A capacity acquisition protocol for channel reservation in CDMA networks

Computer Networks 50 (2006) 1003–1021 www.elsevier.com/locate/comnet

A capacity acquisition protocol for channel reservation in CDMA networks Xudong Wang

*

Kiyon, Inc., R&D Division, 4225 Executive Square, Suite 290, La Jolla, CA 92037, United States Received 20 February 2005; accepted 16 May 2005 Available online 8 August 2005 Responsible Editor: E. Ekici

Abstract In this paper, a capacity acquisition protocol is proposed for channel reservation in CDMA networks. Under this protocol, a cell is virtually divided into three regions (i.e., inner region, forced handoff region, and active handoff region). A new call in the active handoff region works in soft handoff mode upon its admission, while a new call in the inner and forced handoff regions works in single mode. However, in the forced handoff region, calls working in single mode can be forced into soft handoff mode, when extra capacity is needed by soft handoff calls. As a result, no explicit channel reservation is required before a call enters soft handoff. By adjusting the size of the forced handoff region, the capacity acquisition can adapt to traffic load and guarantee a desired call dropping probability. To evaluate the capacity acquisition protocol, an analytical model is derived and is also validated through computer simulations. Numeric results illustrate that the capacity acquisition protocol significantly reduces the call dropping probability.  2005 Elsevier B.V. All rights reserved. Keywords: Capacity acquisition; Soft handoff; CDMA; Channel reservation

1. Introduction Dropping an on-going call is more disturbing than blocking a new call. To resolve this problem, channel reservation for handoff calls can be used in a call admission control (CAC) algorithm to prior-

*

Tel.: +1425 442 5039; fax: +1858 453 3647. E-mail address: [email protected]

itize handoff calls over new arrival calls. However, channel reservation in CDMA networks is nontrivial because of the special features of soft handoff. It is well known that soft handoff of CDMA networks reduces interference and increases the interference-sensitive capacity [1]. This feature must be taken into account by the channel reservation scheme in a CAC algorithm. In addition, two other important features found in this paper need to be considered. One is that soft handoff and the

1389-1286/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.comnet.2005.05.032

1004

X. Wang / Computer Networks 50 (2006) 1003–1021

need of channel reservation occur at different times. The other is that a call working in single mode releases a certain amount of capacity when it is forced into soft handoff mode. Based on these features, a novel channel reservation scheme called capacity acquisition protocol is proposed in this paper for soft handoff calls in CDMA networks. This protocol focuses on uplink operation of a CDMA network. In the capacity acquisition protocol, three regions, i.e., inner region, forced handoff region, and active handoff region, are introduced for each cell. When an admitted call moves into or a new call arrives at the active handoff region, it works in soft handoff mode. In the forced handoff region, an admitted new call works in single mode and thus only communicates with one base station. Since a call in soft handoff mode consumes less capacity than it does in single mode, some capacity is implicitly reserved by a new admitted call in the forced handoff region. When more capacity is needed by soft handoff calls, it can be acquired from new admitted calls in the forced handoff region by forcing them into soft handoff mode. Thus, before a call enters soft handoff, no explicit channel reservation is required to reserve capacity. The size of forced handoff region in the capacity acquisition protocol can be adjusted according to the traffic load in the network. As long as traffic load is lower than an upper bound, a target call dropping probability is guaranteed by the loadadaptive protocol. To date, many algorithms have been proposed for call admission in CDMA networks [2–7]. Neither the signal-to-interference ratio (SIR)-based CAC algorithm in [2] nor the interference levelbased CAC algorithm in [3] considers interference reduction by soft handoff. The interference reduction brought by soft handoff is not considered either in [4], although a call in the soft handoff region can access two base stations. Compared to the schemes in [2–4], the CAC analytical model proposed in [5] achieves better performance, because it takes into account the capacity increase factor introduced by soft handoff. According to this model, the larger is the size of soft handoff region in a cell, the smaller is the call blocking probability of a CDMA network. No differentiation is

performed between soft handoff and new arrival calls in [5]. Algorithms reserving fixed channels [4] for soft handoff calls waste resources. In [6], a ‘‘look around’’ CAC algorithm is proposed to reduce dropped calls. Soft guard channels are exclusively used for handoff calls, which also results in low resource utilization. In [7], an adaptive channel reservation scheme is proposed for soft handoff calls in a CDMA network. When a user with an on-going call moves into a reservation region, it starts a channel reservation procedure, so channels are reserved individually for each handoff call. Thus, each handoff call does not have fixed reservation of capacity and the utilization is improved. However, this method still wastes a large amount of capacity, because the reserved capacity for a soft handoff call are held useless during the period from the approval of reservation request to the initiation of a soft handoff call. In addition, when traffic load (i.e., new call arrival rate) is high, the resource utilization of the adaptive reservation scheme is not guaranteed to be more efficient than that of a fixed reservation scheme, because many users need to have reserved channels. In other words, this scheme is not actually adaptive to traffic load. The rest of this paper is organized as follows. The capacity acquisition protocol is proposed in Section 2, and is analyzed in Section 3. The analytical model is justified by simulations in Section 4 where analytical results are used to compare the new scheme with other channel reservation schemes for CDMA networks. In Section 5, a load-adaptive capacity acquisition protocol and its performance are presented. Practical issues of the capacity acquisition protocol is discussed in Section 6. The paper is concluded in Section 7.

2. Capacity acquisition based on soft handoff The capacity acquisition protocol is motivated by the features of soft handoff. 2.1. Features of soft handoff As shown in Fig. 1, a mobile terminal in soft handoff is able to communicate with base stations

X. Wang / Computer Networks 50 (2006) 1003–1021

1005

2

l ðbbrÞ ; PH B ¼ Py e Base Station B

Base Station A r1

Mobile Terminal

Fig. 1. A soft handoff example.

