towards boundary MSs, as the max-C/I scheme [1] does; When α goes to 1 and assume all wk ’s are identical, the scheduler tends to allocate time slots equally among all MSs, i.e., it works like M-LWDF [4] or Proportional Fairness [5, 2] algorithms. The aggregate throughput becomes smaller given a larger α. 7 Below we will see that the above feature derives the MAC-layer cell breathing given multiple neighboring cells. To support the minRate m k of user k, we follow M-LWDF algorithm [4]: We define wk in (15) as the t-moment depth of a token bucket; the token arrival rate is m k and the leaking rate is the actual throughput ri,k (t)Ii,k (t). As M-LWDF does, we assume that all MSs have the same delay tolerance. With a separation of timescale, where wk is assumed stable over Irrelevant here, α can be larger than 1 [24], but then it compromises the aggregate throughput even more. When αi goes to +∞ the Alpha-Rule achieves max-min fairness or equal per-user throughput.

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small timescales, the above optimization still holds. Note that M-LWDF is only an intra-cell scheduling scheme. It does not consider handoff/cell-site selection, nor does it support intercell load balancing.

gather at different cells, e.g., offices, restaurants, and shopping centers, at different times of a day.

4.6. MAC-layer cell breathing: an explicit, centralized control of cell coverage

To test the performance of such a system, we consider three cases. One is the static case given a single HDR cell, where a fixed number of users are uniformly distributed within the hexagonal range. We will see the performance of weighted Alpha-Rule under the constraint of minRate requirement. Then we will repeat the test for the second case, where MSs are dynamically arriving and departing at/from uniformly distributed locations. Note that call admission control is needed in this case to provide minRate guarantees. In the third case we will examine a multi-cell HDR system with fixed or dynamic ρi (traffic intensity). Note that the uniformly distributed MS locations within each cell represent a pessimistic or conservative scenario for assessing the gains of load balancing, whose effects would be more prominent given more MSs at cell boundaries. For the third case, we define a trio of (MAC-CB, LA-CSS, LA-HO) to differentiate the legacy scheme and ours. Any component in the trio may be ON (1) or OFF (0). Note that LA-CSS or LA-HO equal to 0 implies the SINRbased cell-site selection (SINR-CSS) or SINR-based handoff (SINR-HO), respectively, while SINR-based handoff means no handoff since all MSs are geographically fixed in our simulation tests. In each of the tests, all MSs have the same minRate.

Now focus on Stage 2 in Section 4.2. With periodic load reports from BSs, the central controller learns the global system status. Periodically, say, every tl = 10 s, it issues commands to individual BSs to adjust their α among neighboring cells. When the central controller senses that cell i is more congested than its neighbors, denoted Ni , it asks i to reduce αi . By the Alpha-Rule, cell i with smaller αi allocates less time slots to the MSs under its coverage Ki (t) but located at cell boundary. Therefore, a boundary MS k will find its throughput T˜i,k (t)) in (13) reduced over time. On the other hand, central MSs in cell i see a throughput increase. The LA-HO scheme of boundary MSs may trigger them to switch over to neighboring cells, in pursuing potentially higher throughput due to less competition there. Therefore, the tuning of αi optimizes the user distribution or MAC-layer cell coverage of i and its neighbors Ni , which potentially accommodates more users into the system, and may thus optimize (5) especially under the minRate constraint. The above scheme is named the MAC-layer Cell Breathing (MAC-CB) scheme. Below is the simplest way to realize it: αi (t + tl ) ⎧ E[L i (t)] ⎪ (1 − )αi (t) (cell contraction), if E[L > 1, TH ⎪ ⎨ i (t)] = (1 + )αi (t) (cell expansion), else if E[LTiH(t)] < 1, ⎪ E[L i (t)] ⎪ ⎩ αi (t) (no change), otherwise, where is the step size to tune α in percentage, e.g., = 0.1; L i (t) is the mean load in cell i as defined in (3); L iT H (t) is the average of the loads in i’s neighborhood:  L iT H (t) = i∈Ni L i (t)/|Ni |; tl is the timescale of the tradeoff between the signaling overhead and load-balancing effectiveness during the MAC-CS, e.g., tl = 10 s. Although this scheme seems “centralized,” it achieves the load balancing effect by prompting distributed MS handoffs. In addition, it only imposes very low overhead with the periodic signaling for report and command messages between BSs and the central controller, as illustrated in Fig. 2. Furthermore, this scheme can be easily realized in a distributed way if we allow light-weight direct communications among neighboring BSs, where only the load information is broadcast among neighboring BSs periodically and within a limited region. Consequently, all cell breathes to the rhythms of load oscillation, which is characterized by mobility users to

