Admission Control Design for Integrated WLAN and ... - IEEE Xplore

IEEE WCNC'14 Track 2 (MAC and Cross-Layer Design)

Admission Control Design for Integrated WLAN and OFDMA-based Cellular Networks Phuong Luong, Tri Minh Nguyen, Long Bao Le, and Ngo.c-D˜ung Ðào

Abstract—We propose a QoS-aware admission control scheme (ACS) considering slow and fast calls for the integrated WLAN and OFDMA-based cellular network where only slow calls are allowed to connect with WLAN to maintain low handover overhead. The proposed ACS allows efficient traffic offloading from the macrocell to WLAN and considers QoS requirements for users in terms of minimum rates in all regions. The fractional frequency reuse (FFR) technique is assumed to be employed for interference mitigation in the cellular network. We also propose a novel bandwidth (BW) borrow-return strategy in the proposed ACS to improve the system performance. We then develop an analytical model to derive the blocking probabilities for calls in different areas. Numerical results demonstrate the performance enhancement of the ACS with the BW borrow-return strategy and the usefulness of the proposed analytical model in determining the size of WLAN offloading region.

I. I NTRODUCTION The explosive growth in mobile data traffic driven by advanced mobile devices such as smart phones and tablets has demanded to fundamentally improve the network capacity and coverage. Integration of Wifi and cellular radio access technologies (i.e., WCDMA, OFDMA cellular systems) is one of the key solutions for this problem [1], [2]. The WLAN/cellular interworking can be integrated at the access network level or core network level through an external Internet Protocol (IP) network. The dual mode mobile users can be equipped with multiple network interfaces to access both cellular network and WLAN. Such integration aims to exploit the fact that WLANs involve lower cost and can support higher data rates compared to wireless cellular networks. However, design of such integrated network is challenging since we need to guarantee quality of service (QoS) for the users, manage the network interference, and efficiently offload data traffic from the cellular to WLANs. Toward this end, an efficient admission control scheme must be designed considering user QoS constraints and mobilities [2]–[4]. There have been some efforts in designing admission control strategies for the integrated WLAN and cellular networks. In [2], the authors propose the so-called WLAN-first scheme to offload voice and data requests to the WLAN in the overlapped coverage area considering user QoS. In [4], an optimal admission control in integrated WLAN/CDMA cellular networks is developed to maximize the network revenue. In [3], user mobility is taken into account in the admission control scheme designed for the two-tier macro-micro cell network. In [5], the authors develop an analytical model for the soft fraction frequency reuse (FFR) in the macrocell network. These existing works focus on how to efficiently admit new and handoff calls as well as to optimize the radio Luong Phuong, Tri Minh Nguyen and Long Bao Le are with INRSEMT, University of Quebec, Montreal, QC, Canada; email: {luong.phuong, tri.nguyen, long.le}@emt.inrs.ca. Ngo.c-D˜ung Ðào is with Huawei Technologies Canada Co. Ltd., Ottawa, Canada; email: [email protected].

978-1-4799-3083-8/14/$31.00 ©2014IEEE

resource utilization (WLAN and cellular spectrum). None of these existing admission control strategies and analytical models considers the integrated WLAN and OFDMA-based cellular network that takes into account the impacts of physical characteristics on QoS constraints jointly with other design issues such as user mobility, traffic offloading region, and interference management. In this paper, we propose the QoS-aware admission control scheme (ACS) considering user mobility for both WLAN and OFDMA-based cellular networks. The proposed ACS only allows slow calls to be connected with the WLAN to maintain acceptable handover overhead and it permits calls to be overflowed from WLAN to the macrocell if the calls are blocked in the corresponding WLAN. Moreover, we describe a unified model that characterizes the achievable throughput of the CSMA protocol of WLANs and detailed channel and interference modeling for the FFR-based cellular network so that QoS guarantees for users located in cell-center area (CCA) and cell-edge area (CEA) (called cell-center users (CCUs) and cell-edge users (CEUs), respectively) can be explicitly considered. The proposed ACS also integrates a novel BW borrow-return mechanism where CCUs can borrow the celledge subchannels if needed and these borrowed subchannels are returned later when there are available subchannels in the CCA. We develop an analytical model where we derive call blocking probabilities in different macrocell and WLAN areas. Finally, we present numerical results to illustrate the admission control performance and demonstrate the performance enhancement due to the BW borrow-return strategy and usefulness of the analytical model. The remaining of this paper is organized as follows. In Section II, we present the system model. In Section III, the admission control policy is described whose performance is analyzed in Section IV. In Section V, numerical results are presented followed by conclusion in Section VI. Due to the space constraint, various detailed derivations and proofs are given in the online technical report [11]. II. S YSTEM M ODEL We consider the downlink communications of an integrated WLAN and OFDMA-based cellular network. We assume that there is a number of WLANs deployed within each macrocell of the cellular network whose macro base stations (MBSs) are located at the center of the cells. Users located in the basic coverage area (called 1W area) and extended coverage area of WLAN (called 2W area) whose radius from the WiFi Access Point (WAP) are R1 and R2 , respectively (shown in Fig. 1) are allowed to connect with the WAP if they are slow-speed users. Users in these areas are referred to as high data rate user (HRUs) and low data rate users (LRUs) classes, respectively. In addition, users located outside these WLAN 1W and 2W areas of any WLAN can only connect with the nearest MBS.