ð1Þ

and P SH B ¼ P Prðf ðr1 Þ > f ðr 0 ÞÞ þ PEðf ðr1 Þ=f ðr0 Þjf ðr1 Þ 6 f ðr0 ÞÞ;



ð2Þ

respectively. SH Considering that f is Gaussian, P H B , P A , and SH P B can be expressed as

P SH B



bbr l lnðyÞ ¼ Py e erfc pffiffiffi  pffiffiffi 2 2bbr   l lnðyÞ þ P erfc pffiffiffi ; 2bbr l

ð3Þ

2

and

A and B. For a user at distance r from a base station, the signal attenuation is assumed to be f(r) = rl10f/10 [1], where l and f capture the power loss and shadowing, respectively. For base station i, f = an + bni [1], where n is the common part to all base stations, and ni pertains solely to base station i. Moreover, n and ni are independent Gaussian random variables with mean and standard deviation equal to zero and r, respectively. Based on this assumption, the interference reduction by soft handoff is analyzed as follows: Suppose the received signal power at base station A, denoted by P H A , is required to be P. When the mobile terminal communicates with base station A only, its average transmitting power is PE(f(r1)), and the average interference power level at base station B, denoted by P H B , is PE(f(r1)/f(r0)), where E(Æ) is the expectation function. When soft handoff is used, the mobile terminal communicates with either base station A or base station B, depending on the attenuation f(r0) and f(r1). If f(r0) > f(r1), the mobile terminal must communicate with base station A; otherwise, it communicates with base station B. Thus, the average power levels at base stations A and B, represented SH by P SH A and P B , are P SH A ¼ P Prðf ðr0 Þ > f ðr 1 ÞÞ þ PEðf ðr0 Þ=f ðr1 Þjf ðr0 Þ 6 f ðr1 ÞÞ;



bbr l lnðyÞ erfc pffiffiffi þ pffiffiffi 2 2bbr   l lnðyÞ þ P erfc  pffiffiffi ; 2bbr

l P SH A ¼ Py e

r0

ðbbrÞ2

ðbbrÞ2 2

ð4Þ 

ð5Þ

respectively, b = ln(10)/10, y = r0/r1, and R 1 where 2 pffiffiffi erfcðxÞ ¼ x et = p dt. Thus, the reduced power levels of the mobile terminal under consideration (i.e., reduced interference to other mobile terminals) at base stations A and B, denoted by DP A and DP B , respectively, can be derived according SH H SH to DP A ¼ P H A  pffiffiPffi A and DP B ¼ P B  P B . Suppose l = 4, b ¼ 1= 2, then r = 8, and the power levels (normalized by P) versus distance ratio, denoted by r1/r0, are shown in Figs. 2 and 3, respectively, for base stations A and B. It is obvious that power levels required at base stations are significantly reduced when soft handoff is used. Suppose a mobile terminal works in single mode and communicates with base station A, then the closer it is to base station B, the more significant is the interference reduction. However, two more distinguished features of soft handoff can be found from Figs 2 and 3: • Feature 1: soft handoff and the need of channel reservation actually occur at different times. Assume that the mobile terminal is admitted where r1/r0 is small, i.e., the mobile terminal is closer to base station A in Fig. 1. When the mobile terminal moves towards base station B, its interference to mobile terminals in the cell covered by base station B increases (See the curve without soft handoff in Fig. 3). When the mobile terminal enters soft handoff, the interference is greatly reduced. Thus, before or when the on-going call enters soft handoff mode, there is no need to reserve extra channels because completion of soft handoff is guaranteed. However, when the mobile terminal in soft

1006

X. Wang / Computer Networks 50 (2006) 1003–1021

Normalized Power Levels at Base Station A

1 0.9

With Soft Handoff Without Soft Handoff Reduced Interference

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Ratio r1/r0 Fig. 2. Normalized power levels with and without soft handoff at base station A.

Normalized Power Levels at Base Station B

2.2

With Soft Handoff Without Soft Handoff Reduced Interference

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Ratio r1/r0

Fig. 3. Normalized power levels with and without soft handoff at base station B.

handoff mode continues to move towards base station B, its average power level at base station B steadily increases, and may cause call dropping and blocking in the cell covered by base

station B. To reduce call dropping as well as call blocking probabilities, a certain amount of capacity needs to be acquired to compensate the increased interference.

X. Wang / Computer Networks 50 (2006) 1003–1021

• Feature 2: a single mode call releases a certain amount of capacity when it is forced into soft handoff. For a call that is admitted and works in single mode, if it switches into soft handoff mode, it reduces the interference to all base stations that surround it. In other words, its consumed capacity at all base stations is decreased. The released capacity can be used to compensate the increased interference caused by mobile soft handoff calls. Thus, an admitted call working in single mode implicitly reserves capacity for future acquisition needed by mobile soft handoff calls.

2.2. The novel channel reservation scheme—the capacity acquisition protocol An implicit channel reservation scheme is proposed for soft handoff calls in CDMA networks by utilizing the special features of soft handoff itself. In this scheme a cell is divided into three regions, i.e., inner region, forced handoff region, and active handoff region. In the cellular model shown in Fig. 4, the region starting from the cell boundary up to distance d1 is the active handoff region, while the region from distance d1 to d2 is the forced handoff region. The remaining region of a cell is the inner region. Since the soft handoff region is the overlapping area of neighboring cells, the actual shape of a cell is not a square but similar to a hexagon. Since it is difficult to find the exact location of a mobile terminal in a cell, signal strength is used to determine the region that a mobile terminal is located in. A mobile terminal in the cell covered by base station A monitors the pilot signal from base station A, if the signal strength is larger than a threshold Sfr, the mobile terminal is in the inner region; else if the signal strength is larger than another threshold Saf (Saf < Sfr), the mobile terminal is in forced handoff region. Finally, if the signal strength is less than Saf, the mobile terminal is in the active handoff region. In each region, a mobile terminal keeps a set (called active set) of base stations that it can communicate with. In the inner region, only one base

