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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 2, MARCH 2003

357

Handoff Management Without Intercell Hard Handoffs in a Multifrequency CDMA System Dong-wan Tcha, Go-whan Jin, and Chun-hyun Paik

Abstract—This paper addresses handoff management in a multifrequency code-division multiple-access system with nonuniform traffic loads over cells. We propose a new handoff scheme, called here adaptive handoff management (AHM), in which the intercell hard handoffs, not only incurring equipment cost burden but also degrading call quality, are totally removed. Also strengthened in the AHM is the call-control capability of adaptively reflecting a changing traffic environment. Traffic and mobility analysis is first conducted on a single isolated cell with two cocentered circle boundaries, thereby rendering two key performance measures. We then formulate a mathematical problem of finding optimal parameters of the proposed AHM in which intracell hard handoffs are exploited most effectively. After reporting a simple solution process, computational experiments are conducted to illustrate the superiority of AHM in two key performance criteria. Index Terms—Call control, handoff management, multifrequency code-division multiple access (CDMA), traffic and mobility analysis.

I. INTRODUCTION

I

N A real-world code-division multiple-access (CDMA) system in operation, the numbers of frequencies (or frequency assignments as used by service providers) assigned to cells often vary owing to unbalanced traffic loads imposed on cells [1]–[4]. Since the same frequency can be used at neighboring cells, a designated single frequency is commonly used at all cells in the whole service area at the initial phase of CDMA service provision. Cells are then assigned further frequencies in accordance with the level of demand increase therein, rendering the nonuniform multifrequency assignments over cells. In this multifrequency CDMA system, there often occurs the intercell hard handoff (RHH) that a mobile station (MS), when crossing a cell boundary, is handed off to not only a target cell but also a different frequency used at the target cell. The occurrences of RHHs, however, should be avoided as much as possible from the resulting poor communication quality as compared to the soft handoff (SH) [5]–[7]. Furthermore, implementing an RHH requires that the target cell be time synchronized with the incoming MS [1], [3]. Manuscript received February 19, 2001; revised March 3, 2002. This work was supported by the Korea Science and Engineering Foundation under Grant R01-2001-00508. D. Tcha is with the Graduate School of Management, Korea Advanced Institute of Science, Seoul, Korea. G. Jin is with the School of Information and Technology, Woosong University, Daejon, Korea. C. Paik is with the Department of Information and Industrial Engineering, Dongeui University, Busan, Korea. Digital Object Identifier 10.1109/TVT.2003.808787

In [1], two implementation schemes for smooth RHH operation have been mentioned: use of the beacon pilot and the round-trip signal delay (RTD). In the former, a beacon should be installed at a cell for each frequency that is not assigned to the cell but to some of its neighboring cells. A beacon at a cell generates a pilot signal to make an incoming MS be synchronized to a new frequency for RHH. This method, though easy to implement, incurs the heavy cost of placing beacon equipment at whichever cells they are required. In the latter RTD scheme, the distance from the current base station (BS) to an MS is estimated from the round-trip delay of radio propagation, with which a verdict is made on whether or not the MS is located in the handoff region. An MS, which has been identified as being in the handoff region but does not listen to any pilot channel, is ordered by the BS to instantaneously perform an RHH without any knowledge on the target cell and the frequency to jump onto. So, with the RTD scheme alone, a number of RHHs may be attempted in vain until the MS finds both the target cell and the frequency. To offset such quality degradation of the RTD scheme, one may install an extra receiver at each neighboring cell for exchanging control information, as proposed in [3], with heavy cost incurred. In an attempt to remove the occurrences of such undesirable RHHs in a multifrequency environment, this paper proposes a new method of handoff operation, called adaptive handoff management (AHM), incorporating intracell hard handoffs (AHHs). Note that the operation of AHH does not require any additional equipment since it is performed within the cell [1]. Another advantage to note is that the quality of an ongoing call experiencing the AHH is not as degraded as that under RHH. The organization of this paper is as follows. In Section II, we describe the AHM method. Based on some simplifying assumptions on cell configuration and moving patterns of MSs, the traffic attributes are estimated in Section III. In Section IV, two representative performance measures are given that effectively characterize a multifrequency CDMA system under AHM. Then a mathematical model of finding optimal AHM parameters is presented. In Section V, computational experiences with realistic data are reported to demonstrate the superiority of the AHM method. Conclusions are given in Section VI. II. HANDOFF MANAGEMENT METHOD For exposition convenience, we consider a simplified CDMA cellular configuration consisting of seven circular cells, in which is used throughout the service area the common frequency is assigned only to the cell of and an additional frequency

0018-9545/03$17.00 © 2003 IEEE

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Fig. 2. Fig. 1.

