Call Dropping Performance Analysis of the enb-first Channel Access Policy in LTE-Advanced Relay Networks

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1 2011 IEEE 7th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob) Call Dropping Performance Analysis of the enb-first Channel Access Policy in LTE-Advanced Relay Networks Xian Wang, Shi-Jinn Horng, Ray-Guang Cheng, and Pingzhi Fan Department of Computer Science and Information Engineering National Taiwan University of Science and Technology (NTUST), Taipei 106, Taiwan Department of Electronic Engineering, NTUST, Taipei 106, Taiwan School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan , China Abstract Relay is one of the key technologies used by both the Third Generation Partnership Project (3GPP) Long Term Evolution-Advanced (LTE-Advanced) and IEEE m to ameliorate cell edge throughput. Despite the throughput enhancement achieved by deploying relay stations (RSs), wireless systems supporting relay are vulnerable to frequent handoffs, which deteriorate the dropping performance of realtime communications. This paper proposes a mathematical model to appraise the dropping performance of the enb-first channel access policy in LTE-Advanced relay networks. The enb-first policy prefers an enb-channel over a RS-channel when determining an access channel for a new and a handoff call. Closed-form analytical result is obtained for the dropping probability of the enb-first policy and based on the result a numerical study is conducted to evaluate the influences of various parameters on the dropping performance. The result developed in this paper can be used to adjust the call admission control strategies to get acceptable dropping performance in LTE-Advanced relay networks. I. INTRODUCTION Relay is one of the promising technologies harnessed by both the Third Generation Partnership Project (3GPP) Long Term Evolution-Advanced (LTE-Advanced) and IEEE m to fulfill the requirement for the peak data rate by International Mobile Telecommunications-Advanced (IMT- Advanced), 100 Mb/s for high mobility and 1 Gb/s for low mobility over a bandwidth of 100 MHz 1 3. In cellular systems, coverage and capacity deteriorate at cell boundary due to low Signal-to-Interference-plus-Noise-Ratio (SINR). The rationale of relay technology is to solve this problem by deploying relay stations (RSs) near to cell border and using them to relay radio transmissions between user equipments (UEs)/mobile stations and enode-b (enb)/base station (BS). However, despite the throughput enhancement achieved by deploying RSs, a wireless network supporting relay is vulnerable to the problem of frequent handoff, which can increase the possibility of an ongoing call being dropped, because normally the transmitting power of a RS is smaller than that of an enb and therefore the size of a RS-cell is smaller than that of an enb-cell. Call dropping performance is a crucial Qualityof-Service (QoS) metric concerning realtime communications, which are sensitive to call dropping. This paper concentrates on the dropping performance of LTE-Advanced supporting relay (hereafter referred to as LTE-Advanced relay networks). The results developed in this paper are also applicable to IEEE m, as in the two standards RSs operate in a similar way. In LTE-Advanced relay networks, when determining an access channel for a new and a handoff call, a UE has two options, to access a RS-channel (a channel provided by a RS) or an enb-channel (a channel provided by an enb). Generally, the SINR of a RS-channel is larger than that of an enbchannel and thus the UE can enjoy higher throughput (i.e., better call quality) by communicating through a RS-channel. Therefore, from the perspective of call quality the UE should choose a RS-channel. However, since the size of a RS-cell is usually smaller than that of an enb-cell, the UE has to perform more handoffs if it chooses a RS-channel and the possibility of the call being dropped increases. Then, from the perspective of call