1007

station exists in the active set, while in soft handoff regions (either forced handoff region or active handoff region) at least two base stations must be in the active set so that the mobile terminals can enter soft handoff mode. Based on the investigated features of soft handoff and the introduced regions of a cell, capacity acquisition works as follows: • Reserve capacity implicitly. An admitted call works in a different mode depending on where it is located. When a mobile terminal is in the active handoff region, it needs to work in soft handoff mode. In the inner region, a mobile terminal can only communicate with one base station, so it works in single mode. For a new call originated in the forced handoff region of a base station, e.g., base station A, its admission is performed by assuming that it can only communicate with base station A. From Feature 2, the admitted single mode call carries extra capacity that can be released on the demand of soft handoff calls that need more capacity. Thus, implicit channel reservation is fulfilled by allowing new arrival calls in the forced handoff region to work in single mode. • Detect outage. When a soft handoff call of a mobile terminal moves towards base station B, the received power level at base station B increases. Thus, the SINRs of the received signals of all other mobile terminals decrease. Given a threshold SINRthr, base station B checks the SINR of the received signal of each mobile terminal, denoted by SINRMT, and compares it with the target SINRo. If SINRMT < SINRo + SINRthr, outage is detected. The threshold ensures that outage is detected before it actually occurs. If the soft handoff call under consideration continuously moves towards base station B, outage may take place in the uplink of multiple mobile terminals. In order to avoid dropping multiple calls, it is better to drop the soft handoff call under consideration. In such a way, call dropping probability can be reduced. However, to further reduce the call dropping probability of soft handoff calls, a certain amount of system capacity implicitly carried by new admitted

1008

X. Wang / Computer Networks 50 (2006) 1003–1021

Fig. 4. The cell structure.

calls in the forced handoff region must be used to accommodate the increased received power level of a soft handoff call at base station B, as explained next.

• Acquire implicitly reserved capacity. Suppose a soft handoff call communicates with base stations A and B and moves towards base station B, as shown in Fig. 4. When it requires extra

X. Wang / Computer Networks 50 (2006) 1003–1021

capacity in the cell of base station B, some single mode calls in the forced handoff region in the cell of base station A need to be forced into soft handoff mode. Call dropping probability can be greatly reduced by forcing such single mode calls into soft handoff. Since soft handoff reduces interference, as pointed out by Feature 1, an admitted new call in the forced handoff region can always successfully switch into handoff mode. However, the following procedure is followed so that the necessary capacity can be acquired within a short time. First, base station A finds a mobile terminal in the forced handoff region, e.g. mobile terminal MTa, that is the farthest to it in the sense of the strength of pilot signal. Second, mobile terminal MTa is forced into soft handoff mode. Maximum capacity is released by MTa. The reason is that, if the single mode call is father from base station A (i.e., r1/ r0 is larger), the interference reduction at base station B is larger. After MTa is forced into soft handoff, if SINRMT > SINRo + SINRthr is satisfied, channel acquisition is completed; otherwise, the next single mode call with the farthest distance to base station A is forced into soft handoff. This process repeats until SINRMT > SINRo + SINRthr is satisfied for all the received signals at base station B.

3. Analysis of the capacity acquisition protocol 3.1. Assumptions In a CDMA network, due to the factors such as irregular cell boundaries, traffic characteristics, and the movement of mobile terminals [5], it is complicated to find an accurate model of soft handoff. To simplify the analysis, assumptions are given as follows: • Residual times of a call in all regions are generally distributed [8]. • The new call arrival rate is a Poisson process with rate kn. • The new calls are uniformly distributed in the cells.

1009

• The call holding time Tc is exponentially distributed with mean 1/lc. • The average residual time of a call in a region is proportional to the shortest distance from the center to the boundary of the region. • Mobile terminals move to different directions with equal probability. • A mobile terminal communicates with two base stations when it is in soft handoff mode. Based on these assumptions, an analytical model is proposed next. 3.2. The analytical model Considering a CDMA network before the capacity acquisition protocol is applied, new arrival and soft handoff calls are served in the same queue. Since a call in soft handoff mode generates less interference than it does in single mode, a soft handoff call consumes less amount of capacity than a single mode call. Thus, there are two methods to model the system when the capacity acquisition protocol is not applied. The first option is to treat soft handoff calls differently from new arrival calls in the queueing process, in which the system has fixed system capacity. However, this method complicates the queueing analysis. The other option is to treat the soft handoff and new arrival calls equally in the sense of capacity consumption. However, the server capacity in this method varies with the average arrival rate of soft handoff calls in the system. This method has been widely accepted in the related work [1,5,7], and is also adopted in our analytical model. Thus, the CDMA network without capacity acquisition can be modeled as a queueing system, where the server capacity varies with the number of soft handoff calls, but new arrival and soft handoff calls are processed in the same way. When the capacity acquisition protocol is used to prioritize soft handoff calls over new arrival calls, a soft handoff call blocked from the previous queue system has another chance to be served in the CDMA network by applying capacity acquisition. Thus, blocked soft handoff calls in the previous queue are served in another queue. The capacity of the second queue depends on how

1010

X. Wang / Computer Networks 50 (2006) 1003–1021

n+

h

C1

uch PB1

C2 PB1

h

uch PB

2

Fig. 5. The analytical model.

much capacity can be released by the new admitted calls in the forced soft handoff region. Thus, the overall CDMA network can be analyzed using two sequenced queueing processes, as shown Fig. 5. C1 is the uplink capacity of a cell when new arrival calls in the forced handoff region do not work in soft handoff mode (i.e., before the capacity acquisition protocol is applied), while C2 is the reserved capacity carried by single mode calls in the forced soft handoff region. kh is the generating rate of handoff calls, and lch is the average channel holding time. Moreover, P B1 and P B2 are the call blocking probabilities of the first and the second queueing processes, respectively. According to this model, the call blocking probability PB is equal to the call blocking probability in the first queueing process, i.e., P B ¼ P B1 , while the call dropping probability PD of the system is P D ¼ P B1 P B2 . In order to find the solutions of PB and PD, C1, C2, and kh need to be derived.

