a dynamic programming approach for base station sleeping ... · cluster by cooperation among...

IEICE TRANS. COMMUN., VOL.E95–B, NO.2 FEBRUARY 2012551

PAPER

A Dynamic Programming Approach for Base Station Sleeping inCellular Networks∗

Jie GONG†a), Sheng ZHOU†b), Student Members, and Zhisheng NIU†c), Fellow

SUMMARY The energy consumption of the information and commu-nication technology (ICT) industry, which has become a serious problem,is mostly due to the network infrastructure rather than the mobile terminals.In this paper, we focus on reducing the energy consumption of base stations(BSs) by adjusting their working modes (active or sleep). Specifically, theobjective is to minimize the energy consumption while satisfying quality ofservice (QoS, e.g., blocking probability) requirement and, at the same time,avoiding frequent mode switching to reduce signaling and delay overhead.The problem is modeled as a dynamic programming (DP) problem, whichis NP-hard in general. Based on cooperation among neighboring BSs, alow-complexity algorithm is proposed to reduce the size of state space aswell as that of action space. Simulations demonstrate that, with the pro-posed algorithm, the active BS pattern well meets the time variation andthe non-uniform spatial distribution of system traffic. Moreover, the trade-off between the energy saving from BS sleeping and the cost of switchingis well balanced by the proposed scheme.key words: base station (BS) sleeping, blocking probability, dynamic pro-gramming (DP), neighboring BS cooperation

1. Introduction

The continuously growing demand for ubiquitous informa-tion access leads to the rapid development of the informa-tion and communication technology (ICT) industry, whichhas become one of the leading consumers of energy and isexpected to grow continuously in the future. As a result,energy saving is urgently required by both governments andnetwork venders. For instance, GreenTouch has promised toimprove energy efficiency in wired/wireless networks by afactor of 1,000 by 2015 compared with 2010 [1]. The energyconsumption in ICT industry comes mainly from data cen-ters, backhaul routers and cellular access networks. In cellu-lar networks, the energy consumption of base stations (BSs)is 60% to 80% of that of the whole network [2], and willincrease as network structure migrating from macrocell tomicrocell to meet the increasing demand of radio resources.As a result, the energy consumption of BSs becomes a majorportion of the whole network energy consumption. Since theenergy consumption of a BS mainly comes from basebandsignal processor, controller, air-conditioner and etc., ratherthan transmit power which consumes only 3.1% [3], turning

Manuscript received July 12, 2011.Manuscript revised October 27, 2011.†The authors are with the Tsinghua National Laboratory for In-

formation Science and Technology, Department of Electronic En-gineering, Tsinghua University, Beijing 100084, China.

∗Part of this paper has been presented at IEEE IWQoS’10.a) E-mail: [email protected]) E-mail: [email protected]) E-mail: [email protected]

DOI: 10.1587/transcom.E95.B.551

BSs into sleep mode whenever possible is considered as apromising technique to reduce the energy consumption.

In fact, due to the variation in time domain and the dy-namic distribution among cells in space domain [4], thereare opportunities for some BSs to turn to sleep mode whenthe traffic load in their coverage is low. However, when BSsturn to sleep mode, radio coverage and quality of service(QoS, e.g., blocking probability) must still be guaranteed.Thanks to the concept of cell zooming [5], the users in thesleeping cells can be served by the neighboring active BSsby transmit power adjusting, antenna re-configuration, wire-less relay and BS cooperation technologies. As a conse-quence, BS sleeping is a feasible approach for energy savingin cellular networks.

To design efficient BS sleeping schemes, following is-sues must be carefully studied.

- On the one hand, BS mode switching decision cannotbe made by each BS individually. Not only the loadcondition of a BS itself, but also the load of its neigh-bors needs to be considered. For instance, a BS maynot turn to sleep while its neighboring BSs are overloaded, even if its own traffic load is low. For this rea-son, each BS should make its mode switching decisionvia BS cooperation.

- On the other hand, although cooperation among all theBSs can achieve the optimal sleep policy, it is not appli-cable in real system due to the high complexity. Sub-optimal solution obtained by local cooperation amongneighboring BSs is preferable.

- Finally, taking signaling overhead, device lifetime andswitching energy consumption into account, frequentBS mode switching should be avoided. That is, BSsshould try to minimize the number of switching ac-tions, or in other words, maximize the BS mode hold-ing time, which is defined as the holding duration be-tween two successive switching actions.

In this paper, we exploit the traffic variation featureto design an energy-efficient BS sleeping algorithm, whichis then formulated as a dynamic programming (DP) prob-lem with a combined cost function of energy consumption,switching cost and blocking probability penalty. To reducethe dimension of state space and that of action space, per-cell Q-factor based on the cooperation among neighboringBSs is introduced, and a low-complexity algorithm is pro-posed to find the suboptimal policy. In addition, to matchthe system with BS sleeping behavior, user association and

Copyright c© 2012 The Institute of Electronics, Information and Communication Engineers

552IEICE TRANS. COMMUN., VOL.E95–B, NO.2 FEBRUARY 2012

handover algorithms are re-designed.The rest of the paper is organized as follows. Related

work is summarized in Sect. 2. Section 3 introduces the sys-tem model. The DP problem formulation is presented inSect. 4. In Sect. 5, the proposed cooperative BS sleeping al-gorithm is described. The simulation results are presented toevaluate the proposed framework in Sect. 6. Finally, Sect. 7concludes the paper.

2. Related Work

BS sleeping is drawing more and more attention in recentyears. Reference [6] suggests to switch off half of the cells atnight while keeping the blocking probability below a giventarget. Reference [2] gives a static BS sleep pattern ac-cording to a deterministic traffic variation pattern over time.However, neither the randomness nor the spatial variationof the traffic is considered. Our work focuses on the sce-nario where traffic intensity varies in both time domain andspace domain. In our previous studies [7], preliminary at-tempt of algorithm design is presented. Centralized greedyand distributed heuristic algorithms are proposed to dynam-ically turn on and turn off BSs. Similar work [8] proposes aBS awake selection algorithm. Nevertheless, switching costwas not considered.