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Si denote the normalized throughput of a user of class i, which can be calculated as

R

Si =

Rc

K EU

KCU

R2 K EU

KCU

K EU KCU

Fig. 1.

(4)

where Ps = τ (1−τ )n1 +n2 −1 is the probability that a particular user transmits successfully; Tidle , T s and T c are the average idle, successful transmission and collision transmission duration. Derivations of these parameters are given in the online technical report [11]. Suppose users connected with WAP in the 1W and 2W areas require an average minimim rate of Si,th (b/s) for i=1, 2, respectively. Then, we have the following QoS constraints

f

R1

f

Ps Ts,i Tidle + T s + T c

Si × ri ≥ Si,th ,

f

i = 1, 2.

(5)

From this, we can obtain the set of all feasible combinations (n1 , n2 ) as Ωw = {(n1 , n2 ) : Si ri ≥ Si,th , i = 1, 2} each of which satisfies the QoS constraints in (5).

Integrated cellular/WLAN network

A. QoS Constraints in 802.11 WLAN Suppose that there are n users connected with a particular WAP and these users access the medium by using the distributed coordination function (DCF) based carrier sensing multiple access with collision avoidance (CSMA/CA) mechanism. We assume that all users operate in the saturated traffic regime (i.e., always have data to transmit). Let xi be the distance from the WAP to user i and Pw be the transmit power then the signal to noise ratio (SNR) Γiw at user i taking into account the path loss can be written as Γiw =

Pw hiw L(xiw ) pnoise

(1)

where hiw denotes the channel gain between the WAP and its user i accounting for the antenna gain, fading, and shadowing. In addition, L(xiw ) denotes the corresponding path loss and pnoise is the noise power. From this, we can determine the average rate for user i at distance xi as ∞ Bw log(1 + x)fΓiw (x)dx (2) ri = 0

where Bw is the WLAN communications bandwidth and fΓiw (x) denotes the probability density function of Γiw . To impose the QoS constraints for users in 1W and 2W areas of any WLAN in terms of minimum average rates, we focus on the worst case in the following where all n1 HRUs are located on the boundary of the WLAN 1W area and all n2 LRUs are located on the boundary of the WLAN 2W area where n1 + n2 = n. To proceed, we determine the throughput of one such worst user in each user class connecting with the WAP. Follow the work [6], we can compute the transmission probability τ and collision probability pc as follows: 2(1 − 2pc ) (W0 + 1)(1 − 2pc ) + pc W0 (1 − (2pc )m ) pc = 1 − (1 − τ )n1 +n2 −1 τ=

(3)

where m denotes the maximal number of backoff stages. Recall that ni denotes the number of users in class i with the same rate ri and corresponding successful transmission duration Ts,i and collision duration Tc,i where i = 1, 2. Let

B. QoS Constraints in Cellular Network 1) Strict FFR: We assume that strict FFR is employed [8] where users in each macrocell are divided into two groups: cell-center users (CCUs) and cell-edge users (CEUs) where CCUs are located inside CCA (called 1C area) and CEUs are located inside the CEA (called 2C area). Spectrum allocation under the strict FFR is illustrated in Fig. 1 for a cluster of 3 cells. Under this FFR scheme, we allocate a common band of size K CU to CCUs. The size of the band allocated to each CEA is equal to K EU = (Bc − K CU )/Δ where Bc is the total system bandwidth and Δ is the reuse factor. The neighboring MBSs are coordinated to ensure that their celledge bands are orthogonal as shown in Fig. 1. CEUs and CCUs are restricted to access only the cell-edge band and the cellcenter band, respectively. The transmit power from each MBS to its intended CCUs and CEUs on a particular subchannel is assumed equal to P0 [9]. Hence, the number of cell-center subchannels is k CU = K CU /W and the number of cell-edge subchannels is k EU = K EU /W where W is the bandwidth of one subchannel. 2) Signal to Interference plus Noise (SINR) Model: User i (CCU or CEU) connected with MBS m is interfered by other MBSs that use the same subchannel as user i. Let Q is the set of interfering MBSs of user i. Then, the SINR Γim achieved by user i associated with MBS m at distance xim on one particular subchannel can be written as 2