continuity the UE should select an enb-channel. We call the channel access scheme preferring a RS-channel over an enb-channel the RS-first policy and the opposite scheme the enb-first policy. Therefore, a tool providing insights into the dropping performance of the two policies is urgent for determining which channel access scheme should be adopted. In this paper we propose a mathematical model to evaluate the dropping performance of the enb-first policy. We derive closed-form analytical result for the dropping probability of the enb-first policy and based on the result conduct a numerical study to assess the influences of various parameters on the dropping performance. Network operators can avail of the result developed in this paper to adjust call admission control strategies for RSs and enbs to achieve acceptable dropping performance. The rest of this paper is organized as follows. Section II introduces the architecture of LTE-Advanced relay networks, the enb-first policy in detail, and the mobility model. In Section III a mathematical model is proposed to evaluate the dropping performance. Section IV conducts a numerical study to assess the effects of various parameters on the dropping performance. Section V concludes this paper /11/$ IEEE 43

2 Fig. 1. Architecture of LTE-Advanced relay networks. II. NETWORK ARCHITECTURE, CHANNEL ACCESS POLICY, AND MOBILITY MODEL A. Network Architecture Fig. 1 delineates a typical architecture of LTE-Advanced relay networks, where RSs are deployed near to the border of an enb-cell to improve the channel quality between enb and UEs locating in the border area. From a UE perspective, there is no difference between a RS-cell (the cell controlled by a RS) and an enb-cell (the cell controlled by an enb). A RS acts as an enb for UEs and has its own physical cell identity 4, 5. The architecture depicted in Fig. 1 only considers two-hop relay, which is supported by both LTE-Advanced and IEEE m 1. In Fig. 1 we call the direct wireless link between a UE and a RS/eNB the access link and the wireless link between a RS and an enb the relay link 6. In LTE- Advanced relay networks, the information element Cell Type, providing the coverage information of a cell 7, enables a UE to distinguish a RS-cell from an enb-cell. B. The enb-first Channel Access Policy The enb-first policy: For a new call taking place at a location dually covered by a RS and an enb, the order followed by the UE to request for admission is first the enb and then the RS. The RS is requested only when the admission request is denied by the enb. If both the enb and the RS reject the UE s request for admission, the new call is blocked. A new call originating in a position covered only by an enb requests for admission into the enb-cell; and the call is blocked if the request is rejected. Upon handoff, like the new call admission process, the enb-cell is first tried and then the RS-cell, when the UE is simultaneously covered by an enb and a RS; and if both the enb and the RS deny the UE s handoff request, the call drops. When only an enb-cell is available, the call drops if the handoff request is rejected by the enb. In Fig. 1 we assume that if a place is wirelessly covered by a RS then the place is also covered by the enb through which the RS connects to the radio access network. Therefore, in the enb-first policy we do not consider new and handoff calls occurring in a place solely covered by a RS. In the enb-first policy a UE handoffs its ongoing call only when the SINR of its current access link falls below the minimum SINR threshold required for maintaining the call. This handoff criterion is determined by the networkcontrolled UE-assisted handoff performed in LTE-Advanced relay networks 8. Network-controlled UE-assisted handoff means (a) that during a handoff process a UE is only responsible for measuring the signal strength of neighboring cells and reporting the measurements to the source RS/eNB, (b) that the handoff decision is made by the source RS/eNB, (c) and that