In [9], the authors consider the tradeoff between de-lay and energy consumption and formulate the problem as aMarkov decision process problem and find a two-thresholdoptimal sleeping policy structure. This work and referencestherein provide inspiring examples about how to model theswitching cost. However, how the BS switching actions in-fluence with each other in multicell scenario remains open,which is the focus of our work.

Reference [10] proposes a resource on-demand (RoD)strategy for high-density centralized WLANs. “Green-cluster” is formed by a set of access points (APs) whichare close to each other. A cluster-head AP is sufficient toprovide coverage to users in the cluster, so that other APsin the cluster can be switched off when the traffic load islow. However, the channel model of WLANs is differentfrom that of cellular networks where path-loss effect is dom-inating. Different from this work where cluster is fixed andnon-overlapped, we implicitly adopt the concept of dynamiccluster by cooperation among neighboring BSs.

BS energy saving problem can be modeled as a dy-namic cell planning problem. However, the existing cellplanning algorithms (see [11] and references therein) are toocomplicated to be used for dynamic adjustment. For dy-namic resource control with respect to the spatial and timetraffic variation, one could refer to load balancing schemes(see [12] and [13] for example). Indeed, properly utilizingload balancing is also helpful to BS energy saving, sinceit can reduce the blocking probability effectively. We willdemonstrate how load balancing could improve the BS en-ergy saving performance through simulations.

3. System Model

Consider a downlink cellular network consisting of M BSswith universal frequency reuse. LetM = {1, . . . ,M} denotethe set of BSs. The maximum coverage of BS m is the areawhere BS m can provide the required data rate, and the cellm is defined as the area that is nearest to BS m comparedwith other BSs. As depicted in Fig. 1, the cell radius is Rc

and the BS maximum coverage radius is Rb, which indicatesthat each BS is able to cover its neighbor cells. In the tradi-tional cellular networks where all BSs are active, each cell istaken care of by its own BS. When some BSs turn to sleep,the actual BS coverage extends from their own cells to theneighbors with sleeping BSs. This is reasonable in urbanscenarios, where BSs are densely deployed. The neighborsof BS m are denoted as m(1), . . . ,m(B), where B is the num-ber of neighbors (B = 6 in hexagonal cellular system). De-note Bm = {m,m(1), . . . ,m(B)} as the set of BSs which canprovide service to the users in cell m.

3.1 Traffic Model and Channel Model

The traffic arrives in cell m at time t as a Poisson processwith intensity λm(t). The traffic is assumed uniformly dis-tributed in each cell, but asymmetric among different cells.Assume that the system have the statistic traffic information,i.e., the average arrival rate λ(t) = {λm(t)}Mm=1, which is a pe-riodic function with period T (for example, 24 hours). Eachuser has a minimum rate requirement r0. All users arriverandomly and then remain stationary until the transmissionis finished. The transmission duration of each user followsexponential distribution with mean 1/μ.

Assume that each active BS m has limited radio re-source, i.e., the maximum bandwidth Wmax

m . Notice that thebandwidth here is the generalization of wireless resources

Fig. 1 Cellular network architecture. The cell radius is Rc and the maxi-mum coverage radius is Rb, which indicates the overlapped network struc-ture. When some BSs turn to sleep, the active BSs extend their actualcoverage from their own cells to the neighbors with sleeping BSs.

GONG et al.: A DYNAMIC PROGRAMMING APPROACH FOR BASE STATION SLEEPING IN CELLULAR NETWORKS553

that the BS can allocate, i.e., sub-carriers or time-slots, etc.If user k is associated to BS m, the corresponding bandwidthdemand is

wmk(t) =r0

Cmk(t), (1)

where Cmk(t) is the spectrum efficiency (instantaneous peakrate per unit bandwidth). It varies over time due to shad-owing, multi-path fading and etc. Nevertheless, as the longtime-scale performance is considered here, we ignore thefast fading effects, i.e., we assume that the spectrum effi-ciency is constant during the transmission, which is deter-mined by the large-scale path-loss. The expressions are thensimplified to Cmk and wmk without time index. The inter-cell interference is assumed already being taken care of bycertain reuse or interference management schemes. Inter-ference power is averaged over all possible user positionsassuming all the BSs are in active mode. It is a conservativeestimation since interference is reduced when some BSs goto sleep mode. Based on above assumptions, Cmk dependsonly on the distance lmk from BS m to user k

C(lmk) =

⎧⎪⎪⎨⎪⎪⎩ log2

(1 +

Ptβl−αmk

N0

), 0 < lmk ≤ Rb,

0, lmk > Rb,(2)

where Pt is the transmit power; β is the path-loss con-stant and α is the path-loss exponent; N0 is the noise-plus-interference power.

3.2 BS State and Control Action

The time period T is divided into N + 1 time intervals (eachwith index i) as shown in Fig. 2. Note that to be able totrack the system traffic variation, the length of time intervalτ(i) varies with λ(t) so that on average, constant number ofusers, Kτ, arrive during τ(i). Then we have

Kτ =∫ t(i)+τ(i)

t(i)

M∑m=1

λm(t)dt, (3)

where τ(i) can be calculated by some numerical method.Assume that each BS m ∈ M can work in two modes:

active mode (denoted as s(i)m = 1) and sleep mode (denoted

as s(i)m = 0). In each time interval τ(i), i = 1, . . . ,N, the

system works in the fixed state s(i) = {s(i)m }Mm=1. The state

space is

S = S 1 × S 2 × . . . × S M , (4)

where S m = {0, 1},m = 1, . . . ,M is the set of working modes

Fig. 2 System operation over time. The network keeps a constant states(i) in each time interval τ(i), and operates action u(i) at each time spot t(i).

of BS m.At each time spot t(i), i = 0, . . . ,N, the BSs take the

action u(i) = {u(i)m }Mm=1. The action space is

U = U1 × U2 × . . . × UM , (5)

where Um = {0, 1},m = 1, . . . ,M is the set of actions of BSm. Denote u(i)

m = 1 as the action that BS m switches its work-ing mode and u(i)

m = 0 otherwise, as that BS m maintains itsworking mode.