In a CDMA network, the uplink capacity of a cell is inversely proportional to 1 + f [1], where f is the interference factor that is defined as the total interference from other cell users normalized by the average number of users per cell. Suppose the zeroth cell in a cellular network is considered. We define R1 as the inner region in all cells except the zeroth cell, R2 as the active handoff region in all cells, and R3 as the forced handoff region in all cells. According to the definition of interference factor, if Chard denotes the uplink capacity of a cell in a CDMA network without soft handoff, then C1 of the zeroth cell is C 1 ¼ C hard

1 þ fhard ; 1 þ fR1 þ fR2 þ fR3

ð6Þ

where fR1 ; fR2 ; fR3 are the interference factors due to the mobile terminals in regions R1, R2, and R3, respectively. For the scenario corresponding to C3, all calls in region R3 are in single mode, so the interference factor due to calls in this region is different from fR3 , and is thus denoted as fR0 3 . In the scenario of C4, all mobile terminals in region R3 are in soft handoff mode, so the interference factor corresponding to this region is denoted as fR003 . Thus, C3 and C4 can be derived as C 3 ¼ C hard

1 þ fhard ; 1 þ fR1 þ fR2 þ f 0 R3

ð7Þ

1 þ fhard ; 1 þ fR1 þ fR2 þ f 00 R3

ð8Þ

and

3.3. Derivations of C1 and C2

C 4 ¼ C hard

In order to determine the capacities C1 and C2, two parameters C3 and C4 are introduced. As shown in Fig. 6, C3 denotes the uplink capacity when a cell has only one soft handoff region with size equal to the size of the active handoff region (i.e., the region represented by d1 in Figs. 4 and 6), while C4 denotes the uplink capacity when the single soft handoff region is equal to the total size of the forced handoff region and the active handoff region (i.e., the region represented by d2 in Figs. 4 and 6). Given a cellular CDMA network, C3 and C4 can be determined [1,5], and will be presented in Section 4.1.

respectively. From (6) and (7), C1 and C3 are related as follows:   1 1 C hard ð1 þ fhard Þ  ð9Þ ¼ fR3  fR0 3 : C1 C3 Similarly, the relationship between C1 and C4 can be derived from (6) and (8) as   1 1 C hard ð1 þ fhard Þ  ð10Þ ¼ fR3  fR003 : C1 C4 Considering the scenario corresponding to C1, some calls work in single mode, while others are in soft handoff mode. The densities of single mode

X. Wang / Computer Networks 50 (2006) 1003–1021

1011

Fig. 6. Different handoff regions corresponding to C3 and C4.

n h and soft handoff calls are knkþk and knkþk , respech h tively, where kn is the new call arrival rate and kh is the generating rate of soft handoff calls. From [1], interference due to calls in a region is proportional to the density of calls in this region. In addition, if all calls in R3 are in single mode, their generated interference at the base station in the zeroth cell is fR0 3 N , where N is the average number of calls in a cell. Thus, in the scenario corresponding to C1, the experienced interference at the base station in the zeroth cell due to single mode calls in n R3 must be fR0 3 N knkþk . Similarly, the interference h due to soft handoff calls in R3 can be derived as h fR003 N knkþk . Thus, the interference due to both types h n h of calls in R3 is I R3 ¼ fR0 3 N knkþk þ fR003 N knkþk . h h According to the definition of interference factor, I fR3 ¼ NR3 , so kn kh þ fR003 : ð11Þ fR3 ¼ fR0 3 kn þ kh kn þ kh Thus, kn : ð12Þ fR3  fR003 ¼ ðfR0 3  fR3 Þ kn þ kh Combining (9), (10), and (12), and with some algebra, C1 can be derived as 1 1 kh 1 kn ¼ þ : ð13Þ C 1 C 4 kn þ kh C 3 kn þ kh

Since C4 > C3, so it is easy to show that C1 satisfies C3 < C1 < C4. The difference between C4 and C1 is the reserved capacity carried by the new arrival calls working in single mode in the forced handoff region, so C2 is given by

C2 ¼ C4  C1:

ð14Þ

3.4. Derivations of kh A new arrival call switches into soft handoff mode under the following situations: • For a new call initiated in the inner region, it switches into soft handoff mode if it enters the active handoff region or if it is forced into soft handoff when it enters the forced handoff region before it is terminated. • For a new call initiated in the forced handoff region, it switches into soft handoff mode if it enters the active handoff region before it is terminated. Such a new call may be forced into soft handoff mode when soft handoff calls need more extra capacity to compensate increased interference so that call dropping probability is reduced. • For a new call initiated in the active handoff region, it immediately enters soft handoff mode upon being admitted. If N denotes the number of handoff that are generated by a new arrival call, then the probability that it causes one handoff, denoted by Pr(N = 1), is given by PrðN ¼ 1Þ ¼ P I ð1  P B ÞP Ish xh þ P F ð1  P B ÞP Fsh xh þ P A ð1  P B Þxh ; ð15Þ

1012

X. Wang / Computer Networks 50 (2006) 1003–1021

where PI, PF, PA are the probabilities that the new call arrives in the inner region, forced handoff region, and active handoff region, respectively. Thus, in Eq. (15), the first, second, and third items on the right side represent the probabilities that a handoff call is generated by a call in the inner region, forced handoff region, and active handoff region, respectively. P Ish is the probability that a new call in the inner region requests handoff before it is terminated, while P Fsh is the same probability for a new call in the forced handoff region. xh denotes the probability that no more handoff is requested by a handoff call. Suppose P Is is the probability that a single mode call in the inner region enters the forced handoff region before it is terminated, P Fs is the probability of a single mode call in the forced handoff region enters the active handoff region before it is terminated, P Fi is the probability that a single mode call in the forced handoff region enters the active handoff region under the condition that it has left the inner region, and y Fs denotes the probability that a single mode call in the forced handoff region is forced into soft handoff mode. If a new call initiated in the inner region requests handoff, it must first enter the forced handoff region before it is terminated. The probability of this action is P Is . When this call is in the forced handoff region, handoff occurs when it continues to move and enters the active handoff region or when it is forced into soft handoff. The probability of the former scenario is P Fi , while that of the latter scenario is ð1  P Fi Þy Fs . Thus, P Ish is equal to P Ish ¼ P Is ðP Fi þ ð1  P Fi Þy Fs Þ:

ð16Þ

Similarly, P Fsh can be derived as P Fsh ¼ P Fs þ ð1  P Fs Þy Fs :

• The soft handoff call leaves the handoff region and stays in the inner region until it is terminated. Thus, xh is expressed as xh ¼ P D þ ð1  P D Þ    1  P Hh þ P Hh P a ð1  P Ih Þ ;