An illustrative multifrequency CDMA system.

interest (center cell), as shown in Fig. 1. This setting, though simple, has most of the performance-related attributes of a general multifrequency environment, so that its modeling and analysis can easily be extended to a more complicated situation of multifrequency assignments. MSs undergo either type of handoffs when leaving the center cell with two frequencies, unless otherwise specified. One is the in Fig. 2, is present SH in which a frequency used by an MS, at both the center and the target cells. The other type is the RHH in which the frequency used by an MS, , in the center cell is not supported at the target cell. Before describing the AHM, the following is defined first. As in [1], the area of the center cell is partitioned into two regions: central and peripheral. The boundary between two regions is configured by the RTD from the serving BS to the MSs, the measurement of which is always possible because the MSs are synchronized to the serving BS. The central region means the one within which the measured RTD of an MS does not exceed a predetermined value, which is denoted by REG1 (Fig. 2). The peripheral region, defined vice versa, is denoted by REG2. The radii of cell and REG1 are and , respectively. New calls originated in REG2 as well as inbound handoff calls from outside are assigned , whereas those new calls originated in REG1 . For an MS moving from REG1 to REG2 is enacted while being served by , the AHH to frequency upon crossing the RTD boundary. And for an MS that is curin REG2 and moving toward REG1, the rently supported by is performed randomly with a constant probability AHH to upon the MS’s boundary crossing. Note that under AHM, the MSs in REG2 are all operated and only on , while those in REG1 are operated on both . Therefore, all intercell handoffs are made by the SH under AHM. The key enabler of intercell SH is the AHH, which can easily be implemented since an MS is already synchronized to the frequency to be handed off [1], [8].

Illustration of AHM in the cell with RTD boundary.

The intercell SHs, called simply SHs in the literature, spend less power than RHHs due to the macro-diversity, rendering the so-called SH gain of increasing system capacity and improving communication quality [7], [9], [10]. This beneficial effect of the SH gain, together with the associated low deployment cost, well indicates how advantageous the implementation of AHM will be. The adoption of AHM, though, would bring forth some negative effects: efficiency decrease in the use of an extra frequency , increase in the interference of the common frequency to neighboring cells, and higher AHH occurrences. This negative impact can be kept within a predefined tolerance limit by and , adaptively determining the two parameters of AHM, to varying traffic environments, which will be detailed in Section IV. Our task is then to obtain the optimal operation solution of the proposed AHM method and to estimate the overall effectiveness gained therefrom. For that, we need to estimate several traffic attributes, such as the sojourn times of MSs in each of two regions, and to derive interrelations between traffic attributes and performance measures, the problem of which is indeed very complex even for a simple cell with a single circle boundary as manifested in [11]–[13]. In the next section, required traffic analyses are conducted for a cell with two cocentered circle boundaries, given in Fig. 2. III. TRAFFIC MODELING A. New Call Case Consider a cell, divided into two regions as shown in Fig. 3, on which MSs are randomly located. Assume that the velocity and the direction of MSs are uniformly distributed, respec] and [0, 2 ] and that they remain contively, on intervals [0, stant during their travels. Then the location of an MS marked by the letter in Fig. 3 is represented by its distance and direction from the BS located at the center of the cell. Assume that an MS randomly chooses its travel direction. If we define the travel direction of an MS by the absolute angle

TCHA et al.: HANDOFF MANAGEMENT WITHOUT INTERCELL HARD HANDOFFS

359

Fig. 3. Coordinates of distance and direction for a new call.

between its moving direction and the direction from its position to the cell, the uniformly distributed assumption on the travel direction guarantees the independence of variables and . We have its joint probability density function (pdf) as

Starting from location A in REG1, as shown in Fig. 3(a), the MS’s travel distance becomes (2) With the variable transformation

for otherwise.