The overview of the system operation is as follows.The BSs work in the constant state s(i) during the time in-terval τ(i), i = 1, . . . ,N and the users are served by the cur-rently active BSs. At each time spot t(i), i = 0, 1, . . . ,N − 1,the BSs decide weather to switch their working modes ornot according to the action u(i). If a BS switches from ac-tive mode to sleep mode, the associated users are shifted tothe active neighbors. After the BS mode switching processis finished, the system goes into the next time interval τ(i+1)

with updated state s(i+1).Generally speaking, the object of BS sleeping algo-

rithm is to determine the action u(i), i = 0, . . . ,N − 1 tominimize the system energy consumption given the initialstate s(0) and statistic traffic information λ(t), while at thesame time maintain a predefined blocking probability andavoid frequent mode switching. The problem formulation isdetailed in the next section.

4. Problem Formulation

In the literature, some algorithms have been proposed tominimize energy consumption for a given QoS requirement[2], [6]–[8]. However, these algorithms can not solve theproblem of avoiding frequent mode switching since it intro-duces time correlation, i.e., the actions taken in current timewill influence those taken in the future. DP algorithm [14]is an effective solution for such a complex time-correlatedproblem by optimizing the actions jointly over all the timeslots. Consequently, we formulate the problem as a DPproblem as follows.

A standard DP problem contains the following ele-ments: state, action, state transition and per-stage cost [14].The states and the actions are already described in Sect. 3.2.Note that the system state is actually (s(i), λ(i)), where λ(i) =

{λ(i)m }Mm=1, λ

(i)m = 1/τ(i+1)

∫ t(i+1)

t(i) λm(t)dt is the average arrivalrate during t(i) and t(i+1). We denote s(i) as the system statefor notation convenience, since λ(i) is system-determined pa-rameter and do not change with any action.

Given the current system state s(i) and the control ac-tion u(i), the state transition is determined by

s(i+1) = f (s(i), u(i)) = {|s(i)m − u(i)

m |}Mm=1. (6)

The per-stage cost function g(i)(s(i), u(i)) is composed ofthree parts. The first part is the energy consumption of BSoperation, which is calculated as

g(i)e (s(i), u(i))


=

M∑m=1

[s(i+1)

m Pmax + (1 − s(i+1)m )Pmin

]τ(i+1), (7)

where Pmax is the power consumption in active mode includ-ing signal processing, air-conditioning, power amplifier andetc, Pmin is the minimum power consumption in sleep modeto be able to wake up.

The second part is the BS mode switching cost

g(i)s (s(i), u(i)) =

M∑m=1

Esu(i)m , (8)

where Es is the cost of switching between active mode andsleep mode, which indicates the integration of device en-ergy cost, user handover signaling cost and etc. Minimiz-ing g(i)

s (s(i), u(i)) implies the reduction of No. of switching,which meets the object of avoiding frequent mode switch-ing.

Finally, according to the optimization problem, block-ing probability penalty should be integrated into the costfunction. To relate the BS sleeping action with blockingprobability, we define system blocking probability and areablocking probability below. The stage index i is ignored forsimplicity.

Definition 1. The system blocking probability at state s isthe probability that a newly arrived user k′ is blocked, i.e.,none of the active BSs can provide the required bandwidthto this user:

Psys(s) = Pr

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⋂

m∈M: sm=1,wmk′<∞

⎛⎜⎜⎜⎜⎜⎝wmk′ +∑

k

xmkwmk > Wmaxm

⎞⎟⎟⎟⎟⎟⎠⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ ,(9)

where binary variable xmk = 1 if user k is associated to BSm, and equals 0 otherwise. The summation is over all theexisting users in the system.

Definition 2. The area blocking probability of area A is theconditional probability that a user k′ arrived in A is blocked:

Pa(A, s) =

Pr

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⋂

m∈M: sm=1,wmk′<∞

⎛⎜⎜⎜⎜⎜⎝wmk′ +∑

k

xmkwmk > Wmaxm

⎞⎟⎟⎟⎟⎟⎠ |k′ ∈ A

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ .(10)

As the network is divided into multiple cells, the re-lationship between system blocking probability and areablocking probability is given by the law of total probabil-ity

Psys(s) =M∑

m=1

Pr(k′ ∈ Am)Pa(Am, s), (11)

where Am is the area of cell m. Since cell m can only be

covered by the BSs in Bm, the area blocking probability ofAm can be approximated as

Pa(Am, s) ≈ Pa(Am, sm), (12)

where

Pa(Am, sm) =

Pr

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⋂

n∈Bm: sn=1,wnk′<∞

⎛⎜⎜⎜⎜⎜⎝wnk′ +∑

k

xnkwnk > Wmaxn

⎞⎟⎟⎟⎟⎟⎠ |k′ ∈ Am

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠(13)

is the approximated area blocking probability, which is afunction of BS m’s local state

sm = {sm, sm(1), . . . , sm(B)} (14)

assuming that the BSs and users in all the other cells n �Bm are moved out of the system. Note that the summationis over the existing users in cell n ∈ Bm. It is derived inAppendix and is summarized below:

Pa(Am, sm) =∏

n∈Bm ,sn=1

(λ′nλ′n + μ

)Kmaxn

, (15)

where Kmaxn is expressed as (16), λ′n = λn +∑

j∈Bn∩Bm,s j=0 λ j/I j Monj , Rj = Rc

√(B/I jMon

j + 1), Monj =∑

j′∈B j∩Bms j′ , and I j = 1 if j = m and I j = 2 if j = m(b), b =

1, . . . , B. The operator ·� rounds the real number to thenearest integer no smaller than it.

It can be easily verified that a sufficient condition forPsys(s) ≤ Pthr is

Pa(Am, sm) ≤ Pthr, ∀ m, (17)

where Pthr is a given threshold. Then the blocking probabil-ity penalty is calculated as a sum of area blocking probabil-ity penalty of all cells

g(i)b (s(i), u(i)) =

M∑m=1

h(Pa(Am, s(i+1)), Pthr)

≈M∑

m=1

h(Pa(Am, s(i+1)), Pthr)

=

M∑m=1

h(Pa(Am, f (s(i)m , u

(i)m )), Pthr), (18)

where

u(i)m = {u(i)

m , u(i)m(1), . . . , u

(i)m(B)} (19)

is local action of BS m and f (s(i)m , u

(i)m ) = {|s(i)

n − u(i)n |}n∈Bm .