P0 |him | θim L(xim )

Γim =

l∈Q,l=m 2

2

2

P0 |hil | θil L(xil ) + N0 W

(6)

where |him | (|hil | ) is the channel gain on a particular subchannel from MBS m (interfering MBS l ∈ Q, l = m) to user i and distributed according to an exponential distribution with mean μ. In additions, θim (or θil ) represents the lognormal shadowing from MBS m (or MBS l) to user i, which is distributed according to a lognormal distribution 2 ) where A = 0.1 ln 10 is a scaling LN (Aμm,dB , A2 σm,dB constant and N0 is the noise power spectral density. Also, L(xim ) (or L(xil )) represents the path loss from MBS m (or MBS l) to user i at distance xim (or xil ). The average rate

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of user i (CCU or CEU) associated with MBS m at distance xim can be calculated as ∞ ζim = W log(1 + y)fΓim (y)dy (7) 0

where fΓim is the PDF of Γim that can be determined by numerical method and presented in the online technical report [11]. CU EU and ζmin be the minimum rates achieved by Let ζmin CU EU and ζmin is the worst CCUs and CEUs, respectively (ζmin calculated from (7) where the user is indoor (i.e., user in WLAN area is connected to MBS) and located at the largest distance from the MBS (xim = Rc for CCU and xim = R for CEU). To guarantee the QoS for CCUs and CEUs, the number of subchannels that must be allocated to any CCUs and CEUs in MBS m should satisfy the following constraints 1c ≥ ψm

CU EU rm rm 1c 2c = c ; ψ ≥ = c2c m CU EU ζmin ζmin

(8)

CU EU where rm , rm are the target minimum rates of any CCUs and CEUs in MBS m, respectively.

IV. P ERFORMANCE A NALYSIS A. Model Parameters For performance analysis, we assume an homogeneous system where there are m1 WLANs in the CCA and m2 WLANs in the CEA of any macrocell. We take the isolatedcell approach for performance analysis [3]. For simplicity, we omit the macrocell index m in all notations. In the following, the area in which there is only cellular service is called macrocell only area and the area in which there are both WLAN and cellular services is called double area. The new call arrivals to the macrocell only area and double area are assumed to follow independent Poisson processes. In our model, calls belong to either fast or slow type with probabilities of pf and 1 − pf , respectively. The conversation time and sojourn time for any call in different areas are assumed to be exponentially distributed. A fast call becomes a slow call whenever it enters the WLAN 2W area with probability γfc→w →s . A slow call associating with WLAN becomes a fast call or a slow call whenever it leaves WLAN 2W area and enters the macrocell w→c w→c , γs→s , respectively. only area with probabilities γs→f

III. A DMISSION C ONTROL P OLICY We propose a QoS- and mobility-aware ACS, which is described in the following. For a new slow call or a handoff slow call arriving at the WLAN areas (1W and 2W areas), we assume that it always attempts to connect with WLAN. The call is admitted to the corresponding WLAN if the resulting numbers of calls in both 1W and 2W areas belong to the feasible region of WLAN Ωw . Otherwise, it is blocked from accessing the WLAN and overflowed to the corresponding macrocell. If a slow call arrives at the CCA (i.e., a new slow call or a handoff slow call or an overflowed slow call from WLAN), it will attempt to occupy the cell-center subchannels. If there are not sufficient cell-center subchannels, it will attempt to borrow the cell-edge subchannels. If there are not sufficient cell-edge subchannels to support this call, then it is blocked (dropped). If cell-center subchannels becomes available later (due to a cell-center call termination or leaving), the cell-center slow calls occupying the cell-edge subchannels will be shifted back to cell-center subchannels. We refer to this as the BW borrow-return mechanism in this paper. If a slow call arrives at the CEA (i.e., a new or a handoff slow call or an overflowed slow call from WLAN to the CEA), it attempts to occupy the cell-edge subchannels. If there are not sufficient cell-edge subchannels, then it is blocked (dropped). The fast calls in the CCA and CEA are admitted or dropped similarly to the slow call in CCA and CEA. The handover of a fast call occurs when the corresponding user crosses the cell boundaries (cell-center boundary or celledge boundary) for a fast call or when a slow call leaves the WLAN 2W area and enters the macrocell only area and changes mobility type from slow call to fast call. The handover of slow call occurs as the corresponding user crosses the WLAN boundaries (WLAN 1W boundary and WLAN 2W boundary) or the macro-cell boundaries (cell-center boundary or cell-edge boundary) or when a fast call from macrocell enters the WLAN 2W area and changes to slow call type.