only when the SINR of the UE s current access link is below the minimum SINR threshold does the source RS/eNB dictate the UE to perform handoff. Throughput this paper we assume that the SINR of an enb-channel is larger than the minimum threshold at any place within an enb-cell. This assumption in conjunction with the handoff criterion suggests that after a new or a handoff call is admitted by an enb, no handoff occurs during the remaining residence in the enb-cell. C. Mobility Model Fig. 2 shows the mobility model used in this paper. This model considers that a UE directionally moves alone a strip trace (e.g., a road or a street) seamlessly covered by enbs and that one RS is deployed at each side of an enb-cell. Let RS j and RS ' j be the RSs deployed at the two sides of enb j-cell. The coverage of enb j encompasses three parts, the shade area dually covered by RS j and enb j (called RS j -cell), the light area solely covered by enb j (called en j-cell), and the shade area covered by RS ' j and enb j (called RS ' j-cell). Denote by g (s) the Laplace transform of a function g(t), i.e., g (s) Lg(t) + t g(t)e st dt. All the random variables involved in this paper are continuous and non-negative. Since there are too many random variables in this paper, first we introduce the convention for defining notations for the probability density function (pdf) and the cumulative distribution function (CDF) of a random variable. In the following texts, so far as possible we use f X (t) and F X (t) to represent the pdf and the CDF of a random variable X, respectively, i.e., F X (t) Pr(X < t) t x0 f X (x)dx. Denote, respectively, by r j, t ' j, and r' j the residence times in RS j -cell, en j-cell, and RS ' j-cell. Here, we consider a homogeneous LTE-Advanced relay network, i.e., the structures of all the enb-cells in the network are statistically identical, which indicates (a) thatr 1,r 2,..., t ' 1,t ' 2,..., andr 1,r ' 2, '... are independent, (b) that r 1, r 2,..., and r 1 ', r' 2,... are identically distributed with a common pdf f R (t) and a common CDF F R (t), (c) and that t ' 1, t ' 2,... are identically distributed with a common pdf f (t) and a common CDF F (t). Define t j t ' j +r' j, j 1,2,... Denote by f B (t) and F B (t) the pdf and the CDF of t j, respectively. Due to the independence of t ' j and r j ', it follows 44

3 Fig. 2. Mobility model. that f B (s) f (s)f R (s). In this paper we assume that r j (r j ' ) and t' j are generally distributed and that Er j (r j ' ) 1/ and Et ' j 1/µ. Then, according to the directional mobility model the mean residence time in an enb-cell is Er j +Et ' j+er j ' µ In general, the probability that a new call originates in a RScell (RS ' -cell) or an en -cell is directly proportional to the corresponding mean residence time, i.e., Pr(a call originates in a RS-cell (or a RS ' -cell)) Er j (r ' j ) Er j +Et ' j +Er' j Pr(a call originates in an en -cell) Et ' j Er j +Et ' j +Er' j µ, +2µ. +2µ Denote by P RN and P RH the new call and the handoff call blocking probability at a RS, respectively, with which the RS denies the admission requests of a new call and a handoff call. Let P BN and P BH be the new call and the handoff call blocking probability at an enb, respectively. These four probabilities depend on the call admission control strategies of RSs and enbs, and can be changed to achieve acceptable dropping performance. III. ANALYSIS OF THE CALL DROPPING PROBABILITY Proposition: Supposing that X, exponentially distributed with mean 1/µ, Y 1, Y 2,..., and Y k are k+1 independent random variables, it follows that Pr(X > Y 1 +Y 2 + +Y k ) k fy i (µ), k 1,2,... i1 Proof: Pr(X > Y 1 +Y 2 + +Y k ) { + + y 10 y y k 0 x k j1 yj k } f Yi (y i )µe µx dxdy k dy 2 dy 1 i1 k fy i (µ) i1 which completes the proof. The call dropping probability, denoted by P D, is defined as the probability that a call admitted by a cellular network is blocked during handoff. It follows from this definition that where P D Pr(a call drops the call is admitted) P n P a (1) It follows that P a Pr P n Pr(an admitted call drops), P a Pr(a call is admitted). ( a call originates in a RS-cell, or an en -cell, or a RS ' -cell, and is admitted Pr(a call originates in a RS-cell and is admitted) +Pr(a call originates in an en -cell and is admitted) +Pr(a call originates in a RS ' -cell and is admitted) 2µ (1 P RN P BN )+ (1 P BN ). +2µ +2µ (2) Denote by < X, Y > the event that a new call originates in X-cell and is admitted by Y, X {RS, en, RS ' } and Y ) 45