Note that the penalty is a function of the next system states(i+1) as the action taken in the current time spot is in chargeof the blocking probability in the next time interval.

The penalty cost function h is designed to maintain a


Kmaxn =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢R2

c Wmaxn

2r0

⎛⎜⎜⎜⎜⎜⎜⎜⎝1 +∑

j∈Bn∩Bm,s j=0

λ jIn

I jMonj λn

⎞⎟⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎜⎝∫ Rc

0

ldlC(l)

+∑

j∈Bn∩Bm ,s j=0

λ jIn

Bλn

∫ Rj

Rc

ldlC(l)

⎞⎟⎟⎟⎟⎟⎟⎟⎠−1⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥ , (16)

given blocking probability. Then it is set close to infinitywhen Pa(Am, sm) > Pthr to keep the blocking probabilitybelow the given threshold. Otherwise when the blockingprobability requirement is satisfied, i.e., Pa(Am, sm) ≤ Pthr,the penalty is zero. As a result, the penalty function can bewritten as

h(Pa(Am, sm), Pthr) ={EbPa(Am, sm), if Pa(Am, sm) > Pthr,0, else,

(20)

where Eb is a very large number.In summary, the per-stage cost is given by

g(i)(s(i), u(i)) = g(i)e (s(i), u(i)) + g(i)

s (s(i), u(i))

+g(i)b (s(i), u(i)), i = 0, 1, . . . ,N − 1, (21)

g(N)(s(N)) = 0. (22)

In this paper, given the traffic variation function λ(t)and the initial state s(0), we seek to minimize the total costof all stages

min{u(0),...,u(N−1)}

N−1∑i=0

g(i)(s(i), u(i)), (23)

and find an optimal control policy ν = {ν(0), ν(1), . . . , ν(N−1)}that satisfies

ν = arg min{u(0),...,u(N−1)}

N−1∑i=0

g(i)(s(i), u(i)). (24)

In next section, we first present the standard DP algo-rithm. Then by reducing the state size using per-cell Q-factor, a low-complexity algorithm is proposed. Also, BSsleeping related user association and handover control is dis-cussed, as well as implementation issues.

5. Dynamic Programming Algorithm

5.1 General Solution

DP solves a complex problem by breaking it down into sim-pler subproblems and tackling them recursively. The costminimization problem (23) can be solved by the standardDP algorithm taking the form [14]

J(N)(s(N)) = 0, (25)

J(i)(s(i))= minu(i)∈U

[g(i)(s(i), u(i))+J(i+1)( f (s(i), u(i)))

], (26)

where i = 0, 1, . . . ,N − 1, and the functions J(i)(s(i)) denotethe minimal cost for the tail subproblem that starts at time

spot i with initial state s(i). Proceeding backward inductionof Eq. (26) from N − 1 to 0, the optimal cost is equal toJ(0)(s(0)) for the given s(0). Furthermore, if ν(i) = u(i)(s(i))minimizes the right side of Eq. (26) for each s(i) and i, thepolicy ν = {ν(0), ν(1), . . . , ν(N−1)} is optimal.

Note that the cardinalities of the state space S and theaction space U are both 2M , which increase exponentiallywith the number of BSs M. Due to the curse of dimen-sionality (as termed in [14]), the computational requirementto obtain the optimal control policy is overwhelming if thenetwork size is large. As a consequence, it is very diffi-cult to implement the standard DP algorithm in practicalsystems. In the following, we introduce per-cell Q-factorestimation to reduce the size of state space and propose alow-complexity algorithm to simplify the decision process.

5.2 Q-factor and Space Reduction

Define the Q-factor [14] as follows:

Q(i)(s(i), u(i)) = g(i)(s(i), u(i)) + J(i+1)( f (s(i), u(i))), (27)

where i = 0, 1, . . . ,N − 1. It represents the cost of applyingthe action u(i) at the current state s(i) plus the minimal cost ofthe tail subproblem that starts at time spot i + 1 with initialstate s(i+1) = f (s(i), u(i)). According to (26) and (27), wehave

J(i)(s(i)) = minu(i)∈U

Q(i)(s(i), u(i)), (28)

Q(i)(s(i), u(i)) = g(i)(s(i), u(i))

+ minu(i+1)∈U

Q(i+1)( f (s(i), u(i)), u(i+1)). (29)

To reduce the size of state space, we approximate theQ-factor as a sum of per-cell Q-factors, i.e.,

Q(i)(s(i), u(i)) ≈M∑

m=1

Q(i)m (s(i)

m , u(i)m ), (30)

where the per-cell Q-factor is

Q(i)m (s(i)

m , u(i)m ) = g(i)

m (s(i)m , u

(i)m )

+minu(i+1)

m

Q(i+1)m ( f (s(i)

m , u(i)m ), u(i+1)

m ), (31)

which, similar to Q(i)(s(i), u(i)), is the local cost of applyingthe local action u(i)

m at the current local state s(i)m plus the

minimal local cost of the tail subproblem assuming the BSsand users in all the other cells are moved out of the sytem.The per-cell per-stage cost is

g(i)m (s(i)

m , u(i)m ) =

1B + 1

∑n∈Bm

{[s(i+1)

n Pmax


+(1 − s(i+1)n )Pmin

]τ(i+1) + Esu

(i)n

}+h(Pa(Am, f (s(i)

m , u(i)m )), Pthr), (32)

which includes the energy consumption and the switchingcost of the BSs in Bm, and the area blocking probability ofcell m. The per-cell Q-factor Q(i)

m (s(i)m , u

(i)m ) only needs the

information of the BSs in Bm, which indicates the limitedcooperation among neighboring BSs. It can be recursivelycalculated for each BS m ∈ M. The suboptimal controlpolicy is then given by

ν(i)(s(i)) = arg minu(i)∈U

M∑m=1

Q(i)m (s(i)

m , u(i)m ). (33)

Remark 1 (State Space Reduction): The size of statespace in each stage is substantially reduced from 2M (expo-nential growth w.r.t the number of BSs M) to M2B+1 (lineargrowth w.r.t. M).