5. Performance analysis

5.1. Setup of simulation tests In the multi-cell system as Fig. 1(a), we define the active set for each MS as the set of all cells. Each cell has an omnidirectional antenna. All BSs have the same constant transmission power. The log-normal fading variable si,k (t) has a standard deviation σs = 4 dB. The propagation path loss exponent is γ = 3.7. Here we adopt memoryless Rayleigh fading and neglect the AWGN factor σn2 . So the mean SINR of the channel between k and i is:  

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MSs geographically fixed after the arrival. Thus the system loading is solely represented by asymmetric user density or asymmetric user arrival and departure.

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First look at a single cell of a fixed number (K ) of static MSs with Rayleigh channels. For each given number of MSs, we execute 50 runs of simulation, each lasting 600 seconds. For each run, the uniformly distributed locations of users are generated at the beginning. Their mean SNR are generated from the distribution of HDR systems [8]. All MSs remain ON for the whole simulation period. As Fig. 3 shows, the aggregate throughput generally increases with K , reflecting the multiuser diversity gain. However, the throughput decreases with the increase of required minRate. It is because a higher minRate demands more dedicated resources, and thus has less freedom to explore the diversity gain. The multiuser diversity gain increases with K but eventually reaches the point when the assignment of dedicated resources dominates. It is where the aggregate throughput saturates and starts dropping beyond this point, as shown by the hunched curves with minRate=56 kbps. Obviously the saturation comes earlier with a higher minRate. We repeat the same test given dynamic MS arrival and departure, each MS having an exponential lifetime with a mean value of 20s. The call admission control (CAC) algorithm (14) works to guarantee their minRate requirements. One run of 10000 seconds long is executed. Results are shown in Fig. 4, where the reduction of throughput given a larger α reflects the flexibility of the Alpha-Rule scheduling. It is no surprise that the number of admissible (active) MSs increases with traffic intensity ρ. Interestingly so does the aggregate throughput. In other words, the multiuser diversity gain re-

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mains dominating through the whole region of ρ and shows no sign of saturation. It is because the system now is accepting users selectively within its domain. The admitted users generally have a better channel than the average arrived users because some poor-channel users have been rejected because of their high loads ( E[rmi,kk(t)] ). That is also the reason why the aggregate throughput in Fig. 4 tends to be higher than Fig. 3, where users are uniformly distributed within the cell domain without CAC’s effect. Similarly, given the same ρ, the case of a smaller minRate (say, 10 kbps versus 56 kbps) admits more MSs, which results in a poorer channel quality on average. That is why it delivers a lower aggregate throughput in spite of more (active) MSs accommodated. In fact, with minRate = 10 kbps, almost all MS arrivals are admitted within the whole test range of ρ. The admitted MSs are basically uniformly distributed within the cell. Comparatively, for a higher minRate, the admitted MSs are closer to BS on average than uniform distribution, and thus delivers higher aggregate throughput. In summary, the aggregate throughput depends not only on the population size (K ) in the system, but also the minRate and the mean channel quality (or the geographic distribution of MSs). A lower blocking rate does not necessarily mean a higher throughput. Figure 5 illustrates the role of α more clearly: the aggregate throughput monotonically decreases with α in spite of different ρ or minRate. Not shown here, the fairness in sharing the residual resource after minRate guarantees improves with an increasing α. Furthermore, as we observed before, the system given a smaller minRate requirement would accommodate more MSs, but would have poorer overall channel quality as well. Interestingly, this is illustrated here by comparing the three minRate cases under different loading scenarios: when the load is light, e.g., ρ = 17, a smaller minRate would have a higher aggregate throughput. This