B. Analytical Method Recall that only slow calls can be connected to the WLAN in our proposed ACS. Let z1 (t), z2 (t) denote the number of slow calls located in the 1W and 2W areas of a particular WLAN at time t. Let us define the corresponding two-dimensional Markov Chain (MC) S(t) = {z1 (t), z2 (t)|(z1 (t), z2 (t)) ∈ Ωw } and let Z¯1 , Z¯2 represent the average values of z1 (t), z2 (t), respectively. In addition, let G(t) = {xs (t), xf (t), ys (t), yf (t), us (t), uf (t)|(xs (t) + xf (t))c1c ≤ k CU , (ys (t) + yf (t))c1c + (us (t) + uf (t))c2c ≤ k EU } describe the six-dimensional MC that models the number of slow calls and fast calls on the cell-center band and cell-edge band of a macrocell as being defined as follows: • • •

xs (t), xf (t) denote the numbers of cell-center slow and fast calls which occupy cell-center subchannels. ys (t), yf (t) denote the numbers of cell-center slow and fast calls which occupy cell-edge subchannels. us (t), uf (t) denote the numbers of cell-edge slow and fast calls.

¯s, X ¯ f , Y¯s , Y¯f , U ¯s , U ¯f denote the average values of the Let X corresponding quantities in MC G(t). In general, the two MCs S(t) and G(t) are coupled, which renders the exact analysis very challenging. To resolve this difficulty, we take an iterative analytical approach and analyze these two MCs in isolation [10]. Specifically, we perform stationary analysis for these two MCs in each iteration using the handoff rates, which are updated by using the analysis performed in the previous iteration. This process is repeated until convergence. In the following, we show how to analyze the two MCs S(t) and G(t) and how to update the handoff arrival rates for different areas by using these analytical models. All related parameters are summarized in Table I.

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TABLE I S YSTEM PARAMETERS Parameter

Meaning

m1 (m2 ) λm (λd ) θ c (θ e ) θ 1w (θ 2w ) μ−1 −1 −1 (ωf,2c ) ωf,1c −1 −1 (ωs,2c ) ωs,1c −1 −1 (ω2w ) ω1w (λn→2c ) λn→2c hf hs 2c→1c 2c→1c (λhs ) λhf 1c→2c 1c→2c (λhs ) λhf 1w→2w λhs 2w→1w λhs 2w→1c 2w→2c λhs (λhs ) 2w→1c 2w→2c λhf (λhf ) 1c→2w 2c→2w (λhf ) λhf 1c→2w 2c→2w (λhs ) λhs

Numbers of WLANs in CCA (CEA) Traffic density of new call in macrocell-only (double) area Cell-center (cell-edge) area WLAN 1W (WLAN 2W) area Mean conversation of a call Sojourn time of a fast call in the CCA (CEA) Sojourn time of a slow call in the CCA (CEA) Sojourn time of a call in 1W (2W) area Handoff rate for fast (slow) calls to the CEA from neighboring cell Handoff rate for fast (slow) calls to the CCA from the corresponding CEA Handoff rate for fast (slow) calls to the CEA from the corresponding CCA Handoff rate for slow calls to 2W area from the corresponding 1W area Handoff rate for calls to 1W area from the corresponding 2W area Handoff rate for slow calls to CCA (CEA) from 2W areas located in the corresponding area Handoff rate for fast calls to CCA (CEA) from 2W areas located in the corresponding area Handoff rate for fast calls from CCA (CEA) to 2W area due to mobility change Handoff rate for slow calls from CCA (CEA) to 2W area

1) Calculation of call arrival rates: The new slow calls arrival rates in 1W, 2W, CCA and CEA can be expressed as 1w 2w ; λ2w λ1w ns = λd (1 − pf )θ ns = λd (1 − pf )θ

areas located in CCA. The blocking probabilities in WLAN located in CEA is calculated similarly. The transition rates q(i, j) from predecessor state i into state j can be written as

c 2w c 2w λ1c ); λ1c ) q(z1 + 1, z2 ; z1 , z2 ) = (μ + ωs,1w )(z1 + 1); (z1 + 1, z2 ) ∈ Ωw ns = λm (1 − pf )(θ − m1 θ nf = λm pf (θ − m1 θ 2c e 2w 2c e 2w λns = λm (1 − pf )(θ − m2 θ ); λnf = λm pf (θ − m2 θ ). q(z1 , z2 + 1; z1 , z2 ) = (μ + ωs,2w )(z2 + 1); (z1 , z2 + 1) ∈ Ωw (9) q(z1 − 1, z2 ; z1 , z2 ) = λ1w,1c + λ2w→1w ; (z1 , z2 ) ∈ Ωw ns hs