Although the size of state space is reduced by intro-ducing per-cell Q-factor, the minimization progress (33),which requires exhaustive search over the action space U,is still of high complexity. Based on the per-cell Q-factor,we propose an iterative decision making algorithm. The ba-sic idea is to iteratively find the optimal local action ν∗m ={ν∗m, ν∗m(1), . . . , ν

∗m(B)} of each BS to minimize the sum of per-

cell Q-factors, and update the local elements of the globalaction accordingly. Until the sum of per-cell Q-factors doesnot decrease, the iteration terminates and the action is deter-mined simultaneously. The detailed description of the algo-rithm is summarized in Algorithm 1.

Algorithm 1 Action Iteration1: for i = 0 to N − 1 do2: Set u∗ = 0, Q = ∞,Qmin = Eb.3: while Qmin < Q do4: Set Q = Qmin.5: for m = 1 to M do6: Find the optimal local action ν∗m of the problem

minνm

m∑n=1

Q(i)n (s(i)

n , un), νm ∈ {0, 1}B+1,

where un is determined as: ul = u∗l , if l � Bm; ul = |u∗l −νl |, if l ∈ Bm.

7: Update u∗: if l ∈ Bm, u∗l = |u∗l − ν∗l |; else, u∗l = u∗l .8: end for9: Update Qmin =

∑Mn=1 Q(i)

n (s(i)n , u∗n).

10: end while11: Set ν(i) = u∗, s(i+1) = f (s(i), ν(i)).12: end for

Remark 2 (Action Space Reduction): In the greedysearch step 6, the size of decision space is 2B+1. Obviously,the iteration (from step 3 to step 10) converges in a finitenumber of iterations. Simulations show that the number ofiterations is no more than 4 mostly. As a result, the actionsearch complexity in each stage is reduced from O(2M) toO(M2B+1).

5.3 Systematic Design

Recall that during the time interval τ(i), i = 1, . . . ,N, theusers are served by the currently active BSs. At each timespot t(i), i = 0, 1, . . . ,N − 1, if a BS switches from activemode to sleep mode, the associated users are shifted to theactive neighbors. As the accessible BSs provide differentsignal strength and are of various load conditions, user as-sociation and handover should be carefully designed to op-timize resource allocation.

5.3.1 User Association

Load balancing scheme is implemented for the user asso-ciation to reduce system blocking probability. In the lit-erature, load balancing has been extensively studied andsome efficient scheduling methods have been proposed. Wemake use of the load-aware cell-site selection scheme [15].If user k arrives in cell m, its candidate serving BS set isCk = {n ∈ Bm|sn = 1}. The user selects the serving BSfrom Ck with higher channel quality C(lnk) and lower trafficload Wn as well, where Wn is the allocated bandwidth of BSn. Notice that there are several candidate serving BSs in Ck

and their remaining bandwidth maybe not enough to acceptuser k, that is, Wmax

n − Wn < wnk. Consequently, the usershould try the BSs in Ck one by one to reduce the blockingprobability. In the proposed algorithm, this is carried outby setting up a BS list according to both the channel qualityC(lnk) and the traffic load Wn, and searching from the top ofthe list. The algorithm terminates as long as the user can beaccepted. If none of the BSs can provide enough bandwidth,the user is blocked. The algorithm is detailed in Algorithm2. Note that | · | is the cardinality of a set.

Algorithm 2 User Association1: Set up a BS list Lk = {n1, n2, . . . |n j ∈ Ck} with cn1 ≥ cn2 ≥ . . ., where

cn = C(lnk)Wmaxn /Wn.

2: while |Ck | > 0 do3: Take BS n from the top of Ck.4: if Wmax

n −Wn ≥ wnk then5: xnk = 1, Wn = Wmax

n − wnk.The algorithm terminates.

6: else7: Remove n from Ck.8: end if9: end while

10: if |Ck | = 0 then11: User k is blocked.12: end if

5.3.2 User Handover

At each time spot t(i), i = 0, 1, . . . ,N − 1, the users whichassociate with the BSs turning from active mode to sleepmode, should change their association to the neighboringactive BSs. Denote


H (i) = {k|xmk = 1, s(i)m = 1, s(i+1)

m = 0,m ∈ M} (34)

as the set of users to be handed over. To minimize the num-ber of droppings, the handover algorithm also takes the ideaof load balancing. The process is similar with Algorithm 2except for the list setting up. As there are multiple users tobe simultaneously considered, we build up a BS-user pairlist instead of the BS list. Once a user handover is success,the pairs which contain the user are removed from the listimmediately. The algorithm does not terminate until the listbecomes empty. The users remained in H (i) are dropped.The handover algorithm is presented in Algorithm 3.

Algorithm 3 User Handover

1: Set up a BS-user pair list L(i) = {(m1, k1), (m2, k2), . . . |s(i+1)m j= 1, k j ∈

H (i),C(lm jk j ) > 0} with c(m1 ,k1) ≥ c(m2 ,k2) ≥ . . ., where c(m,k) =

C(lmk)Wmaxm /Wm.

2: while |L(i)| > 0 do3: Take the BS-user pair (m, k) from the top of L(i).4: if Wmax

m −Wm ≥ wmk and k ∈ H (i) then5: xmk = 1, Wm = Wmax

m − wmk, H (i) = H (i) \ {k}. Remove all thepairs (·, k) from L(i).

6: else7: Remove the pair (m, k) from L(i).8: end if9: end while

10: if H (i) � ∅ then11: Users k ∈ H (i) are dropped.12: end if

5.4 Implementation Issue

Since the proposed algorithm offers an off-line solution, dif-ferent policies are implemented for different traffic variationpattern. A typical example is that policies for workday andweekend should be distinguished.

In real networks, the statistic features of traffic distri-bution and variation may change. For instance, the increaseof the total number of subscribers enhances the average traf-fic intensity; a newly opened business center will become anew hotspot in the daytime, which changes the traffic distri-bution in space domain. To be able to track the long-termvariation of traffic, the system should establish a dataset andrecord the number of calls in each cell. Depending on thestatistic information obtained from the dataset, the systemcan operate the proposed algorithm to update the BS sleeppattern whenever necessary.