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5.3. Two-tier case: robustness to load dynamics

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phenomenon is gradually reversed with increasingly heavier loads or larger ρ, reflecting the dominance in throughput of either mean channel quality or multiuser diversity gain. Figure 6 shows the QoS (minRate) guarantees for MSs: each MS measures its mean throughput by the end of its lifetime and then compares the throughput to the minRate requirement. Note it is an arguable issue regarding the time scale over which the minRate should be guaranteed for the bursty elastic services. Not surprisingly, the violation ratio increases with a more demanding minRate requirement. In addition, it decreases with α because a larger α assigns more resources to poor-channel users among which most violations occur. Generally speaking, the QoS is within an acceptable range, and can be expected to improve if adopting a possibly more rigorous scheduling scheme, say, a hybrid of weighted Alpha-Rule and Exp-Rule [6].

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respectively, compared to (0, 0, 0). Due to the resource pooling effect among cells, both schemes see that the mean loads of the two tiers become more equivalent than input dynamics. The load change mitigates congestions in over-loaded cells and improves resource utilization in under-loaded ones. With (1, 0, 1), the numerous events of (accumulated) handoff arise from the cell breathing effect, characterized by the varying α’s and the responses of individual MSs. With (1, 1, 1), the load balancing effect is even better due to LA-CSS’s effects. Much less occurrences of handoff and cell-breathing are because LA-CSS precludes most load-aware handoffs. However, LA-CSS can never invalidate LA-HO because in practice, MSs’ environment changes after their initial cell-site selections due to mobility. In summary, the dynamic tests show the robustness of our load-balancing scheme to bursty load changes. 5.4. Two-tier case: stationary but asymmetric loads We also study a two-tier system of stationary MS intensities. As before, MSs have a average life of 20 seconds, and minRate = 28.8 Kbps. Not shown here, further tests given minRate = 56 Kbps reveal similar results. Cells in the second tier have ρ1 = 20 each, while the cell in the first tier may have a stationary but different ρ0 in the range of [1, 120]. For each ρ0 , we evaluate per-cell and aggregate performance over a simulation period of 5000 seconds. In the previous section and in [25], we have shown that the load balancing advantages increase from (0, 0, 0) to (1, 0, 1) and (1, 1, 1). To show the separate role of MAC-CB, LA-CSS, and LA-HO in more details, here we substitute schemes (0, 0, 1) and (0, 1, 1) for the legacy scheme (0, 0, 0), and regard (0, 0, 1) as the “basic” scheme. Figure 10 shows that the per-cell throughput can be quite different for different schemes. For cell 0 and roughly across Springer