In general, handoff events affect the system dynamics, which depend on the geographic configuration of the network [10]. To capture accurately the call handoff rates to different areas, we introduce teletraffic flow coefficients βi,j representing the average fractions of a call (slow or fast) which are handovered from area i to area j. In fact, βi,j can be calculated based on the perimeters of corresponding areas assuming that all moving directions are equally likely. Description of these coefficients is given in the online technical report [11]. Now, the handoff rates of slow calls or fast calls from the CCA and CEA to other areas can be expressed as

1w→2w q(z1 , z2 − 1; z1 , z2 ) = λ2w,1c + λ1c→2w + λ1c→2w + λhs ; ns hs hf (z1 , z2 ) ∈ Ωw (12)

where we assume that a suitable mapping is employed so that a state i can be mapped to the corresponding “expanded” state (z1 (t), z2 (t)). Let π(i) represent the stationary probability of state i where the states in the state space of S are labeled from 0 to smax . Given the above transition rates, the stationary probabilities of all states can be determined from the set of flow balance equations and the total probability property as follows:

¯s ; λn→2c ¯f = βn,2c ωs,2c U = βn,2c ωf,2c U λn→2c hs hf ¯s ; λ2c→1c = β2c,1c ωf,2c U ¯f λ2c→1c = β2c,1c ωs,2c U

hs 2c→2w λhs 2c→2w λhf 1c→2c λhf 1c→2w λhs 1c→2w λhf

s max

hf

q(i, j)π(i) = 0, j = 0, 1, . . . , smax ;

i=0

s max

π(i)

= 1.

i=0

¯s /m2 ; λ1c→2c ¯ s + Y¯s ) = β2c,2w ωs,2c U = β1c,2c ωs,1c (X hs c→w ¯ Let us define λ1w = λ1w,1c + λ2w→1w and λ2w = λ2w,1c + ns ns hs = β2c,2w ωf,2c γf →s Uf /m2 1c→2w 1c→2w 1w→2w + λ + λ . Then, we can calculate the λ hs hf hs ¯ f + Y¯f ) = β1c,2c ωf,1c (X blocking probabilities for slow calls in WLAN 1W and 2W ¯ s + Y¯s )/m1 = β1c,2w ωs,1c (X areas as c→w ¯ ¯ = β1c,2w ωf,1c γf →s (Xf + Yf )/m1 . (10) π(z1 , z2 ); B2w = π(z1 , z2 ) (13) B1w = Similarly, the handoff rates of slow calls from WLAN 1W (z1 ,z2 )∈S1 (z1 ,z2 )∈S2 area and 2W area to other areas can be calculated as where S1 and S2 are the sets of “blocking states” (z1 , z2 ), 2w→1w = ωs,1w Z¯1 ; λhs = β2w,1w ωs,2w Z¯2 λ1w→2w hs n1 , n2 ) : which are defined as S1 = {(z1 , z2 )|(z1 , z2 ) = ( 2w→1c w→c ¯ Z2 λhs = m1 β2w,1c ωs,2w γs→s n 1 = max {n1 } for (n1 , n2 ) ∈ Ωw } and S2 = 2w→1c w→c ¯ 2 ) : n 2 = max {n2 } for (n1 , n2 ) ∈ {(z1 , z2 )|(z1 , z2 ) = (n1 , n Z2 λhf = m1 β2w,1c ωs,2w γs→f Ωw }. 2w→2c w→c ¯ λhs = m2 β2w,2c ωs,2w γs→s Z2 Using the Little’s theorem, we can compute the average 2w→2c w→c ¯ Z2 . λhf = m2 β2w,2c ωs,2w γs→f (11) number of slow calls in WLAN 1W and 2W areas as 2) Stationary Analysis of the WLAN: As we defined before, MC S(t) = {z1 (t), z2 (t)|(z1 (t), z2 (t)) ∈ Ωw } captures the states of a particular WLAN. In the following, we show how to calculate the blocking probabilities in WLAN 1W and 2W

Z¯1 =

λ1w λ2w (1 − B1w ); Z¯2 = (1 − B2w ) μ + ωs,1w μ + ωs,2w

which are used to update the handoff arrival rates in (11).