ð18Þ

where P Hh is the probability that a handoff call leaves the handoff region before it is terminated, Pa denotes the conditional probability that a mobile terminal moves from the handoff region to the inner region under the condition that the mobile terminal leaves the handoff region [5], and P Ih is the probability that the handoff call moves into the inner region and then leaves the region before the call is terminated. When N = 2, the probability that an admitted call causes two handoffs, denoted by Pr(N = 2), is PrðN ¼ 2Þ ¼ P I ð1  P B ÞP Ish ð1  P D Þy h xh þ P F ð1  P B ÞP Fsh ð1  P D Þy h xh þ P A ð1  P B Þð1  P D Þy Ai xh ;

ð19Þ

where y Ai is the probability of requesting another handoff by the new call in the active handoff region, and yh is the probability that a handoff call makes another handoff. If a soft handoff call successfully switches into handoff mode, it must make another handoff and the new handoff call will not be dropped. Thus, yh(1  PD) = 1xh, so yh is yh ¼

1  xh : 1  PD

ð20Þ

Similarly, when N = 3, Pr(N = 3) is 2

PrðN ¼ 3Þ ¼ P I ð1  P B ÞP Ish fð1  P D Þy h g xh 2

ð17Þ

No more handoff occurs in a call under the following situations: • The soft handoff call is dropped. • If the soft handoff call is not dropped, the soft handoff call does not leave the soft handoff region (including both forced handoff region and active handoff region) before it is terminated.

þ P F ð1  P B ÞP Fsh fð1  P D Þy h g xh þ P A ð1  P B Þð1  P D Þy Ai ð1  P D Þy h xh . ð21Þ In general, Pr(N = n) is given by n1

PrðN ¼ nÞ ¼ P I ð1  P B ÞP Ish ½ð1  P D Þy h 

xh

þ P F ð1  P B ÞP Fsh ½ð1  P D Þy h  þ P A ð1  P B Þy Ai ½ð1  P D Þy h 

n1

n2

xh

xh . ð22Þ

X. Wang / Computer Networks 50 (2006) 1003–1021

Thus, given the new call arrival rate kn, the the average rate of handoff calls kh must be 1 X nPrðN ¼ nÞ kh ¼ kn n¼1



¼ kn P I P Ish þ P F P Fsh



ð1  ð1  P D Þy h Þ

2

1 ð1  ð1  P D Þy h Þ

4. Performance of the capacity acquisition protocol ! 1 : 2 ð23Þ

3.5. Iterative solution of PB and PD

ðkn þ kh ÞC1 P b0 ; C 1 !lCch1

ð24Þ

where lch is the average channel holding time and Pb0 is given by P b0 ¼

1 C1 P i¼0

:

ð25Þ

ðkn þkh Þi i!lich

The blocked handoff calls access the reserved capacity C2, so in the second queueing process m = C2. Thus, the call blocking probability P B2 is C

P B2 ¼

ðkh P B1 Þ 2 P d0 ; C 2 !lCch2

1 C2 P i¼0

ðkh P B1 Þi i!lich

:

Before iteratively calculate the values of PB and PD, the parameters such as C3, C4 in (13), PI, PF, PA in (15), P Is ; P Fs ; P Fi ; y Fs in (16) and (17), y Ai in (19), P Hh ; P Ih ; P a in (18), and lch in (24) need to be determined. These parameters have been defined in the previous section. But for the reason of clarity, they are summarized in Table 1. The generally distributed residual time in a region is assumed to be exponentially distributed. Although it is shown that exponential distribution does not provide a good approximation to the residual time of a PCS network [10], it is still appropriate for cellular networks with a large cell size. Moreover, to have a fair comparison with other schemes such as [7], the same assumption (i.e., exponentially distributed residual time) as that in [7] is used.

ð26Þ

where Pd0 is given by P d0 ¼

In this section the analytical model is first verified through simulations. Based on the validated analytical model, the capacity acquisition protocol is then compared with other channel reservation schemes. 4.1. System parameters of analytical model

Both queueing processes in Fig. 5 are an M/M/ m/m queueing system. In the first one, m = C1, so the call blocking probability P B1 is P B1 ¼

rithm is out of the scope of this paper. However, given the constraints of 0 < PB < 1 and 0 < PD < 1, the iterative computation in our experiments has not met a problem to find a unique point for PB and PD.

ð1  P B Þxh

þ P A ð1  P B Þxh P A ð1  P B Þxh y Ai þ yh

1013

ð27Þ

Based on P B1 and P B2 , the call blocking probability PB and call dropping probability PD are equal to P B1 and P B1 P B2 , respectively. Since PB, PD, C1, C2, and kh are correlated, no close-form solution is available. Thus, PB and PD need to can calculated iteratively. Proof of the existence and uniqueness of a solution for this iterative algo-

• PI, PF, and PA. Since new arrival calls are assumed to be uniformly distributed in a cell, the probability of a new call arriving in a particular region is proportional to the size of the region. If k1 = d1/a and k2 = d2/a, then PI = (1  k2)2, PA = k1(2  k1), and PF = 1  PI  PA. • rh and rn. These two parameters can be determined from the area ratios, i.e., rh = PF/ (PF + PA) and rn = PF/(PI + PM + PA). • C3 and C4. C3 and C4 are the system capacities corresponding to two different sizes of handoff regions, which can be determined by considering the characteristics of soft handoff [1,5].

1014

X. Wang / Computer Networks 50 (2006) 1003–1021

Table 1 Notations used in performance analysis PI

The probability that a new call arrives in inner region

PF PA C3 C4

The probability that a new call arrives in forced handoff region The probability that a new call arrives in active handoff region The system capacity of a cell when the soft handoff region is just the active handoff region The system capacity of a cell when the soft handoff region includes both the forced handoff region and the active handoff region The probability that a call in the inner region enters the forced handoff region region before it is terminated The probability that a call in the forced handoff region enters the active handoff region region before it is terminated The probability that a call in the forced handoff region enters the active handoff region region under the condition that it has left the inner region The probability that a handoff call moves into the inner region and leaves the region before it is terminate The probability that a handoff call leaves the handoff region before it is terminated The conditional probability that a mobile terminal moves from the handoff region to the inner region under the condition that the mobile terminal leaves the current handoff region The probability that a new call in the forced handoff region requests a handoff The probability that a new call in the active handoff region requests another handoff The average channel holding time