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the whole region of ρ0 , the throughput increases from (0, 0, 1) to (0, 1, 1), (1, 0, 1), and then to (1, 1, 1). (1, 1, 1) has the largest gain due to its strongest load balancing effects among all the schemes. However, the tier 1 shows different results from tier 0 for the following reasons: when tier 0 is under-loaded (ρ0 < 20), the schemes shift MSs from the cell boundary of tier 1 into that of tier 0, which results in higher multiuser diversity gain but poor average channel in tier 0, and better average channel in tier 1. Note that the most prominent role of MAC-CB is to trade resource fairness for higher aggregate throughput. So both tiers see higher throughput with (1, 0, 1) and (1, 1, 1), i.e., MAC-CB is ON, than with (0, 0, 1) and (0, 1, 1). On the other hand, when tier 0 is over-loaded (ρ0 > 35), the multiuser diversity gain is close to saturation in both tiers, whence the average channel quality is dominating the throughput performance. In this scenario, the shift of boundary MSs from tier 0 to tier 1 upgrades and degrades the average channel quality in tiers 0 and 1, respectively. Therefore, while one scheme increases the throughput in tier 0 over another, it impairs that in tier 1 over others. The effectiveness of different schemes in load balancing is reflected by their different impacts on the throughput. Clearly (1, 1, 1) shifts the most MSs out of the congested area, and thus has the strongest impact on the throughput (at both tier 0 and 1). (1, 0, 1) has similar performance as (1, 1, 1) because the ON of MAC-CB enables LA-HO to compensate the lack of LA-CSS in a long run. Now let us check the aggregate performance of the system. First is the aggregate throughput. Because of the dual impacts of load balancing on average channel quality and multi-user diversity gain, and the offsetting changes among different tiers, our load balancing schemes do not always increase the aggregate throughput. However, either the increment or the

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decrement of aggregate throughput must be trivial, as shown by the gap of the ordinate value in Fig. 11(a) that ranges from the maximum 4.04 to the minimum 3.72 (both multiplied by 104 ). In other words, the changes in the single cell of tier 0 and in the six cells of tier 1 basically offset each other. However, the load balancing effect significantly reduces the aggregate blocking rate, as Fig. 11(b) shows, especially for the case of minRate equal to 56 kbps. We see that (1, 1, 1) and (0, 1, 1) basically overlap with each other (and with x-axis for minRate equal to 28.8 kbps), both having significantly lower blocking rate than (0, 0, 1) and (1, 0, 1). This observation emphasizes the outstanding importance of LA-CSS in reducing the blocking rate of initial MS arrivals, which is in sharp contrast to that of MAC-CB. The seeming ineffectiveness of MAC-CB in reducing the blocking rate when LA-CSS is ON is because of the following facts: As we have seen from Fig. 9, LA-CSS precludes most of LA-HO occurrences due to our setup of static MSs, while MACCB can reduce the blocking only through LA-HO. Therefore, we may expect more prominent benefits of MAC-CB given a mobile setup where a significant number of users move across cell boundaries and change the system state after the initial cell-site selection procedure. However, MAC-CB can improve the throughput of hot-spot cell quite significantly, as we have seen from Fig. 10. In fact, even Fig. 11(a) reveals the relatively outstanding role of MAC-CB in achieving high throughput by the comparison between (1, 1, 1) and (0, 1, 1) or (1, 0, 1) and (0, 0, 1). Actually the MAC-CB has more prominent role in systems where multiple-input multipleoutput (MIMO) antenna techniques widen the throughput gap between PF (α = 1) and max-C/I (α = 0) [24]. Not shown

here, MAC-CB impacts load balancing through the weighted Alpha-Rule, which controls the throughput of boundary users more effectively in MIMO systems.

5.5. Three-tier case: stationary but asymmetric loads Having realized the different roles of MAC-CB, LA-CSS, and LA-HO, now we come back to the typical schemes of (0, 0, 0) to (1, 0, 1) and (1, 1, 1), but here we scale up the system to three tiers multi-cell with heavy loads at the second-tier (tier 1), i.e., the middle circle of the rings. Similarly we fixed ρ of the tier 1 and 2 as ρ1 = 60 and ρ2 = 20 while testing a range of ρ0 in [1, 120]. This setup creates a test scenario where the load balancing effect, if any, has less distortion from the boundary effect in the setup where the out-most ring of cells has only inner neighbors. As we can see from Fig. 12, per-cell throughput generally improves from (0, 0, 0) to (1, 0, 1) and (1, 1, 1) at the inner two tiers. It deteriorates at tier 2 because more poor-channel (boundary) users are shifted from tier 1 here, competing for resources with strong-channel users. In other words, the detrimental impact of load balancing on mean channel quality overwhelms the multiuser diversity gain especially when the latter is close to saturation. As shown in Fig. 13, our schemes (1, 1, 1) and (1, 0, 1) can effectively balance the loads at different tiers, which translates to the smaller gaps among curves corresponding to each of the two schemes than that of (0, 0, 0). Specially, from the scheme (0, 0, 0) to (1, 0, 1) and (1, 1, 1), the load of tier 1 decreases and tier 2 increases, while the Springer