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TABLE II I TERATIVE A LGORITHM FOR P ERFORMANCE A NALYSIS

3) Stationary Analysis of the Cell: We consider the isolated macrocell model represented by MC G(t) that depends on the process S(t) of WLANs. The MC G(t) has the state space G = {(xs , xf , ys , yf , us , uf )| 0 ≤ x ≤ k CU , 0 ≤ y + u ≤ k EU } where x = (xs + xf )c1c , y = (yz + yf )c1c and u = (us + uf )c2c . Since performing the stationary analysis of this 6-dimensional MC involves very high computational complexity, we propose to isolate the analysis of this MC into the analysis of cell-center and cell-edge chains and their dependence is captured through appropriate conditional probabilities. The cell-center model is represented by an MC G1c (t) with the state space G1c = {(xs , xf ); 0 ≤ x ≤ k CU } and the cell-edge one is described by the MC G2c (t) with a state space G2c = {(ys , yf , us , uf ); 0 ≤ y + u ≤ k EU }. 4) Stationary Analysis of the Cell-center: Let q 1c (i, j) ´f ) denote the transition rates from predecessor state i (´ xs , x to state j (xs , xf ) and π 1c (i) denote the stationary probability of state i for MC G1c (t). Let us define

Step 1: Initialize the values of all handoff arrival rates to be zero. ¯2 . ¯1 , Z Step 2: Analyze the MC S(t) and calculate Z Step 3: Analyze the MCs G1c (t) and G2c (t) and calculate ¯ f , Y¯s , Y¯f , U ¯s , U ¯f . ¯s , X X Step 4: Update handoff arrival rates using (10), (11) and return to Step 2 until convergence. TABLE III S IMULATION PARAMETERS

2c→1c + λ2w→1c + m1 (λ1w B1w + λ2w B2w ) λs,1c = λ1c ns + λhs hs

WLAN

Value

Cellular

Value

Pw hWAP niw Liw fc Bw W0 pnoise σ L1 /L2 SIF S/DIF S δ

0.1 W 10 m 1 10 dB 2.4 GHz 20 MHz 32 123 dB 20 μs 2304 bytes 10 μs/50 μs 1 μs

P0 hMBS nim Lim fc Bc W N0 σj CU rm EU rm kCU /kEU

20 W 25 m 1 12 dB 2 GHz 10 MHz 200 KHz 200 dB 8 dB 6 b/s/Hz 6 b/s/Hz 12

2c→1c λf,1c = λ1c + λ2w→1c . nf + λhf hf

Then, conditioning on the subset of the state space of G such that (y = 0, 0 ≤ y + u ≤ k EU ), the cell-center probability transition rates are given in the online technical report [11]. λf,1c λs,1c Let ρs,1c = μ+ω and ρf,1c = μ+ω . Denote the s,1c f,1c maximum number of calls can be occupied in the cell-center CU bands as Nc = kc1c . We can obtain the slow and fast call blocking probability given no cell-center slow and fast calls occupying the cell-edge subchannels (y = 0) as π 1c (xs , xf ) P (xs + xf = Nc |y = 0) = Nc

Bs,1c = Bf,1c = P (xs + xf = Nc , y + u > Λc )

¯ s + Y¯s = ρs,1c (1 − Bs,1c ); X ¯ f + Y¯f = ρf,1c (1 − Bf,1c ) X

xs

Let us denote B = P (xs + xf = Nc |y = 0). 5) Stationary Analysis of the Cell-edge: The MC of celledge G2c (t) has the state space G2c = {(ys , yf , us , uf ); 0 ≤ y + u ≤ k EU }. Let q 2c (i, j) denote the transition rates from ´s , u ´f ), to state j, predecessor state i, equivalent to (´ ys , y´f , u equivalent to (ys , yf , us , uf ). Denote π 2c (i) as the stationary probability of state i where the states in the state space G2c are 2c labeled from 0 to s2c max . The transition rates q (i, j) from state i to state j and the calculation of its stationary probabilities are presented in the online technical report [11]. Let us define the subset of state space G2c as Ω = {i representing states (ys , yf , us , uf ) : y + u > Λ} where Λ = k EU − c2c ). The blocking probability of slow and fast call in CEA can be obtained as π 2c (i). (15) Bs,2c = Bf,2c = P (y + u > Λ) = i∈Ω