6. Simulation Study

The simulation layout is 10 by 10 hexagon cells with wrapup to avoid boundary effect, which is shown in Fig. 3. Thelink parameters are set according to ITU micro-cell test en-vironment [16]. The cell radius is Rc = 200 m. Accordingto the coverage assumption, the BS’s maximum coverage isset Rb = 520 m. We set Pmax = 1 kW which is a generalBS power level, and ignore the power consumption in sleep

Fig. 3 Simulation layout and a traffic distribution example. Nh = 3hotspots are formed and move along the red-dashed line anticlockwiseevery 24 hours a cycle. The highest load is λh(t), and the others areαlλh(t), l = 1, 2, 3, 0 ≤ α3 ≤ α2 ≤ α1 ≤ 1, respectively.

mode, i.e., Pmin = 0. Actually, we do not rely on the realvalue since the results are shown in terms of number of ac-tive BSs. Other than the bandwidth for interference manage-ment, the available bandwidth is Wmax

m = 5 MHz. User raterequirement is r0 = 122 kbps. Transmission duration param-eter is μ = 1/180 s−1. The transmit power is Pt = 41 dBm.The noise-plus-interference power N0 is calculated by set-ting the reference SNR at distance 200 m to be 0 dB. Path-loss model is PL dB(lmk) = 33.05+36.7 log10(lmk). The num-ber of user arrivals in each time interval is Kτ = 1×104. Theblocking probability penalty is Eb = 1×108 J and the thresh-old is Pthr = 1%. The time-varying and asymmetric trafficdistribution is configured according to [17] and detailed asfollows:

- Average arrival rate (or traffic intensity) of the wholenetwork λ(t) =

∑Mm=1 λm(t) varies along time domain

with period of T = 24h.- Nh hotspots are generated and move along some direc-

tions randomly every 24 hours a cycle. Assume eachhotspot covers 2-tiers of the hotspot center cell.

- Set the arrival rates of the hotspot center cells asλm(t) = λh(t). Then the arrival rates of the lst-tier ofhotspot center cells are λm(t) = αlλh(t), l = 1, 2, andthe others are λm(t) = α3λh(t), where 0 ≤ α3 ≤ α2 ≤α1 ≤ 1.

Figure 3 shows a traffic distribution example with Nh =

3 hotspots. The simulation is performed as follows. Wefirst calculate the sleeping policy with respect to the statistictraffic information λ(t) and the given initial state s(0). Thenthe random user arrival is generated in accordance with λ(t)to test the performance of the policy obtained by the pro-posed algorithm. The initial state s(0) is set by activatinghalf of the BSs in the network uniformly and then openingtwo more BSs in each hotspot. The mobility is consideredin two ways. Firstly, the handover caused by fast mobility isimplicitly modeled by user departure in one cell and arrival


Fig. 4 Number of active BSs compared with average traffic intensity intime space with different traffic configurations.

in another. Secondly, the slow mobility is represented by thehotspots movement.

6.1 BS Sleeping Pattern

In this part of simulation, parameter settings are: Es = 2.5×105 J/switch, α1 = 0.88, α2 = 0.63, α3 = 0.50.

BS mode switching behavior along with the averagetraffic intensity is presented in Fig. 4. It is shown that ourproposed DP algorithm tracks the variation of the averagetraffic intensity well in time domain with different simula-tion configurations. Note that for a given traffic intensityλ1, the curves of number of active BSs for Nh = 1 and3 are very close. The reason is that for a given averagetraffic intensity in each time period, the number of activeBSs required is almost the same to guarantee required wire-less resources. To illustrate the spatial consistency betweenthe traffic distribution and the number of active BSs, wetake the stage i = 20 with the traffic intensity λ1 and thenumber of hotspots Nh = 3 as an example. We calculates′m = s(i)

m +∑

m( j), j=1,...,Bs(i)

m( j)/2 to imply the number of active

BSs around each cell. Comparing Fig. 5 with Fig. 6, we cansee that more BSs are active in the highly loaded area, whileless BSs are active in the area with low load. Still, in thelow load area, there generally are some active BSs in orderto guarantee the network coverage. As a result, the activeBS distribution well meets the spatial distribution of trafficintensity.

In addition, the blocking probability in each time inter-val is maintained below the target (1%) almost all the time(see Fig. 7) for different traffic configurations. The averageblocking probability over 24 hours is around 0.3% for traf-fic intensity λ1, and is getting lower for higher traffic in-tensity λ2, which shows that the area blocking probabilityestimation is conservative, especially for high traffic sce-nario. More elaborate area blocking probability analysis canbe performed to further improve the energy saving perfor-mance.

Fig. 5 Traffic distribution in spatial domain (λ1,Nh = 3).

Fig. 6 BS state distribution in spatial domain (λ1,Nh = 3).

Fig. 7 System blocking probability variation versus time with differenttraffic configurations.

6.2 Comparing with Uniform BS Sleeping

We compare the proposed DP algorithm with the uniform BSsleeping approach proposed in [2], where active BSs are uni-formly located in the network with traffic intensity λ1 (seeFig. 4). In addition, since the sleep pattern is not restrictedas long as the coverage is guaranteed in our settings, the uni-form BS sleeping algorithm is modified from binary patterns


Fig. 8 Comparison of proposed DP BS sleeping algorithm and UniformBS sleeping algorithm.

to multiple patterns to track the time variation more flexibly.For comparison fairness, Algorithm 2 and Algorithm 3 areapplied for user association and user handover respectively.The number of active BSs are determined according to

Non(t) = 55 + 5 ×⌊5(λ(t) − λmin)λmax − λmin

⌋, (35)

which is a function of average traffic intensity λ(t), λmin <λ(t) < λmax. As a result, Non(t) ∈ {55, 60, · · · , 75}. Here�·� rounds the real number to the nearest integer no largerthan it. We set Nh = 3 and Es = 2.5 × 105 J/switch for thesimulations.