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Three–tier multicell system: ρ = 60, ρ =10, minRate=28.8kbps 1 2 (0, 0, 0), tier0 (1, 0, 1), tier0 (1, 1, 1), tier0 (0, 0, 0), tier1 (1, 0, 1), tier1 (1, 1, 1), tier1 (0, 0, 0), tier2 (1, 0, 1), tier2 (1, 1, 1), tier2

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increases or decreases of tier 0 depend on it being under- or over-loaded. The per-cell blocking rate here is similar to the two-tier case. For all tiers, the rate almost unanimously decreases from (0, 0, 0) to (1, 0, 1) and (1, 1, 1), as Fig. 14 shows. A special case is tier 0 with (1, 1, 1): When ρ0 is very small, too many edge MSs shifted from tier 1 here make the load of tier 0 even higher than tier 1, although the number of admitted MSs in tier 0 remains low. However, due to the limited number of MSs in tier 0, this has negligible effect on the total blocking rate, as we will see soon. In summary, the per-cell performance shows that our load balancing scheme is indeed effective in reducing congestions and increasing resource utilization across the system. The per-cell throughput improvement depends on specific sceSpringer

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narios, reflecting the inherent tradeoff between more satisfied MSs and better mean channel quality (or higher throughput) of satisfied MSs in the system. Similar to the two-tier cases, the global downlink throughput of the three-tier system does not not change much with or without our load balancing schemes due to the tradeoff between the mean channel quality of admitted users and the total number user of users admitted. So let us focus on the overall call blocking rate instead. Figure 15 clearly shows that the global blocking rate decreases significantly given our schemes (1, 1, 1) and (1, 0, 1). Therefore, a multi-cell system as a whole will benefit significantly from the load balancing; the system will accommodate more satisfied users and will boost its revenue in general.

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6. Discussion 6.1. Related work Recently, Das et al. [11] proposed a coordinated scheduling and load balancing scheme for the multi-cell system of highspeed shared channels. They defined a centralized scheduler in the system to determine the optimal BS-MS matching by periodically searching a complete list of all possibilities. The list is sorted by radio distance (i.e., SINR) and the decision is refined iteratively according to a threshold defined by the closest-radio matching. The dynamic matching across the system, together with independent scheduling within each cell, is named the “2-tier scheduling”. For a fixed number of mobile users, the 2-tier scheduling scheme is shown to achieve higher per-user throughput than the static matching scheme, named the “baseline scheduler”. Another recent work [19] investigates several critical issues in multi-cell downlink packet data systems. It thoroughly analyzes cell capacity, throughput, and blocking probability for given scheduling and admission control schemes in a single cell. It then extends to a multi-cell scenario with considerations of inter-cell interference. A careful examination tells us that the angle and focus of [19] is different from ours which is to optimize the design of multicell packet data systems through cross-layer coordinations among load balancing, scheduling, and handoff/cell-site selection. For example, “cell breathing” under the same term is analyzed in [19] as a natural phenomenon in response to the location-dependent admission control under low (i.e., cell exhaling) and heavy loads (i.e., cell inhaling) in a single cell. In contrast, we propose a MAC-layer “cell breathing” to proactively control the load balancing among neighboring cells. Our scheme differs from existing work (e.g., [11, 19] and references therein): Ours does not require capacity analysis, neither a centralized scheduler. Both the BS-MS matching and MS’s handoffs in our scheme are determined by MSs in a distributed and asynchronous manner based on individual’s measurements of real-time load and throughput. Moreover, our central controller does not directly control specific MSs. Instead, it coordinates cell breathing/coverage via tunable schedulers in neighboring cells, which implicitly prompts MSs to switch over to the “inhaling” cells with lower load and higher throughput. Comparatively our scheme only requires localized distributed optimizations assisted by light-weight central tuning. 6.2. Practical concerns Essentially, the issue of load balancing in a multi-cell system of high-speed downlink shared channel requires an efficient tradeoff between smaller blocking rate, higher throughput,