4 {RS, enb, RS ' }. The quantity P n can be decomposed as P n Pr(an admitted call drops) where Pr(< RS, RS > and the call drops) +Pr(< RS, enb > and the call drops) +Pr(< en, enb > and the call drops) +Pr(< RS ', enb > and the call drops) +Pr(< RS ', RS ' > and the call drops) Pr(< RS, RS >)P LL +Pr(< RS, enb >)P LB +Pr(< en, enb >)P BB +Pr(< RS ', enb >)P RB +Pr(< RS ', RS ' >)P RR (3) P LL Pr(a call drops < RS, RS >), P LB Pr(a call drops < RS, enb >), P BB Pr(a call drops < en, enb >), P RB Pr(a call drops < RS ', enb >), P RR Pr(a call drops < RS ', RS ' >). In the enb-first policy, we have Pr(< RS, RS >) Pr(< RS ', RS ' >) µ P BN (1 P RN ), (4) +2µ Pr(< RS, enb >) Pr(< RS ', enb >) µ (1 P BN ), (5) +2µ Pr(< en, enb >) (1 P BN ). (6) +2µ A. The Derivation of P LL Fig. 3 shows a timing diagram for the derivation of P LL, where a UE initiates a new call in RS 1 -cell and traverses K enb-cells before completing the call in enb K+1 -cell. Denote by t c with pdf f c (t) the call holding time, which is the time a UE intends to remain active after initiating a call 9. Assume that t c follows an exponential distribution of mean 1/µ c, i.e., the pdf of t c is f c (t) µ c e µct, t 0. Denote by χ(r 1 ) with pdf f χ(r) (t) the time interval between the initiation of the call and when the UE moves out of RS 1 - cell. It follows from the residual life theorem that χ(r 1 ) is the residual distribution of r 1 10, i.e., + f χ(r) (t) f R (τ)dτ 1 F R (t), τt f χ(r) (s) 1 fr (s). s Referring to Fig. 3, it follows that P LL Pr(a call drops < RS, RS >) Pr(t c > χ(r 1 ))P BH Pr(t c > χ(r 1 )+t 1 + +r K +t K ) (1 P BH ) + (1 P BH )(1+P BH P RH P BH ) K 1 P RH P BH Pr(t c > χ(r 1 )+t 1 + +t K +r K+1 ) (1 P BH ) + (1 P BH )(1+P BH P RH P BH ) K 1 P BH (1 P RH )P BH (7) where the first, the second, and the third items represent, respectively, the probabilities that the call is blocked at positions P 1, P 2, and P 3 shown in Fig. 3. The second item can be parsed as Pr(t c > χ(r 1 )+t 1 + +t K ) Pr(the UE can reach P 2 ) (1 P BH ) Pr(the call handoffs successfully at P 1 ), (1 P BH )(1+P BH P RH P BH ) K 1 (1 P BH )+P BH (1 P RH )(1 P BH ) K 1 ( ) the call is not blocked when the UE Pr, traverses enb 2 -cell,...,and enb K -cell P RH P BH Pr(the handoff at position P 2 fails). Applying the proposition to (7) leads to { } P BH fχ(r) (µ c) 1+(1 P BH )P RH fr (µ c)fb (µ c) P LL 1 (1 P BH )(1+P BH P RH P BH )fr (µ c)fb (µ. c) (8) B. The Derivation of P LB On the analogy of the derivation of P LL, it follows from Fig. 3 that P LB Pr(a call drops < RS, enb >) Pr(t c > χ(r 1 )+t 1 + +r K +t K ) (1 P BH )(1+P BH P RH P BH ) K 1 P RH P BH Pr(t c > χ(r 1 )+t 1 + +t K +r K+1 ) + (1 P BH )(1+P BH P RH P BH ) K 1 P BH (1 P RH )P BH P BH fχ(r) (µ c)fb (µ c) P RH +P BH (1 P RH )fr (µ c) 1 (1 P BH )(1+P BH P RH P BH )fr (µ c)fb (µ c). The difference between the last equation and (7) is due to the fact that the handoff at position P 1 in Fig. 3 in the case of < RS, RS > is sidestepped in the case of < RS, enb >. (9) 46