In Fig. 8, the average number of active BSs and the av-erage blocking probability are compared. Firstly, we setα1 = α2 = α3 = 1, which indicates the uniform trafficdistribution over the whole network. This is the same sce-nario studied in [2]. The proposed DP algorithm shows lit-tle energy cost and blocking probability decrease. This isbecause that the optimal solution for uniform traffic distri-bution should be turning off BSs uniformly. So intuitively,the uniform BS sleeping algorithm, which even though usesa pre-defined sleep pattern, performs very close to the op-timal solution. As a result, the proposed solution can notimprove very much. Then we decrease the value of α1, α2

and α3 to enhance the degree of asymmetric traffic distri-bution. As the traffic distribution becomes more and moreasymmetric, the performance gaps become larger. Specifi-cally, the improvement is small in number of active BSs, butis significant in blocking probability. The reason for smallimprovement in number of active BSs is stated in Sect. 6.1.While the proposed algorithm greatly reduces the blockingprobability since it optimizes the resource allocation amongspace domain according to the traffic distribution.

The figure also shows the following result, which isa little bit surprising: both the number of active BSs andthe blocking probability of the proposed DP algorithm de-crease as the parameters α1, α2 and α3 decrease. As a mat-ter of fact, the blocking events mainly comes from two as-pects: 1) blocking caused by over loading in the hotspotcells; 2) blocking caused by the high bandwidth require-ment of the users in sleeping cells, which are denoted as

Fig. 9 System blocking probability and dropping probability versusswitching cost Es. LB: proposed load balancing based BS selection anduser handover algorithm; SS: strongest signal based algorithm.

coverage edge users. In current simulation settings, the sys-tems is in low traffic scenario. As a consequence, the block-ing events caused by coverage edge users outweigh thosecaused by over loaded hotspot. As the traffic distributionbecomes more and more asymmetric, more and more usersare taken care of in the hotspots, and the number of cover-age edge users becomes less. Hence, the blocking probabil-ity becomes lower and more BSs can sleep. Note that if thesystem traffic is extremely high on the contrary, the blockingevents happened in hotspots outweigh those caused by cov-erage edge users, the blocking probability might increase.

6.3 Switching Cost

Extensive simulations are run to test the influence ofthe switching cost Es on the performance. We setλ1,Nh = 3, α1 = 0.88, α2 = 0.63, α3 = 0.50 for the simu-lations.

With different switching cost Es = 0, 2.5× 105, . . . , 1×106 (J/switch), the average numbers of active BSs in theperiod of 24 hours are 62.9, 63.9, 65.2, 66.0 and 67.2 re-spectively. The blocking probability and the dropping prob-ability are depicted in Fig. 9. The proposed load balancingbased algorithms for user association and handover are com-pared with the strongest signal based ones, where the selec-tion criterion is simply C(lmk) and the selection process issimilar with Algorithm 2 and 3. The result shows that byeffectively utilizing the wireless resources, load balancingis helpful for reducing the number of blocking and drop-ping events. It also illustrates that with the increase of Es,the energy consumption increases, while both the blockingprobability and the dropping probability decrease. It can beconcluded that there is a tradeoff between the energy savedfrom turning BSs into sleep mode and the energy cost ofBSs’ mode switching. Because high switching cost preventsthe BS switching from active to sleep, blocking probabilityis reduced.

Figure 10 shows the cumulative distribution function(CDF) of BS mode holding time. Without the switchingpenalty, more than 70% of BSs’ measured mode holding


Fig. 10 Cumulative distribution function of mode holding time withdifferent switching cost Es (J/switch).

Table 1 Handover performance with different switching cost.

Es (J/switch) switch/stage handover/stage dropping/stage

0 32.6 385.7 19.6

2.5 × 105 10.0 108.5 4.16

5 × 105 4.06 41.74 0.72

7.5 × 105 1.85 17.73 0.20

1 × 106 1.63 16.03 0.17

time is less than 1 hour. Such frequent mode switchingmaybe not acceptable for BS equipments in the real system.It not only consumes additional energy, but also brings largeamount of handover, which causes exploding signaling over-head and user QoS degradation (shown in Table 1). This re-sult explains the necessity of integrating switching cost intothe total cost. As the value of Es increase, the BS modeholding time increase accordingly, which shows that our al-gorithm well balances the tradeoff between energy savingfrom sleep and cost from switching.

7. Conclusion

In this paper, a low-complexity BS sleeping algorithm hasbeen proposed to find the suboptimal BS sleeping policyvia DP. With our strategy, network energy consumption isgreatly reduced while the required call blocking probabil-ity is guaranteed. The number of BSs in active mode wellmatches the variation of the network traffic in both timeand spatial domain. As a result, our algorithm outperformsthe existing uniform sleeping algorithm. By adjusting theswitching cost parameter Es, the tradeoff between the en-ergy saved from BS sleeping and the energy cost of BS modeswitching is well balanced. The limitation is that our algo-rithm relies on the traffic feature. If the traffic is uniformlydistributed, we can get little performance gain. Also if thetraffic is always heavy, our algorithm cannot work. Futurework may include integrating relaying and BS cooperationinto the energy saving framework to enhance coverage [18],and building a testbed to evaluate the performance in thereal system. In addition, more general energy consumptionmodel with multiple modes, other than the binary model

adopted in this paper, would be a valuable extension of thepresent paper.

Acknowledgments

The research work is partially sponsored by the NationalBasic Research Program of China (973 Program: No.2012CB316001); by the Nature Science Foundation ofChina (No.61021001, No.60925002); and by Hitachi R&DHeadquarter.

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Appendix: Derivation of Area Blocking Probability

In this section, we ignore the stage index i for simplicity.According to the fact that a newly arrived user in cell m isblocked if all the active BSs in Bm are out of bandwidth, wehave

Pa(Am, sm) = Pr

⎛⎜⎜⎜⎜⎜⎜⎝ ⋂n∈Bm ,sn=1

Wn ≥ Wmaxn

⎞⎟⎟⎟⎟⎟⎟⎠=

∏n∈Bm ,sn=1

Pr(Wn ≥ Wmaxn ), (A· 1)

where the second equality holds because the bandwidth uti-lization of BSs are independent with each other.