and stricter QoS (minimum rate) guarantees. Since revenue mostly links to the total number of satisfied users accommodated by such systems, the blocking rate should be the most important metric provided all accepted MSs see satisfactory QoSs. Our load balancing scheme helps to reduce the blocking and maximize the resource utilization within the system. With such a scheme, aggregate throughput generally remains stable. When the load is reasonably heavy, a good load balancing scheme shifts “redundant” users from congested cells to under-loaded ones. The associated improvement with average channel quality in congested cells and the multiuser diversity gain in under-loaded ones may prevail, improving the aggregate throughput. Otherwise, the deterioration of average channel quality for accommodating more boundary MSs may dominate, slightly lowering the aggregate throughput. However, no matter what, the blocking rate will be reduced significantly, featuring the advantages of our schemes. In our setup, we used the ON/OFF model of MSs to represent the load oscillation in the system, while in practice the oscillation is also caused by user mobility. For our study of load-aware schemes, this ON/OFF model has captured the essence of load dynamics and the asymmetry in a mobile system. The reason is as follows: Both ON/OFF and mobility of MSs may cause significant channel and throughput changes to boundary MSs or MSs moving during their service, a phenomenon observed by the MSs through constant measurements, while the load-aware schemes will be triggered in response to the measured changes regardless of mobility or ON/OFF. The control time scales in our scheme cover call level handoff (th ) and system level cell coordination (tl ). Those parameters, together with the intervals to report intra-cell loads to the central controller, are usually engineering tuning knobs. They may be set by BSs or MSs independently. Generally speaking, our scheme incorporates a cross-layer coordination among distributed BS-MS matching and handoff, and centralized cell breathing, both assisted by physical and MAC layer measurements. This framework is flexible and scales well with the system size and loads. In addition, it is very compatible with the current technologies. For example, the centrally-controlled cells breathe independently of the physical-layer power control, an important feature of shared channel systems. In a multiuser and multi-cell system, this cross-layer system level optimization compensates the great efforts to improve the point-to-point spectrum efficiency at the physical layer. From the point of view of global system, a new MS adopting SINR-based cell-site selection is actually selecting the cell whose aggregate load would have the smallest increment among all, regardless of the actual loading level. On the other hand, LA-CSS considers the existing load of different cells and tries to pick the one whose existing load is the Springer

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smallest. This has an inherent load balancing impact. For the system as a whole, the maximization of aggregate throughput and the global utility may not coincide, depending on the utility function. Similarly, the reduction of blocking rate or an increasing number of satisfied users does not necessarily improve the aggregate throughput. Just for the purpose of throughput improvement, we may have to block some users with bad channels to maximize the spectral efficiency, which is unacceptable in practice. Note that our scheme is independent of the actual distribution of MS locations. Our test of uniform distributed MS arrivals constitutes a conservative case in terms of performance. Suppose a higher percentage of users are distributed at the cell boundary, a situation similar to the case when the shadow fading instead of the path loss dominates the channel, then we may expect from our load balancing scheme even larger improvements in blocking rate and aggregate throughput. For LA-HO in particular, in order to balance between sensitivity to load fluctuation and overhead associated with each handoff, an active MS k checks (13) only periodically rather than at each time slot. The value of th depends on k’s velocity speed and the timescale of measured load fluctuation. To avoid synchronous handoff among MSs, each MS keeps an independent timer that counts down to 0 before reset to th again. The timer starts upon the random arrival of each MS, and thus avoid isochronous, load-ware handoffs among MSs. As mentioned before, we did not consider forced handoffs that arise when channel quality degrades below certain threshold, say, when MSs cross cell boundaries. In addition, we only adopted the simplest CAC without direct retry and other refinements. However, our scheme works independently of these different configurations.