(1)

Now, consider an MS whose (new) call is generated in region REG1 or REG2. An MS’s travel path from its origination point to either boundary will be denoted by ( ). The first element indicates the region of originathe traversed regions, and the last element tion, represents either the RTD ( ) or the cell boundary ). For compact exposition, the Arabic numbers 1 and 2 ( are used to express the regions REG1 and REG2 and the letters and the RTD and cell boundaries, respectively. be the travel distance of the new calls (MSs) with Let travel path . Hereafter, the quantities pertaining to new calls will be denoted by superscript . For illustration, only the re) sults and the derivation process of the travel path ( are now listed. For those of other remaining cases, refer to [14]. Refer to [15] and [16] for similar approaches on other applications.

and we have the joint pdf of

for

and

(3)

as

(4)

indicates the Jacobian transformation. We have then where shown in (5) at the bottom of the the marginal pdf of page. be the travel duration (or cell-residence time) Let ). Since of the MS with travel path (

for for

for

(5)

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, its pdf is given by (6) as shown at the bottom of the next page, where

B. Handoff Call Case Consider an MS handed off to the center cell from its neighboring cell (an inbound handoff call). Note that in this case, 2 2] and that the range of random variable becomes [ other assumptions on an MS’s moving pattern remain the same ) be the travel path as for a new call. Let ( of an inbound handoff call, assuming that the corresponding MS is generated at the cell boundary, as shown in Fig. 4. All quantities pertaining to an inbound handoff call will be denoted by superscript . We now list the results of two travel paths ) and ( ), with others omitted. ( By the variable transformation as done for a new call, the pdfs are given as of

for

Fig. 4. Coordinates of distance and direction for an inbound handoff call.

Now, consider the case of travel path ( that

(7)

from which we have, using the assumption on the moving pattern of an MS, (8) as shown at the bottom of the page, where represents the cell-residence time of an inbound handoff call with the corresponding travel path and

for

). Noting

(9)

), and using the same method as the case of ( as shown in (10) at the bottom of we have the pdf of the page, where

for (6) for

for (8) for

for (10) for


IV. PERFORMANCE MEASURES AND OPTIMAL OPERATION

361

where

A. Performance Measures In an attempt to quantify the impact of implementing the AHM, we consider two performance measures: the outage probability and the rate of AHH. The outage probability is the probability that servicing an ongoing call is discontinued when a required level of quality service is not guaranteed any further owing to heavy traffic congestion at a cell [6]. The rate of AHH means the number of MSs making AHHs per unit time, which is introduced to identify the level of their negative effect on system performance [1], [8]. of a call is exponentially disAssume that the duration [11], [17], [18] and that new and tributed with mean 1 inbound handoff calls at the cell are generated according to inand , respectively. dependent Poisson processes with rates denoting the probability that a new call ( ) or With ) with travel path experiences an inbound handoff call ( an intra- or an intercell handoff, we have

OL

OL To exploit this approximate measure, we need to calculate the and . Let the random variable offered loads of frequencies be the minimum of the duration of a call and its travel with travel path , that is duration (15) from which its pdf is obtained as

(11) and , the rate of AHH from Given two AHM parameters to is represented by and that in the reverse . With these notations, the following direction by relations are found after some manipulations:

(12) (13) is the sum of The total rate of AHHs and . Now turn our attention to the outage probability. Given the offered load (OL) to the cell in the single-frequency CDMA system, Viterbi et al. [6] obtained an approximated outage probability (OP) as simple as OP

(14)

(16) denoting its mean and given and , we can obWith and OL , as shown in tain two offered loads OL (17) and (18) at the bottom of the page, where and NOL are, respectively, the interference contribution from and the traffic load offered to an adjacent cell [1], [6]. is calculated by Note that the offered load of frequency considering the traffic of both neighboring cells and the center cell. But for , we consider only the traffic of the center cell where it is assigned. The outage probability, denoted by , of frequency can now be obtained . by (14) and offered loads OL B. Optimal Operation Two performance measures, the outage probability and the rate of AHH, were shown to be obtained when the AHM paand are given. In this section, we aim at finding rameters the optimal AHM parameters that minimize the rate of AHH while satisfying the prespecified quality of service (QOS) on the outage probability of each frequency assigned to the center

OL

NOL

(17)

OL (18)