5 Fig. 3. Timing diagram for the derivations of P LL and P LB. Fig. 4. Timing diagram for the derivation of P BB. C. The Derivation of P BB Fig. 4 depicts a timing diagram for the derivation of P BB, where a UE starts a new call in en 1-cell. Denote by χ(t ' 1) with pdf f χ(b )(t) the time interval between the beginning ' of the new call and when the UE moves out of en 1 -cell. According to the residual life theorem 10, χ(t ' 1 ) follows the residual distribution of t ' 1, i.e., f χ( )(t) µ + τt f (τ)dτ µ 1 F (t), f χ( ) (s) µ 1 f B (s) '. s Referring to Fig. 4, we have P BB Pr(a call drops < en, enb >) Pr(t c > χ(t ' 1 )+r' 1 + +r K +t K ) (1 P BH )(1+P BH P RH P BH ) K 1 P RH P BH Pr(t c > χ(t ' 1)+r 1 ' + +t K +r K+1 ) + (1 P BH )(1+P BH P RH P BH ) K 1 P BH (1 P RH )P BH P BH f χ(b ' ) (µ c)fr (µ c) P RH +P BH (1 P RH )fr (µ c) 1 (1 P BH )(1+P BH P RH P BH )fr (µ c)fb (µ c). (10) D. The Derivations of P RB and P RR Fig.5 shows a timing diagram for the derivations ofp RB and P RR, where a UE commences a new call in RS ' 1-cell. Denote by χ(r 1 ' ) the time interval between the commencement of the new call and when the UE moves out of RS ' 1-cell. The residual life theorem reveals that χ(r 1 ' ) follows the residual distribution of r 1 ' 10. Since r 1 and r 1 ' are identically distributed, χ(r 1) ' and χ(r 1 ) (cf. Fig. 3) are also identically distributed and thus share the common pdf f χ(r) (t). Note that in the current case whether the new call is admitted by RS ' 1 or by enb 1 exerts no impact on the subsequent handoffs performed by the UE. It follows that P RB Pr(a call drops < RS ', enb >) P RR Pr(a call drops < RS ', RS ' >) Pr(t c > χ(r 1)+ +r ' K +t K ) (1 P BH )(1+P BH P RH P BH ) K 1 P RH P BH Pr(t c > χ(r 1 ' )+ +r K +t K +r K+1 ) + (1 P BH )(1+P BH P RH P BH ) K 1 P BH (1 P RH )P BH P BH fχ(r) (µ c) P RH +P BH (1 P RH )fr (µ c) 1 (1 P BH )(1+P BH P RH P BH )fr (µ c)fb (µ c). (11) 47

6 Fig. 5. Timing diagram for the derivations of P RB and P RR. E. The Dropping Probability of the enb-first Policy Combing equations (1) (6) and (8) (11), we finally reach the call dropping probability of the enb-first policy µ P BN (1 P RN )P BH fχ(r) +2µ (µ c) { } 1+(1 P BH )P RH f R(µ c )fb(µ c ) µ + (1 P BN )P BH fχ(r) +2µ (µ c)f B(µ c ) P RH +P BH (1 P RH )fr (µ c) + (1 P BN )P BH f χ(b +2µ ' ) (µ c)fr (µ c) P RH +P BH (1 P RH )fr (µ c) µ + (1 P RN P BN )P BH fχ(r) µ R +2µ (µ c) P RH +P BH (1 P RH )fr(µ c ) P D. 1 (1 PBH )(1+P BH P RH P BH ) fr (µ c)fb (µ c) 1 2µ P RNP BN + P BN +2µ (12) F. Validity Check In this section we use a special case, P RN P RH 1, to demonstrate the validity of the result derived in this paper. In this case, the RNs in LTE-Advanced relay networks do not function and all the new and handoff calls are handled by the enbs. Thus, when P RN P RH 1, the LTE-Advanced relay network reduces to a personal communication service (PCS) network without relay architecture, whose dropping performance has been extensively studied in the literature In under the assumption that both the call holding time and the cell residence time are generally distributed, Fang, Chlamtac, and Lin investigated the call dropping performance for the PCS network. Denote by p f the handoff call blocking probability at a BS, by f(t) the pdf of the cell residence time, and byf r (t) the pdf of the residual cell residence time. The dropping probability of the PCS network is given by P D,PCS p Ω c Res zp p f f r (z) z1 (1 p f )f (z) f c ( z) which is obtained by making some necessary modifications to the original formulas developed in 13, (7), 14, (13), and 15, (29) so the definition for the call dropping probability in keeps consistent with the one adopted in this paper. Since in this paper we assume that the call holding time is exponentially distributed (i.e., Ω c {µ c }), it follows from the last equation that P D,PCS p f f r(µ c ) 1 (1 p f )f (µ c ). (13) In LTE-Advanced relay networks, a UE can initiate a new call in a RS-cell, an en -cell, and a RS ' -cell. It follows from Figs. 3 5 that, when the new call is initiated in a RScell, an en -cell, and a RS ' -cell, the corresponding residual cell residence times are χ(r 1 ) + t 1, χ(t ' 1) + r ' 1, and χ(r ' 1), respectively. Therefore, when P RN P RH 1, the LTE- Advanced relay network becomes the PCS network where the associated parameters are embodied as µ p f P BH, f (s) f R (s)f B (s), fr (s) fχ(r) +2µ (s)f B (s)+ f χ(b +2µ ' ) (s)f R (s) µ + fχ(r) +2µ (s). Substituting the above equations into (13), we