7. Conclusion In this paper, we propose a multi-cell coordination scheme for cellular systems of high-speed downlink shared channels, where a dilemma exists as follows: On the one hand, there is no physical-layer power control or MAC-layer soft-handoff. On the other hand, inter-cell interference and asymmetric load distribution in multiple cells are hindering the global system performance, which traditionally requires dynamic power control or soft-handoff. Our proposed concepts such as the MAC-layer “cell breathing” and load-awareness in hardhandoff/cell-site selection act as an answer to this dilemma, assisted by the weighted Alpha-Rule, an intra-cell opportunistic scheduling algorithm with minRate guarantees and tunable fairness. All together our schemes reduce the blocking rate of MS arrivals across the whole system by 50% to 100% or even more, e.g., refer to Figs. 11(b) and 15. It also increases system utilization and mitigates regional congestions. Due Springer

to the geographical distribution of MSs and the associated path loss, a load balancing scheme may increase the number of satisfied users, but may not always increase the overall system throughput. That is the fundamental tradeoff we found. However, our scheme can improve the throughput of the congested cell at a well-controlled cost of others. For specific cases, we observed about 13% throughput increase at the hot-spot, e.g., Figs. 10 and 12, with only ±2.5% changes to the overall throughput, e.g., Fig. 11(a). Evaluations show that our scheme is robust to asymmetric and dynamic traffic arrivals. Acknowledgments The authors are grateful to Dr. Sem Borst for his careful review of our manuscript and his insightful suggestions.

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Aimin Sang received a Ph.D. from the University of Texas at Austin in 2001. His Ph.D. dissertation is on the measurement-based traffic management for QoS guarantee in multiservice networks. From May 2000 to July 2002, he was a member of technical staff and software engineer at Santera System Inc., a startup company in designing and implementing the next-generation multi-service gateway. His duty was to design, implement, and test core traffic management algorithms on the switch fabric and control boards, integrating IP routing, ATM switching, and Class 4 and 5 telephony switching functionalities for multi-service Internet access at the Central Offices. From July 2002 to Nov. 2002, he was a post-doc at UT-Austin, researching on VPN provisioning and ad hoc sensor networks. He joined NEC Lab America in Nov. 2002. Dr. Sang is currently a research staff member in Broadband & Mobile Networking Department, NEC Lab. America, focusing on crosslayer design of 4G wireless systems, such as 4G Cellular base station, WiMax/WLAN systems, and their inter-networking architecture. His duty is to develop the core technologies including the radio resource management and QoS schemes over an IP-optimized MC-CDMA or OFCDM/MIMO air interfaces. He is also interested in ad hoc sensor networks and personal area networks. Xiaodong Wang received the B.S. degree in Electrical Engineering and Applied Mathematics (with the highest honor) from Shanghai Jiao Tong University, Shanghai, China, in 1992; the M.S. degree in Electrical and Computer Engineering from Purdue University in 1995; and the Ph.D degree in Electrical Engineering from Princeton University in 1998. From July 1998 to December 2001, he was an Assistant Professor in the Department of Electrical Engineering, Texas A&M University. In January 2002, he joined the faculty of the Department of Electrical Engineering, Columbia University. Dr. Wang’s research interests fall in the general areas of computing, signal processing and communications. He has worked in the areas of digital communications, digital signal processing, parallel and distributed computing, nanoelectronics and bioinformatics, and has published extensively in these areas. Among his publications is a recent book entitled “Wireless Communication Systems: Advanced Techniques for Signal Reception”, published by Prentice Hall, Upper Saddle River, in 2003. His current research interests include wireless communications, Monte Carlo-based statistical signal processing, and genomic signal processing. Dr. Wang received the 1999 NSF CAREER Award, and the 2001 IEEE Communications Society and Information Theory Society Joint Paper Award. He currently serves as an Associate Editor for the IEEE Transactions on Communications, the IEEE Transactions on Wireless Communications, the IEEE Transactions on Signal Processing, and the IEEE Transactions on Information Theory. Mohammad Madihian received the Ph.D. Degree in Electronic Engineering from Shizuoka University, Japan, in 1983. He joined NEC Central Research Laboratories, Kawasaki, Japan, where he worked on research and development of Si and GaAs device-based digital as well as microwave and millimeter-wave monolithic IC’s. In 1999, he moved to NEC Laboratories America, Inc., Princeton, New Jersey, and is presently the Department Head and Chief Patent Officer. He conducts PHY/MAC layer signal processing activities for high-speed wireless networks and