P Is P Fs P Fs P Ih P Hh Pa y Fs y Ai lch

Given the pshadowing parameters r = 8 and ffiffiffi a ¼ b ¼ 1= 2, the system capacity increasing factor corresponding to the different sizes of soft handoff region is shown in Table 2, where the size of handoff region is represented by distance d2 that is from the inner region boundary to the cell boundary. From Table 2, if the capacity without using soft handoff is 30, then C4 will be 30 · 1.89 = 56.7 when d2 = 0.3. • P Is ; P Fs ; P Fi ; P Ih ; and P Hh . Since the residual time is exponentially distributed, by using the memoryless property of an exponential distribution, P Is ¼ P Ih . Also, the average residual time in a region is proportional to the shortest distance from the center to the boundary of I IF the region, so P Is ¼ lIlþl , P Fs ¼ lIFlþl , and c c F P Fi ¼ lFlþl [5], where c

1 1 ¼ lcell ð1  k 2 Þ, l1IF ¼ lI 1 1 ðk 2  K 1 Þ, and l1F ¼ lcell ð1  k 1 Þ, k 1 ¼ d 1 =a, lcell H and k 2 ¼ d 2 =a. Similarly, P Hh ¼ lHlþl where c 1 1 1 1 1 ¼ Or ðl  l Þ and l ¼ l ð1 þ k 2 Þ. Or is a l H

O

I

O

• Pa. It is assumed that a mobile terminal moves to different directions with the same probability. ad ffiffi 2 . Thus, as derived in [5], P a ¼ aþðp 21Þd 2 • y Fs and y Ai . From the memoryless property of exponential process, y Fs ¼ y Ai ¼ y h . 1 • lch. From [5], l1ch ¼ lc þl . O In the analytical model, a normalized cell is assumed, i.e, a = 1. Also, it is assumed that 1/lc = 1/ lcell = 100 s, and Or = 1. The uplink capacity of a cell without soft handoff is assumed to be 30 channels. d1, d2 and kn are the input parameters of experiments. Experiments are carried out as follows. First, the analytical model is verified through computer simulation. Then, based on the analytical results, the capacity acquisition protocol is compared with other schemes when d1 = 0.1 and d2 = 0.3 are assumed. 4.2. Comparison with simulations

cell

parameter dependent on the shape and size of the overlap region and the mobility model [5].

In order to verify the analytical model, computer simulation is developed according to the

Table 2 Capacity increasing factors Size of soft handoff region (d)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Capacity increasing factor

1.42

1.74

1.89

1.95

1.97

1.97

1.97

1.97

1.97

X. Wang / Computer Networks 50 (2006) 1003–1021

operation procedure described in Section 2.2. The assumptions of cell, traffic, and mobility models used in the simulation are the same as those used in analysis. The layout of cells is the same as Fig. 4. The radius of a cell is equal to 1000 m. The distances d1 and d2 are equal to 100 and 300 m, respectively. Nine cells are simulated. Since the number of cells is limited, a call may move out of the area of simulated cells. Thus, wrapped topologies are simulated to eliminate the boundary effect [11]. In each cell, the new calls are generated according to a Poisson process, and call duration is exponentially distributed with average equal to 100 s. An admitted call in a cell moves to different directions with equal probability. The moving speed of a call is uniformly distributed in [0, 10] meters per second. Channel attenuation and shadowing experienced by a call is simulated according to the model described in Section 2.1. In such a model, l = 4.0 and r = 8.0. When checking if a new call can be accepted or if a handoff call needs to be dropped, look around technique is used, i.e., the SINR of calls in all cells must be verified. If the SINR of some calls cannot be satisfied when a new call is generated, the new call is blocked. For a handoff call, if the SINR is not satisfied, a certain number of single mode calls working in forced handoff need to be switched into soft handoff mode until the SINR of all calls are satisfied. Otherwise, the handoff call under consideration is dropped. In the simulation, the processing gain G is assumed to be 16. The target SINR used in simulation is determined as follows. A call experiences interference from calls in its own cell and that in other cells as well. Suppose the received power of a call is P and the number of calls simultaneously supported in a cell without soft handoff is N, then interference from the calls of its own cell is (N  1)P. As used in analytical model, N = 30. Suppose fhard is the other cell interference normalized by the number of calls per cell. By using the same method in [5] and considering the cell layout in Fig. 4 and the channel model in Section 2.1, the value of fhard can be calculated, which is equal to 2.55. Thus, the SINR of a call at the base station is ðN 1ÞPGP ¼ 0:152. The threshold þfhard NP

1015

SINRthr described in Section 2.2 is assumed to be 0.052 in the simulation. For both simulation and theoretical analysis, call blocking and call dropping probabilities with respect to different traffic load are illustrated in Fig. 7. The match between simulation and analytical results proves that the analytical model has captured the characteristics of the new channel reservation scheme for soft handoff in CDMA networks. It is a valid model to analyze the performance of the new channel reservation scheme. 4.3. Comparison with existing schemes 4.3.1. Comparisons with the scheme without channel reservation In this experiment, our proposed scheme is compared with a scheme that does not use channel reservation [5]. In such a scheme, although no channel reservation is used, a large soft handoff region is used in order to decrease both call blocking probability and call dropping probability. To have a fair comparison, the size of the handoff region in such a scheme, represented by distance d, is assumed to be 0.3, i.e., the handoff region has the same size as the total size of the forced handoff region and active handoff region in our new scheme. Thus, this experiment actually illustrates the different performance between the schemes with and without using the calls in the forced handoff region to carry reserved capacity for soft handoff calls. The results are shown in Fig. 8. Since the scheme without using channel reservation does not differentiate the new arrival calls and handoff calls, the call dropping probability and call blocking probability have the same value. However, in our proposed scheme, the call dropping probability is greatly reduced when compared to call blocking probability. For example, the call dropping probability is lower than the call blocking probability by more than 40% even when traffic load is higher than 0.6 calls/s/cell. The reason is that the single mode calls in the forced handoff region carry the capacity that can be used by soft handoff calls to compensate the increased interference. Since the reduced interference brought by

X. Wang / Computer Networks 50 (2006) 1003–1021

Probabilities of Call Blocking and Dropping

1016 10

0

10

–1

10

–2

10

–3

10

–4

Analysis (Blocking) Analysis (Dropping) Simulation (Blocking) Simulation (Dropping)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

New Call Arrival Rate (calls/s/cell)

Probabilities of Call Blocking and Dropping

Fig. 7. Simulation versus analytical results.