get the dropping probability for the current case, which can also be reached by substituting P RN P RH 1 into (12). IV. NUMERICAL STUDY In this section we employ some numerical examples to evaluate the influences of various parameters upon the dropping performance of the enb-first policy. Throughout this section except otherwise stated we make the following assumptions. (a) The RS j -cell (RS ' j -cell) residence time r j (r j ' ) and the en j -cell residence time t ' j follow exponential distributions of means 1/ and 1/µ, respectively. (b) Let 1/µ c 5, (1/µ )/(1/ ) /µ 9, and P RN,P RH,P BN,P BH 48

7 P RN 0.01, 0.20, 0.30, 0.10 P RN 0.80, 0.20, 0.30, 0.10 P RN 0.40, 0.20, 0.01, 0.10 P RN 0.40, 0.20, 0.80, γ R 10, γ B 1 γ R 0.1, γ B 1 γ B 10, γ R 1 γ B 0.1, γ R 1 call dropping prob.( 10-2 ) call dropping prob.( 10-2 ) µ / c µ / c Fig. 6. Call dropping probability versus /µ c. Varying the new call blocking probabilities at a RS and an enb P RN and P BN. call dropping prob.( 10-2 ) P RN 0.40, 0.01, 0.30, 0.10 P RN 0.40, 0.80, 0.30, 0.10 P RN 0.40, 0.20, 0.30, 0.01 P RN 0.40, 0.20, 0.30, µ / c Fig. 7. Call dropping probability versus /µ c. Varying the handoff call blocking probabilities at a RS and an enb P RH and P BH. 0.4, 0.2, 0.3, 0.1. Note that these values are randomly selected for a demonstrating purpose. Figs. 6 and 7 assess the influences of the new call and the handoff call blocking probability at a RS and an enb on the dropping performance. From the two figures we can draw the following conclusions. (a) The dropping probability rises with the increase of /µ c. (b) Compared with the handoff call blocking probabilities P RH and P BH, the new call blocking probabilities P RN and P BN have no pronounced effect on the dropping performance. (c) The effect of P BH is far more obtrusive than that of P RH, because handoff to an enb cannot be averted when 1/µ c is larger. Fig. 8 appraises the sensitivity of the dropping performance to the variances of the RS j -cell (RS ' j -cell) residence time r j (r j ' ) and the enb' j -cell residence time t' j. In Fig. 8 r j and t ' j Fig. 8. Call dropping probability versus /µ c. Varying the variances of the RS j -cell (RS ' j -cell) residence time r j (r j ' ) and the enb' j-cell residence time t ' j. follow gamma distributions of shape parameters γ R and γ, and scale parameters 1/(γ R ) and 1/(γ µ ), respectively, i.e., ( ) γr fr (s) γr, s+γ R ( ) γb f ' (s) γµ. s+γ µ The means and the variances of r j and t ' j are 1/ and 1/µ, and 1/(γ R µ 2 R ) and 1/(γ µ2 B ), respectively. The variances of ' r j and t ' j magnify 100 times when γ R and γ change from 10 to 0.1. Fig. 8 suggests that the variances of r j and t ' j have no palpable influence on the dropping performance. Therefore, we can use exponential distributions to model the RS j -cell (RS ' j- cell) and the en j-cell residence time without causing big discrepancy in the dropping probability. V. CONCLUSIONS Relay is one of the crucial technologies employed by both 3GPP LTE-Advanced and IEEE m, two candidate standards for IMT-Advanced, to improve the cell edge throughput. Despite the throughput benefit achieved by RSs, RSs make wireless systems vulnerable to frequent handoffs, which degrade the dropping performance of realtime communications. This paper has proffered a mathematical model to evaluate the dropping performance of the enb-first channel access policy, which favors an enb-channel over a RS-channel when determining an access channel for a new and a handoff call. Closed-form analytical formula has been derived for the dropping probability of the enb-first policy and based on the formula a numerical study has been carried out to assess the influences of various parameters on the dropping performance. The model proposed in this paper can be exploited to adjust the call admission control strategies of RSs and enbs to 49