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cell

subject to

OP

OP

where OP indicates the prespecified QOS level for fre. and designate the range quency is allowed to vary in practice. Particularly, within which should be carefully determined by considering the soft handoff region. The problem ( ) is a nonlinear programming model with both the objective and the constraint functions nonlinear. Furthermore, the explicit forms of these functions with respect to operation parameters are not known. This makes it difficult to find an efficient algorithm in the literature for ( ). A simple search method is instead suggested, in which the range of search is dramatically reduced by Theorem 1 given below. Before presenting the theorem, we need the following OL Lemma 1: The offered load of frequency (respectively, the rate of AHHs ) decreases (respectively, increases) in not only but also . Validating Remarks: 1) Simple reasoning is provided, avoiding a long and tedious proof. As increases, the occurrences of AHHs to frequency of REG1 would be increased. The offered load of frequency in REG1 becomes lessened, which in turn increases AHHs from REG1 to REG2. Enlarging REG1 by would increase the number of MSs operated increasing on , yielding the same effect as the increase of . in both parame2) The increasing property of OL ters still holds for since defined as such. Theorem 1: Given a total offered load, consider two sets and , respectively, defined by OP OP where

. Then, OP OP , for and . If the rate of AHH is, respecand , then tively, minimized at Proof: From the soft capacity of the CDMA system, the traffic offered to the cell should all be carried by either of the and . Since the offered load of frequency two frequencies in set is larger than in set , it is obvious to deduce the first result. For the second result, we start with the case of . We can always find an such that because OP decreases in . By Lemma 1, we have . Consider the other . If there exists a parameter such that case of , then . Otherwise, , and using noting OP such that the results of Lemma 1, we can always find and . 1) Remarks: This theorem means that the rate of AHHs, , decreases as the relative portion of OL in the total traffic load offered to the center cell increases. There-

Fig. 5. Outage probability changes in traffic ratio ().

fore, the optimal solution of problem ( ) would be attained at a . feasible solution maximizing OL 2) Solution Procedure: With this characterization, an op) of problem ( ) can be obtained by timal solution pair ( ), satisfying the QOS consearching only candidate pairs ( straints, with the largest outage probability of frequency . V. NUMERICAL EXAMPLES Consider a CDMA cellular system consisting of seven cells where a common frequency is assigned throughout the system and an additional frequency is assigned to the center cell with . The parameter values are arbitrarily chosen to radius s fit the reality . Assuming that the rate of new calls at neighand boring cells is half that at the center cell, the inbound handoff rate to the center cell is calculated from (11). The interference contribution from each neighboring cell is assumed to be 6% of that from the current cell [7]. We first provide empirical evidence of the monotone prop. To make the erties of two performance measures in and testing meaningful, a heavy traffic environment was considered of the center cell at a large by setting the new call arrival rate , Figs. 5 value of 1700 calls/h (Figs. 5–8). With and 6 show how both performance measures change in . As increases, the number of calls using increases, making the OP larger. Also note that outage probability of frequency increases in slower than , owing to its lesser dependence on (Fig. 6). In Figs. 7 and 8, we show how both measures vary with while is fixed at 0.6. In , the proportion of MSs using ( ) increases (decreases), giving rise to the changing patterns and of OP and OP in Fig. 7. Fig. 8 shows how change in . The above changing patterns convince us that under the proposed AHM scheme, the interference of frequencies, particularly, , can be kept within a prespecified level while minimizing the occurrences of signaling-overhead incurring AHHs. Focus was thus placed on showing via the experiments how such optimal parameters can be obtained under varied traffic environments with the problem (P). The QOS levels on outage probabilities of both frequencies were uniformly set at 0.02.


Fig. 6. Changes of AHH rates in traffic ratio ().

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Fig. 9. Optimal AHM parameters (R call arrival rates.

;

) corresponding to differing new

Fig. 7. Outage probability changes in RTD boundary (R ). Fig. 10.

Fig. 8.

Changes of AHH rates in RTD boundary (R ).