10

0

10

–1

10

–2

10

–3

10

–4

New Scheme (Blocking) New Scheme (Dropping) No Reservation (Blocking) No Reservation (Dropping)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

New Call Arrival Rate (calls/s/cell) Fig. 8. Comparisons with the scheme without channel reservation.

forced handoff calls also affects the admission of the new arrival calls, the call blocking probability

is only slightly higher than that of the scheme without using channel reservation.

X. Wang / Computer Networks 50 (2006) 1003–1021

4.3.2. Comparisons with the fixed reservation scheme In order to differentiate new arrival calls and handoff calls, a simple method is to reserve a fixed number of channels for handoff calls [4]. The results of our scheme and the fixed channel reservation scheme are compared in Fig. 9, where five channels are reserved for soft handoff calls in the fixed channel reservation scheme. As shown in Fig. 9, in both schemes, the call dropping probability is much lower than the call blocking probability. When the traffic load is higher than 0.7 calls/s/cell, although the call blocking probability in the fixed channel reservation scheme is only slightly higher than that of the new channel channel reservation, the call dropping probability is much higher than that of the new scheme. The reason is that fixed reservation cause low utilization of channels. Due to this reason, if the call dropping probability in the fixed reservation scheme needs to be decreased, the call blocking probability must increase. This illustrates the advantage of the new channel reservation scheme.

1017

4.3.3. Comparisons with the adaptive reservation scheme In this experiment, our scheme is compared to the adaptive channel reservation scheme proposed in [7]. In the adaptive channel reservation scheme, the soft handoff regions determined by thresholds TADD and TDROP, and the reservation region are represented by distances dADD, dDROP, and dRSR, respectively. In order to have a fair comparison, the size of the handoff region determined by threshold TADD in the adaptive channel reservation scheme is equal to the size of the active handoff region, and the size of the reservation region is equal to the size of the forced handoff region. Thus, dADD = 0.1 and dRSR = 0.2. As in [7], dDROP is assumed to be 0.3. The call blocking and dropping probabilities of the capacity acquisition protocol and the adaptive reservation scheme are shown in Fig. 10. The call dropping probability of the adaptive channel reservation scheme is improved compared to the fixed channel reservation scheme. However, it is still much higher than the new scheme at all traffic loads. When traffic load is between 0.5 and

Probabilities of Call Blocking and Dropping

10 0

10 –1

10 –2

10 –3

10 –4

New Scheme (Blocking) New Scheme (Dropping) Fixed Reservation (Blocking) Fixed Reservation (Dropping)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

New Call Arrival Rate (calls/s/cell) Fig. 9. Comparisons with the scheme with fixed channel reservation.

0.9

X. Wang / Computer Networks 50 (2006) 1003–1021

Probabilities of Call Blocking and Dropping

1018 10

0

10

–1

10

–2

10

–3

10

–4

New Scheme (Blocking) New Scheme (Dropping) Adaptive Reservation (Blocking) Adaptive Reservation (Dropping)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

New Call Arrival Rate (calls/s/cell) Fig. 10. Comparisons with the adaptive channel reservation scheme.

0.9 calls/s/cell, the call dropping probability is more than 10% higher than the new scheme. During this load range, the call blocking probability is almost the same as that the new scheme. However, when traffic load is less than 0.5 calls/s/cell, the call blocking probability of the adaptive channel reservation scheme becomes much higher than our new scheme.

5. A load-adaptive capacity acquisition protocol and its performance Given a fixed forced handoff region in the capacity acquisition protocol, if it is small, the call dropping probability will be very large when the new call arrival rate is high. On the other hand, if the size of the forced handoff region is large, many calls will unnecessarily work in soft handoff mode when traffic load is low, which wastes system capacity because soft handoff calls decrease the available channels on the forward link of a base station [9]. In order to keep the call dropping probability as low as possible and maximize the available channels on the forward link, a load-

adaptive capacity acquisition protocol is needed. In this scheme, the size of the forced handoff region d2 is adjusted adaptively according to the traffic load in the network. When the new call arrival rate increases so that the call dropping probability exceeds a desired value CD, d2 is reduced to enlarge the size of forced handoff region. In such a way, more capacity from single mode calls can be borrowed by the soft handoff calls that need extra capacity. Given the desired call dropping probability CD and call arrival rate kn, the optimal value of d2 can be iteratively calculated by using the analytical model in Section 3. However, a more practical solution is under investigation. Based on the analytical model, experiments of two scenarios are carried out to investigate the load-adaptive capacity acquisition protocol. The desired call dropping probability of one scenario is less than 0.01, while that of the other is less than 0.05. The results of call blocking and dropping probabilities are shown in Figs. 11 and 12, respectively, for both scenarios. In Fig. 13, the size of forced-handoff region (in terms of distance d2) versus traffic load is also illustrated.

Call Blocking Probability

X. Wang / Computer Networks 50 (2006) 1003–1021

10

–1

10

–2

1019

Desired Call Dropping Probability < 0.01 Desired Call Dropping Probability < 0.05

10

–3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

New Call Arrival Rate (calls/s/cell)

Call Dropping Probability

Fig. 11. Call blocking probability when using dynamic forced handoff region.

10

–1

10

–2

Desired Call Dropping Probability < 0.01 Desired Call Dropping Probability < 0.05

10

–3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

New Call Arrival Rate (calls/s/cell) Fig. 12. Call dropping probability when using dynamic forced handoff region.

At the same traffic load, for the scenario requiring a lower desired call dropping probability, a larger size of the forced handoff region is needed, as

shown in Fig. 13. Due to the larger size of the forced handoff region, the call blocking probability of this scenario is also smaller, as illustrated in

1020

X. Wang / Computer Networks 50 (2006) 1003–1021

Desired Call Dropping Probability < 0.01 Desired Call Dropping Probability < 0.05

Size of Forced–Handoff Region d2

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1

0.2

0.3

0.4

0.5

0.6

0.7

New Call Arrival Rate (calls/s/cell) Fig. 13. The dynamic size of the forced handoff region versus traffic load.