Using the Little’s theorem, the average number of slow and fast calls in CEA can be computed as λs,2c ¯f = λf,2c (1 − Bf,2c ) (1 − Bs,2c ); U μ + ωs,2c μ + ωf,2c

which are used to update the handoff arrival rates in (10). We now derive the blocking probabilities of slow and fast calls in CCA. Recall that a cell-center call will be blocked if

(16)

where the derivation of Bs,1c = Bf,1c = P (xs +xf = Nc , y + u > Λc ) is given in the online technical report [11]. The average number of slow and fast calls in CCA can be computed by using the Little’s theorem

xs +xf =Nc

(Nc −xs ) /(Nc − xs )! xs =0 (ρs,1c ) /xs ! × (ρf,1c ) = . (14) Nc (N −x ) c s xs (ρf,1c )xf /xf ! xs =0 (ρs,1c ) /xs ! × xf =0

¯s = U

it cannot find sufficient subchannels, which are pre-allocated to CCA and CEA. Let us define Λc = k EU − c1c , then the blocking probability of slow and fast call in CCA can be calculated as

which are used to update the handoff arrival rates in (10). Summary of the proposed analytical framework is provided in Table II. V. N UMERICAL R ESULTS We evaluate the performance of proposed ACS for the setting where there are m1 = 20 and m2 = 80 WLANs in the CCA and CEA of each macrocell. We consider a multicell OFDMA downlink system with 19 macrocells and each macrocell has 48 subchannels over the system bandwidth of 10 MHz. The radius of a macrocell is set equal to R = 500 m and radius of CCA is set equal to Rc = 280 m. The path loss L(xiw ) for WLAN or L(xim ) for macrocells is calculated as [7] L(xiw ) = [44.9 − 6.55 log(hW AP )] log(xiw ) + 34.46 + 5.83 log(hW AP ) + 23 log(fc /5) + niw Liw , where hW AP is the height of WAP, fc is the carrier frequency, niw is the number of walls between WAP to user i and Liw is the wall loss from WAP to user i. L(xim ) is computed similarly. The new call arrival rate in each area is equal to the traffic density measured in calls/min/km2 multiplied with the corresponding area. We assume the traffic density in the WLAN 1W area is k times larger than that in other areas. Simulation parameters are summarized in Table III and Table IV. With the chosen simulation parameters in these two tables, we have c1c = 2 and c2c = 3. In Fig. 2(a), we illustrate the blocking probabilities of slow calls in WLAN 1W and 2W areas located in CCA versus the

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TABLE IV S IMULATION PARAMETERS

1.0

0.10 WLAN 1W area WLAN 2W area

Value

pf γfc→w →s w→c γs→s w→c γs→f ω1w

0.4 0.5 0.35 0.65 0.1

μ ωf,1c ωf,2c ωs,1c (ωs,2c ) ω2w

1 min 0.3 0.3 0.15 0.3

Blocking probability

Parameter


Value

CEA

0.8

0.08

Parameter

0.06

0.04

0.6

0.4

0.02

0.2

0.00

0.0

CCA

BW borrow-return no BW borrow-return

VI. C ONCLUSION In this paper, we have proposed an ACS for WLAN and OFDMA-based heterogeneous network considering user mobility and QoS requirements for users in terms of minimum rates in all regions. The proposed ACS also integrates the BW borrow-return strategy for CCA and CEA in macrocell to enhance the system performance. We have analyzed the blocking probabilities and demonstrated the performance enhancement

0

20 40 60 80 2 Traffic density (call/min/km )

100

20 40 60 80 2 Traffic density (call/min/km )

(a)

100

(b)

Fig. 2. (a) Blocking probability for calls connecting with WLAN in 1W and 2W areas (b) Blocking probability for calls connecting with MBS in CCA and CEA (k = 20, R1 = 10m and R2 = 30m). 0.20