Fig. 9 shows how the optimal parameter values and change in the new call arrival rate. From the resultant curves, the whole range of traffic load can be divided into three suband , indicates ranges. The first subrange, having the light load environment in which a single frequency suffices for the traffic demand. The second subrange is with and , which shows the medium level of traffic load requiring two frequencies. In this case, the AHM can be activated, completely removing AHHs from REG2 to REG1. The case of

Outage probabilities under the optimal AHM parameters.

heavy load corresponds to the third subregion with and , in which the AHM reduces the overload on frequency by systematically forcing a larger number of MSs to use the additional frequency . In the AHM, we adjust the parameter to take the preemptive responsibility of the RTD boundary is first infor traffic load increase. As the load increases, creased to its largest allowable value, and then the traffic ratio starts increasing to take charge of further load increase. Note that this order of load bearing aims at minimizing the occurrences of AHHs. The performance characteristics at optimal operation parameters are summarized in Figs. 10 and 11, which show how the corresponding outage probability and AHH rate, respectively, change in the new call arrival rate. VI. CONCLUSION In this paper, we have presented an adaptive handoff management method in a multifrequency CDMA cellular system. The existing handoff methods in a multifrequency system cannot but employ RHHs, which not only incur additional cost burden but also degrade the quality of calls undergoing handoff. But in the proposed AHM method, these undesirable RHHs can be completely removed by introducing AHHs for the MSs crossing the RTD boundary. Another key advantage of using the AHM

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Fig. 11. Rate of AHHs under the optimal AHM parameters.

method is its ability of adaptively changing its two parameters in relation to the traffic environment. Several traffic attributes were first estimated by analyzing a single isolated cell of cocentered bicircled shape, based on which the performance measures characterizing the multifrequency environment were derived. We then formulated an optimization problem of finding the optimal AHM parameters and observed some interesting properties holding at optimal solutions, thereby dramatically simplifying the associated search process. Extensive computational experiments were conducted, which demonstrate the effectiveness of the AHM method in a multifrequency CDMA cellular system. The proposed AHM, though greatly advantageous, has some shortcomings, like the degradation of trunk efficiency and the increase in the interference of common frequency to neighboring cells. Therefore, the method is particularly effective where a cell of interest is surrounded by neighboring cells with light traffic, such being quite often encountered in practice. The overall effect of the AHM method on system capacity and the signaling requirements for AHHs would be interesting issues worth investigating. REFERENCES [1] CDMA System Engineering Training Handbook, Qualcomm Inc., 1993. [2] S. K. Kwon, H. G. Jeon, and H. Lee, “A channel assignment scheme for integrated services in DS-CDMA cellular systems,” in Proc. IEEE ICUPC ’97, vol. 1, October 1997, pp. 642–645. [3] P. Satarasinghe, “A novel method for CDMA hard handoff,” in Proc. IEEE Globecom ’96, London, U.K., 1996, pp. 1766–1768. [4] J. S. Wu, J. K. Chung, and Y. C. Yang, “Proposed multi-channel access schemes for hot-spot underlying CDMA cellular systems,” IEICE Trans. Commun., vol. E81 B, no. 4, pp. 745–753, Apr. 1998. [5] “Mobile station-base station compatibility standard for dual-mode wideband spread spectrum cellular system,” Telecommunications Industry Association, Washington, DC, EIA/TIA IS-95, 1993. [6] A. M. Viterbi and A. J. Viterbi, “Erlang capacity of a power controlled CDMA system,” IEEE J. Select. Areas Commun., vol. 11, pp. 892–900, 1993. [7] A. J. Viterbi, A. M. Viterbi, K. S. Gilhousen, and E. Zehavi, “Soft handoff extends CDMA cell coverage and increase reverse link capacity,” IEEE J. Select. Areas Commun., vol. 12, no. 8, pp. 1281–1288, 1994. [8] Handbook of CDMA System Design, Engineering and Optimization, K. I. Kim, Ed., Prentice-Hall, NJ, 2000. [9] P. R. Patel, U. S. Goni, E. Miller, and P. P. S. Carter, “A simple analysis of CDMA soft handoff gain and its effect on the cell’s coverage area,” in Wireless Information Networks, J. Holtzman, Ed. Boston, MA: Kluwer, 1996, pp. 155–172.