If sn = 1, n ∈ Bm, the users in cell n can be served byBS n. The density of users in cell n is Kn/πR2

c , where Kn

is the number of users in cell n. Under the assumption thatthe user distribution in each cell is uniform, the bandwidthutilization of BS n for the users in cell n is calculated as

Wnn =

∫ Rc

0wnk

Kn

πR2c

2πldl

= Kn2r0

R2c

∫ Rc

0

ldlC(l). (A· 2)

If s j = 0, j ∈ Bm, due to the nature of load balancingtechnique, the area of cell j is evenly assigned to its neighboractive BSs. Assume that the shifted traffic are uniformlydistributed in the 1/B annulus sector with larger radius Rj

and smaller radius Rc. The bandwidth requirement of theshifted traffic is

Wjn =

∫ Rj

Rc

wnkKj

πR2c

2πB

ldl

= Kj2r0

BR2c

∫ Rj

Rc

ldlC(l), (A· 3)

where Rj is set to evenly assign the cell area to its neighboractive BSs, i.e.,

Rj = Rc

√B

I jMonj

+ 1, (A· 4)

where Monj =

∑j′∈B j∩Bm

s j′ is the number of active neighbor

BSs of sleeping BS j, I j = 1 if j = m and I j = 2 if j =m(b), b = 1, . . . , B. Note that local information sets sm andλm do not contain the full local information of BS m(b), b =1, . . . , B. Therefore, we introduce the parameter I j assumingthat the local information of BS m(b) is symmetric, i.e., thestate and the arrival rate of BS j′ ∈ Bm(b) \ Bm are the same

as these of BS j′ ∈ Bm(b) ∩ Bm.In summary, the bandwidth utilization of active BS n is

Wn = Wnn +∑

j∈Bn∩Bm,s j=0

WjnIn

= K′nγn, (A· 5)

where K′n = Kn +∑

j∈Bn∩Bm,s j=0InKj/(I j Mon

j ) is the total num-

ber of user served by BS n, and

γn =

2r0

R2c

(∫ Rc

0ldl

C(l) +∑

j∈Bn∩Bm ,s j=0λ j In

Bλn

∫ Rj

Rc

ldlC(l)

)1 +

∑j∈Bn∩Bm ,s j=0

λ j In

I j Monj λn

, (A· 6)

where we make use of the fact that Kn/λn = Kj/λ j.At the same time, the traffic load in cell n is evenly

shifted to its neighbor active BSs. Similarly, we assume thathalf of the traffic of BS m(b), b = 1, . . . , B is shifted to ac-cessible active BSs in Bm. As a result, the traffic load of BSn(sn = 1) is

λ′n = λn +∑

j∈Bn∩Bm ,s j=0

λ j

I jMonj

. (A· 7)

As the radio resource is shared by active users, thenumber of users K′n associated with BS n evolves like thenumber of customers in a processor-sharing queue withPoisson arrivals and i.i.d. service times [19]. The key prop-erty of the processor-sharing queue is that the stationary dis-tribution of the number of customers is insensitive to thedistribution of service times. Hence the stationary distribu-tion of the number of active users is given by Pr(K′n = k) =(ρn)k(1 − ρn) with mean E[K′n] = ρn/(1 − ρn), where ρn isthe average traffic load of BS n. Applying Little’s law [20],we get E[K′n] = λ′n/μ, which results in ρn = λ

′n/(λ

′n + μ).

Finally, the area blocking probability is expressed as

Pa(Am, sm) =∏

n∈Bm ,sn=1

Pr(K′n ≥ Wmaxn /γn),

=∏

n∈Bm ,sn=1

ρWmax

n /γn�n . (A· 8)

Summarizing the equations derived above, we obtainthe expression of the approximated area blocking probabil-ity as stated in Sect. 4.

Jie Gong was born in Hunan in 1986. Hereceived his Bachelor’s degree in Department ofElectronic Engineering in Tsinghua University,Beijing, China, in 2008 and is currently a Ph.D.degree student there. His research interest is incooperative communication and green commu-nication.


Sheng Zhou was born in Shanghai in 1983.He received his B.S. degree from Tsinghua Uni-versity, Beijing, China, in 2005. Now he is aPh.D. candidate in Dept. Electronic Engineer-ing, Tsinghua University. His research inter-est includes resource allocation and transmis-sion protocol design for wireless MIMO sys-tems.

Zhisheng Niu graduated from NorthernJiaotong University, Beijing, China, in 1985,and got his M.E. and D.E. degrees from Toyo-hashi University of Technology, Toyohashi,Japan, in 1989 and 1992, respectively. In 1994,he joined with Tsinghua University, Beijing,China, where he is now a full professor at theDepartment of Electronic Engineering and thedeputy dean of the School of Information Sci-ence and Technology in charge of research activ-ities and international collaboration. He is also

an adjunction professor of Beijing Jiaotong University. From April 1992to March 1994, he was with Fujitsu Laboratories Ltd., Kawasaki, Japan.From October 1995 to February 1996, he was a visiting research fellowof the Communications Research Laboratory of the Ministry of Posts andTelecommunications of Japan. From February 1997 to February 1998, hewas a visiting senior researcher of Central Research Laboratory, HitachiLtd. He also visited Saga University, Japan, and Polytechnic University,USA, in 2001 and 2002, respectively. Prof. Niu’s current research inter-ests include teletraffic theory and queueing theory, performance evalua-tion of broadband multimedia networks, radio resource management, mo-bile Internet, wireless ad hoc networks and wireless sensor networks, andStratospheric Communication Systems. He received the PAACS Friend-ship Award from the IEICE of Japan in 1991 and the Best Paper Awardfrom the 13th Asia-Pacific Conference on Communications (APCC2007).Dr. Niu is a senior member of the IEEE and the Chinese Institute of Elec-tronics (CIE) and a fellow of the IEICE, Japan. He has been the TPC Chairof APCC2004 and the TPC Co-chair of IEEE ICC2008. He is now thedirector of IEEE Communication Society Asia-Pacific Board.

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