8 get acceptable dropping performance in LTE-Advanced relay networks. Note that the call dropping performance is dictated by the call holding time t c, the RS-cell and en -cell residence times r j and t ' j, and the new call and handoff call blocking probabilities at a RS and an enb. Since it is shown that the dropping performance is insensitive to the variances of r j and t ' j, exponential distributions can be used to fit the field data of t c, r j, and t ' j. Since there is only one parameter, the mean, associated with an exponential distribution, it is trivial to model the field data by exponential distributions. With the distributions of t c, r j, and t ' j at hand, the dropping probability now depends only on the new call and handoff call blocking probabilities at a RS and an enb, which are results of the call admission control strategies of RSs and enbs. Thus, through adjusting the call admission control strategies acceptable dropping performance can be reached. ACKNOWLEDGMENT This work was supported by the National Science Foundation of China under Grants and , by the 111 project under Grant , by Doctoral Program Foundation of Institutions of Higher Education of China under Grant , by the Fundamental Research Funds for the Central Universities under Grant 2009QK18, and by the Open Research Fund of Key Laboratory of Information Coding and Transmission, Southwest Jiaotong University. REFERENCES 1 Y. Yang, H. L. Hu, and G. Q. Mao, Relay technologies for WiMAX and LTE-Advanced mobile systems, IEEE Commun. Mag., vol. 47, no. 10, pp , Oct K. Loa, C.-C. Wu, S.-T. Sheu, and et al, IMT-Advanced relay standards, IEEE Commun. Mag., vol. 48, no. 8, pp , Aug A. Hashimoto, H. Yorshino, and H. Atarashi, Roadmap of IMT- Advanced development, IEEE Microw. Mag., vol. 9, no. 4, pp , Aug GPP TR V9.0.0, Further advancements for E-UTRA physical layer aspects, Tech. Spec. Group Radio Access Network Rel. 9, Mar S. W. Peters and R. W. H. Jr., The future of WiMAX: Multihop relaying with IEEE j, IEEE Commun. Mag., vol. 47, no. 1, pp , Jan S.-R. Yang, C.-C. Kao, W.-C. Kan, and T.-C. Shih, Handoff minimization through a relay station grouping algorithm with efficient radioresource scheduling policies for IEEE j multihop relay networks, IEEE Trans. Veh. Technol., vol. 59, no. 5, pp , Jun GPP TS V10.0.0, X2 Application Protocol (X2AP), Tech. Spec. Group Radio Access Network Rel. 10, Dec GPP TS V10.2.0, Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Overall description, Tech. Spec. Group Radio Access Network Rel. 10, Dec P. V. Orlik and S. S. Rappaport, A model for teletraffic performance and channel holding time characterization in wireless cellular communication with general session and dwell time distributions, IEEE J. Sel. Areas Commun., vol. 16, no. 5, pp , Jun D. R. Cox, Renewal Theory, 2nd ed. London: Methuen, M. A. Marsan, G. Ginella, R. Maglione, and M. Meo, Performance analysis of hierarchical cellular networks with generally distributed call holding times and dwell times, IEEE Trans. Wireless Commun., vol. 3, no. 1, pp , Jan W. Li, Y. Fang, and R. R. Henry, Actual call connection time characterization for wireless mobile networks under a general channel allocation scheme, IEEE Trans. Wireless Commun., vol. 1, no. 4, pp , Oct Y. Fang, I. Chlamtac, and Y.-B. Lin, Call performance for a PCS network, IEEE J. Sel. Areas Commun., vol. 15, no. 8, pp , Oct , Modeling PCS networks under general call holding time and cell residence time distributions, IEEE/ACM Trans. Netw., vol. 5, no. 6, pp , Dec Y. Fang, Modeling and performance analysis for wireless mobile networks: A new analytical approach, IEEE/ACM Trans. Netw., vol. 13, no. 5, pp , Oct S. Pattaramalai, V. A. Aalo, and G. P. Efthymoglou, Evaluation of call performance in cellular networks with generalized cell dwell time and call holding time distributions in the presence of channel fading, IEEE Trans. Veh. Technol., vol. 58, no. 6, pp , Jul V. A. Aalo and G. P. Efthymoglou, Evaluation of call dropping probability for a heterogeneous wireless network with uniformly distributed handoff failure rates, in Proc. IEEE GLOBECOM, Miami, Florida, Dec. 2010, pp