[10] D. Wong and T. J. Lim, “Soft handoffs in CDMA mobile systems,” IEEE Personal Commun., pp. 6–17, Dec. 1997. [11] D. Hong and S. S. Rappaport, “Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and nonprioritized handoff procedures,” IEEE Trans. Veh. Technol., vol. VT-35, pp. 72–92, 1986. [12] M. Ruggieri, F. Graziosi, and F. Santucci, “Modeling of the handover dwell time in cellular mobile communication systems,” IEEE Trans. Veh. Technol., vol. 47, pp. 489–497, 1998. [13] M. M. Zonoozi and P. Dassanayake, “User mobility modeling and characterization of mobility patterns,” IEEE J. Select. Areas Commun., vol. 15, no. 7, pp. 1239–1252, 1997. [14] G. W. Jin, “On channel management in CDMA cellular systems,” Ph.D. dissertation, Dept. of Management Science, Korea Advanced Inst. of Technology, 1998. [15] C. H. Paik, G. W. Jin, J. H. Ahn, and D. W. Tcha, “Integrated call control in a cellular system,” IEEE Trans. Veh. Technol., vol. 50, no. 1, pp. 97–108, 2001. [16] D. W. Tcha, S. Y. Kang, and G. W. Jin, “Load analysis of the soft handoff scheme in a CDMA cellular system,” IEEE J. Select. Areas Commun., vol. 19, pp. 1147–1152, 2001. [17] R. Guérin, “Channel occupancy time distribution in a cellular radio system,” IEEE Trans. Veh. Technol., vol. VT-35, no. 3, pp. 89–99, 1987. [18] C. N. Wu, Y. R. Tsai, and J. F. Chang, “A quality-based birth-and-death queuing model for evaluating the performance of an integrated voice/date CDMA cellular system,” IEEE Trans. Veh. Technol., vol. 48, no. 1, pp. 83–89, 1999.

Dong-wan Tcha received the B.S. degree in electronics from Seoul National University, Seoul, Korea, in 1969 and the M.S. and Ph.D. degrees in operations research from Northwestern University, Evanston, IL, in 1972 and 1975, respectively. In 1975, he joined the Faculty of the Korea Advanced Institute of Science and Technology, Seoul, where he is currently a Professor at the Graduate School of Management. He was a Visiting Scientist at the IBM T.J. Watson Research Center from 1981 to 1982, a Guest Scientist at the German Aerospace Research Establishment (DFVLR) in 1986, and a Humboldt Fellow at the Technical University of Darmstadt, Germany, in 1987. His research has been in the areas of network analysis, combinatorial optimization, and communication systems. He was Editor of the Journal of Korea Operations Research and Management Science Society (J. KORMS) from 1983 to 1985 and Invited Editor of the Special Issue of Telecommunication Systems on Modeling and Analysis of Telecommunicaton Systems in Korea, 2000. He was President of KORMS during 1998–1999 and a General Cochair of the INFORMS 2000 Seoul International Conference. He also was a Director responsible for academic activities at the Korean Institute of Communication Sciences and Chairman of the SIG on Telecommunications Management from 1993 to 1994. Currently, he is a Member of the Advisory Editorial Board of the Journal of Information Technology and Management. Dr. Tcha has published numerous papers in the IEEE TRANSACTIONS ON COMMUNICATIONS, IEEE TRANSACTIONS ON COMPUTERS, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and IEEE TRANSACTIONS ON NETWORKING. Go-whan Jin received the B.S. degree in industrial engineering from Sung Kyun Kwan University, Seoul, Korea, in 1987 and the M.S. degree in industrial engineering and Ph.D. degree in management science from the Korea Advanced Institute of Science and Technology, Seoul, in 1990 and 1999, respectively. He was a Senior Member of Research Staff at the Electronics and Telecommunications Research Institute from 1990 to 2000, a Director of the Technical Planning Division at Spread Telecom in 2001, and CEO of MoIn Telecom in 2002. Currently, he is an Assistant Professor of information science and technology at Woosong University, Daejon, Korea. His research interests include traffic performance modeling of cellular radio network, its applications to wireless communications, and MIS/e-business in wireless Internet. Chun-hyun Paik received the B.B.A. degree in management from Yonsei University, Seoul, Korea, in 1986 and the M.S. and Ph.D. degrees in management science from the Korea Advanced Institute of Science and Technology, Daejon, Korea, in 1989 and 1994, respectively. He was a Senior Researcher at SK Telecom Research Center from 1994 to 1997. Currently, he is an Associate Professor of information and industrial engineering at Dongeui University, Busan, Korea. His research interests include analysis of communication systems with emphasis on optimal design, control, and performance evaluation of wireless networks.