Fig. 11. However, the difference in call blocking probability of those two scenarios is small, because most of the increased capacity introduced by forced handoff calls is used by soft handoff calls instead of new arrival calls. For the same desired call dropping probability, the size of the forced handoff region needs to be increased as the traffic load increases. However, since the size of forced handoff region is limited, i.e., d2 < 1, the desired call dropping probability cannot be guaranteed when the traffic load approaches an upper bound. When a higher call dropping probability is desired, the upper bound is lower. For example, as shown in Figs. 12 and 13, the bound is 0.67 calls/s/cell when the call dropping probability is desired to be less than 0.05. However, when the call dropping probability needs to be less than 0.01, the upper bound is 0.55. As illustrated in Table 2, the uplink capacity of a cell does not increase when the size of the handoff region in terms of distance d is larger than 0.5. However, as shown in Figs. 12 and 13, when the traffic load is so high that distance d2 is larger than 0.5, it is still effective to increase the size of the forced handoff region to guarantee a desired dropping probability. The reason is that the number of calls

that can be forced into soft handoff still increases even when the size of the forced handoff region (d2) is larger than 0.5, which increases the reserved capacity and improves the probability of successful capacity acquisition for soft handoff calls.

6. Practicality of the capacity acquisition protocol There are a few practical issues concerning the implementation of the capacity acquisition protocol. • SINR measurement. SINR is used in the capacity acquisition protocol to determine if enough capacity has been acquired. SINR measurement is usually available as one of the building blocks for power control in CDMA networks. The accuracy of SINR measurement depends on the performance of the estimation algorithm. Tradeoff between accuracy and measurement periods must be considered for SINR measurement [12]. • Operation in the downlink. In the downlink, the base station controller (BSC) can also dynamically select a base station with lowest power to

X. Wang / Computer Networks 50 (2006) 1003–1021

communicate with the mobile terminal in soft handoff mode. However, this may cause ‘‘ping–pong’’ effect [13] and thus make this mechanism infeasible. Consequently, how to apply the capacity acquisition protocol to the downlink operation needs further investigation. Despite the difficulty in the downlink, the capacity acquisition protocol is effective to enhance the performance of uplink.

7. Conclusions An implicit channel reservation was proposed for soft handoff calls in CDMA networks. The effectiveness of this scheme was based on the features of soft handoff. An analytical model was also derived for the new channel reservation scheme. It was validated through computer simulations. The proposed capacity acquisition protocol was shown to outperform other existing channel reservation schemes for CDMA networks. It was also extended into a traffic-load adaptive channel reservation scheme. How to propose a similar protocol for the downlink operation is subject to future research. In addition, how to extend the capacity acquisition protocol to a CDMA network supporting both voice and data calls is another interesting research topic.

References [1] A.J. Viterbi et al., Soft handoff extends CDMA cell coverage and increase reverse link capacity, IEEE J. Select. Areas Commun. 12 (8) (1994) 1281–1288. [2] Z. Liu, M.E. Zarki, SIR-based call admission control for DS-CDMA cellular systems, IEEE J. Select. Areas Commun. 12 (4) (1994) 638–644. [3] Y. Ishikawa, N. Umeda, Capacity design and performance of call admission control in cellular CDMA systems, IEEE J. Select. Areas Commun. 15 (8) (1997) 1627–1635. [4] S.L. Su, J.Y. Chen, J.H. Huang, Performance analysis of soft handoff in CDMA cellular networks, IEEE J. Select. Areas Commun. 14 (9) (1996) 1762–1769.

1021

[5] D.K. Kim, D.K. Sung, Characterization of soft handoff in CDMA systems, IEEE Trans. Vehic. Technol. 48 (4) (1999) 1195–1202. [6] Y. Ma, J.J. Han, K.S. Trivedi, Call admission control for reducing dropped calls in code division multiple access (CDMA) cellular systems, in: Proc. IEEE INFOCOM 2000, March 2000, pp. 1481–1490. [7] J.W. Chang, D.K. Sung, Adaptive channel reservation scheme for soft handoff in DS-CDMA cellular systems, IEEE Trans. Vehic. Technol. 50 (2) (2001) 341–353. [8] Y.-B. Lin, S. Mohan, A. Noerpel, Queueing priority channel assignment strategies for PCS handoff and initial access, IEEE Trans. Vehic. Technol. 43 (3) (1994) 704–712. [9] C.C. Lee, R. Steele, Effect of soft and softer handoffs on CDMA system capacity, IEEE Trans. Vehic. Technol. 47 (3) (1998) 830–841. [10] Y. Fang, I. Chlamtac, Teletraffic analysis and mobility modeling of PCS networks, IEEE Trans. Commun. 47 (7) (1999) 1062–1072. [11] Y.-B. Lin, V.W. Mak, Eliminating the boundary effect of a large scale personal communication service network simulation, ACM Trans. Modeling Comput. Simul. 4 (2) (1994) 165–190. [12] H.-J. Su, E. Geraniotis, Adaptive closed-loop power control with quantized feedback and loop filtering, IEEE Trans. Wireless Commun. 1 (1) (2002) 76–86. [13] A.J. Viterbi, CDMA: Principles of Spread Spectrum Communication, Prentice Hall PTR, 1995.

Xudong Wang received his B.E. and Ph.D. degrees from Shanghai Jiao Tong University, Shanghai, China, in 1992 and 1997, respectively. From 1998 to 2003, he was with the Broadband and Wireless Networking (BWN) Lab at Georgia Institute of Technology. He also received the Ph.D. degree from Georgia Institute of Technology in 2003. Currently, he is a senior researcher with Kiyon, Inc., where he leads a research and development team working on MAC, routing, and transport protocols for wireless mesh networks. His research interests also include software radios, cross-layer design, and communication protocols for cellular, mobile ad hoc, sensor, and ultra-wideband networks. He is a guest editor for the special issue on wireless mesh networks in IEEE Wireless Communications Magazines. He has been a technical committee member of many international conferences, and a technical reviewer for numerous international journals and conferences. He has two patents pending in wireless mesh networks. He is a member of IEEE, ACM, and ACM SIGMOBILE.