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Wireless Netw personal communications applications. He has authored or co-authored more than 130 scientific publications including 20 invited talks, and holds 35 Japan/US patents. Dr. Madihian has received the IEEE MTT-S Best Paper Microwave Prize in 1988, and the IEEE Fellow Award in 1998. He holds 8 NEC Distinguished R&D Achievement Awards. He has served as Guest Editor to the IEEE Journal of Solid-State Circuits, Japan IEICE Transactions on Electronics, and IEEE Transactions on Microwave Theory and Techniques. He is presently serving on the IEEE Speaker’s Bureau, IEEE Compound Semiconductor IC Symposium (CSICS) Executive Committee, IEEE Radio and Wireless Conference Steering Committee, IEEE International Microwave Symposium (IMS) Technical Program Committee, IEEE MTT-6 Subcommittee, IEEE MTT Editorial Board, and Technical Program Committee of International Conference on Solid State Devices and Materials (SSDM). Dr. Madihian is an Adjunct Professor at Electrical and Computer Engineering Department, Drexel University, Philadelphia, Pennsylvania. Richard D. Gitlin Is currently President of Innovatia Networks a wireless startup company and a member of the Board of Directors of PCTEL [NASDAQ: PCTI]. Previously he was Visiting Professor of Electrical Engineering at Columbia University and Vice President, Technology of NEC Laboratories America. After receiving his doctorate from Columbia University, he was with Lucent Technologies (Bell Labs), where for more than 32 years he held several research and executive positions, including

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Senior Vice President, Communications Systems Research and Chief Technical Officer and VP of R&D of Lucent’s Data Networking Business Unit. Throughout his career Dr. Gitlin has both personally conducted and led pioneering research and development in digital communications and networking, digital signal processing, wireless systems, and broadband networking that has resulted in many innovative products, including: the industry leading ATLANTA ATM Chipset, the world’s first 20 gigabit/sec ATM switch, wire-speed and quality of service [QoS]aware IP switches, multicode CDMA (IS-95B), and the record-setting BLAST broadband fixed-wireless loop system based on advanced spatial domain (smart antenna) processing. Earlier in his career he led the team that pioneered the V.32/V.34 voice-band modems, and in 1986 he was a co-inventor of the DSL technology. He has more than 90 referred publications, is the recipient of three prize papers, has delivered numerous keynotes, and he holds 43 US patents, and co-author of the text Data Communications. He currently serves on the Editorial Boards of Mobile Networks and Applications and the Journal of Communications Networks (JCN). Dr. Gitlin has been elected as a member of the US National Academy of Engineering, is a Fellow of the IEEE, and is a Bell Laboratories Fellow. Dr. Gitlin has served as Chair of the Communication Theory Committee of the IEEE Communications Society, as a member of the COMSOC Awards Board, as Editor for communication theory of the IEEE Transactions on Communications, as a member of the Board of Governors of the IEEE Communications Society, and a member of the Nominations and Elections Board. He has served on the Advisory Committee for Computer Science and Engineering (CISE) of the National Science Foundation.