0.45 λ = 10

0.40

λ = 15


0.15


traffic density where k is set equal to 20. This figure shows that the blocking probability in WLAN 1W area is smaller than that in WLAN 2W area and the difference between the two is larger as the traffic density becomes higher. This is because the average rate of HRUs is larger than that of LRUs. We do not show the blocking probabilities in WLAN 1W and 2W area in CEA since the results are quite similar. Fig. 2(b) shows the blocking probabilities of calls in CCA and CEA with and without employing the proposed BW borrow-return mechanism. Note that the blocking probabilities of the slow and fast calls are the same. Again, this figure demonstrates that the blocking probabilities in CCA and CEA increase with the traffic density. In addition, the blocking probability for calls in the CCA with BW borrow-return mechanism is much lower than that without using it. Moreover, the blocking probability of calls in CEA with and without employing the BW borrow-return mechanism is almost the same. This confirms the great advantage of this proposed mechanism. In Figs. 3(a), (b), we illustrate the blocking probabilities for calls connecting with WAP and MBS in different areas versus the radius R2 of WLAN 2W area, respectively. We show these results for the two different values of traffic density in the macrocell only area, namely λm = 10, 15 (calls/min/km2 ). The blocking probabilities for calls in WLAN 1W and 2W areas increase quickly as the radius R2 increases. This can be explained as follows. When the radius of WLAN 2W area increases, the data rate of LRUs decreases quickly, which reduces the feasible WLAN admission control region Ωw . Therefore, blocking probabilities of calls in WLAN 1W and 2W increase. In addition, as the radius R2 of WLAN 2W area increases, the blocking probabilities of calls in the WLAN 1W and 2W areas increase, which result in the increase of the overflowed traffic rate from WLAN to the macrocell. However, larger R2 implies that the lager volume of traffic is offloaded from the macrocell to the WLAN, which helps relieve the congestion in the macrocell area. Therefore, the blocking probabilities for calls in CCA and CEA decrease then increase as we increase R2 . These figures suggest that the good value of R2 to achieve the small blocking probabilities for calls in CCA and CEA would be about 15m, which demonstrates the usefulness of the analytical model.

WLAN 2W

0.10

0.05

λ = 15

0.30 0.25 0.20

CEA

0.15 0.10

WLAN 1W 0.00 30

λ = 10

0.35

32

34

36

38

40

42

44

Radius of WLAN 2W area (m)

46

48

50

CCA

0.05

0.00 10 12 14 16 18 20 22 24 26 28 30 32 34 Radius of WLAN 2W area (m)

(a)

(b)

Fig. 3. (a) Blocking probability for calls connecting with WLAN in 1W and 2W areas versus R2 (b) Blocking probability for calls connecting with MBS in CCA and CEA versus R2 (traffic density λm = 10, 15 calls/min/km2 ).

due to the BW borrow-return strategy and usefulness of the proposed ACS via numerical studies. R EFERENCES [1] M. Bennis, M. Simsek, A. Czylwik, S. Valentin and M. Debbah, “When cellular meets WiFi in wireless small cell networks,” IEEE Comm. Magazine, vol. 51, no. 6, June 2013. [2] W. Song, H. Jiang, and W. Zhuang, “Performance analysis of the WLAN-first scheme in cellular/WLAN interworking,” IEEE Trans. Wireless Commun., vol. 6, no. 5, May 2007. [3] K. Maheshwari and A. Kumar, “Performance analysis of microcellization for supporting two mobility classes in cellular wireless networks,” IEEE Trans. Vehicular Tech., vol. 49, no. 2, March 2000. [4] F. Yu and V. Krishnamurthy, “Optimal joint session admission control in integrated WLAN and CDMA cellular networks with vertical handoff,” IEEE Trans. Mobile Comp., vol. 6, no. 1, Jan. 2007. [5] S.P. Chung and Y-W. Chen, “Performance analysis of call admission control in SFR-based LTE systems,” IEEE Commun. Letter, vol. 16, no. 7, July 2012. [6] G. Bianchi, “Performance analysis of the IEEE 802.11 distributed coordination function,” IEEE J. Sel. Areas Commun., vol. 18, no. 3, March. 2000. [7] L. B. Le, D. Niyato, E. Hossain, D. I. Kim, and D. T. Hoang, “QoSaware and energy-eficient resource management in OFDMA femtocells,” IEEE Trans. Wireless Commun., vol. 12, no. 1, pp. 180-194, Jan. 2013. [8] G. Boudreau, J. Panicker, N. Guo, R. Chang, N. Wang, and S. v. Nortel, “Interference coordination and cancellation for 4G networks,” IEEE Commun. Mag., vol. 47, no. 4, pp. 74-81, Apr. 2009. [9] T. D. Novlan, R. K. Ganti, A. Ghosh, and J. G. Andrews, “Analytical evaluation of fractional frequency reuse for OFDMA cellular networks,” IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 4294-4305, Dec. 2011. [10] S. S. Rappaport and L-R. Hu, “Microcellular communication systems with hierachical macrocell overlays: Traffic performance models and analysis,” Proc. IEEE., vol. 82, no. 9, Sept. 1994. [11] P. Luong, T. M. Nguyen, L. B. Le, and N.-D. Dao, “Admission control design for integrated WLAN and OFDMA-based cellular networks,” Technical report. Online: http://www.necphylab.com/pub/ReportPhuong14.pdf

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