Wirel. Commun. Mob. Comput. 2002; 2:169– 186 (DOI: 10.1002/wcm.43)
Load-balancing channel assignment for dual-band PCS
networks
Ming-Feng Chang and Long-Sheng Li*,† Department of Computer Science and Information Engineering
National Chiao Tung University Hsinchu
Taiwan, Republic of China
Summary
This paper investigates the channel assignment problem of dual-band PCS systems where single-band and dual-band handsets co-exist. Load-balancing channel assignment schemes are proposed to improve the system performance. To balance the loads of both bands, the BSC selects a band to serve a call request of a dual-band handset based on the loads of both bands. In addition, a channel re-assignment scheme is used to further improve the system capacity. Analytic models and computer simulations have been developed to evaluate the performance of the load-balancing schemes. The results indicate that both load-balancing and channel re-assignment
techniques significantly increase the system capacity as the percentage of dual-band handsets increases. Furthermore, the load-balancing with channel re-assignment scheme that combines both techniques achieves the best system performance even when the percentage of dual-band handset is as low as 25%. In addition, we describe an approach to reduce the signal overhead of the load-balancing schemes. Copyright 2002 John Wiley & Sons, Ltd.
KEY WORDS
personal communications service (PCS) dual-band
load-balancing channel assignment
Published online: 8 January 2002
ŁCorrespondence to: L.-S. Li, Department of Computer Science and Information Engineering, National Chiao Tung
University, Hsinchu, Taiwan, Republic of China.
†E-mail: sheng@mail.ncyu.edu.tw
Contract/grant sponsor: MDE Program of Excellence Research; contract/grant number: 89-E-FA04-4. Contract/grant sponsor: National Science Council; contract/grant number: 89-2213-E-009-201.
1. Introduction
Personal Communication Services (PCSs) have expe-rienced an enormous growth during the last decade [1, 2]. The drive forces behind this growth is the reduc-tion in the cost of handsets and service costs. Because of the enormous subscriber growth in most wire-less networks, it becomes more and more impor-tant to provide sufficient network capacity. There are several techniques to enhance system capacity, such as microcells, half rate channels and dual-band systems [3, 4]. The microcell approach reduces the cell size and builds more base stations. As a result, the total number of channels and the system capac-ity increase. The microcell has a limitation on the cell size due to signal interference and dropped calls for fast moving mobiles [5, 6]. The imple-mentation of half rate channels in a GSM mobile ratio network provides theoretically twice the net-work capacity of the full rate system. However, this capacity gain can only be achieved if mobile hand-sets support the half rate transmission. Dual-band systems increase radio channels by extending the radio bandwidth. A typical example is a dual-band GSM system which integrates GSM 900 and DCS 1800 [2, 7]. Since the GSM family shares the same network protocols, it is straightforward to integrate GSM 900 and DCS 1800 networks [4, 8]. In addi-tion, dual-band handsets have become more popular to take advantage of the dual-band networks. The GSM family offering multi-band terminals and net-works has become the popular digital standard of PCS [9, 10].
The carried traffic of a PCS network can be improved by using the techniques of dynamic chan-nel assignment and chanchan-nel re-assignment. Das et al. [11] proposed an efficient dynamic channel assignment scheme using channel borrowing between neighbor-ing cells. They migrate channels through a struc-tured borrowing mechanism to balance the loads of the cells. The results showed the scheme obtained a performance improvement of 12 per cent in terms of call blocking under moderate and heavy traffic conditions. Qiao et al. [12] proposed mobile relay stations within each cell to divert traffic in one cell to another. Their study indicated that the inte-gration of the cellular and mobile/wireless relaying technologies can dynamically balance traffic between neighboring cells in a cellular system. Kuek and Wong [13] presented an ordered dynamic channel assignment with re-assignment scheme in microcells where a call connected to macrocells is re-assigned
to microcells when channels in microcells become available.
Systems that employ microcells with overlaying macrocells to increase system capacity were proposed in Reference [14]. Rappaport and Hu [14] studied the performance of the overlaid network where new calls and handoff calls can enter at both cell levels. Rams-dale and Harrold [8] discussed a dual-band system where GSM 900 is deployed in normal cells to form a contiguous coverage layer and DCS 1800 is deployed in microcells as a different layer of discontinuous regions to enhance the capacity. A channel assign-ment scheme was developed to prevent high speed mobiles from using the radio channels of micro-cells. Rodriguez et al. [15] investigated the channel assignment problem of a dual cellular system support-ing AMPS and D-AMPS. The subscribers use ana-log (AMPS) handsets or dual-mode (AMPS and D-AMPS) handsets, since each AMPS carrier can afford one analog channel or six digital channels. They pro-posed channel assignment schemes where dual-mode handsets use a digital channel whenever possible. Tegler et al. [4] analyzed the capacity improvement in the GSM/DCS dual-band system where all hand-sets are dual-band. Computer simulations were con-ducted to measure the maximum system capacity. Lai [16] studied the interconnection issues of dual-band GSM system. The study indicates that a homo-geneous connection, where both GSM 900 and DCS 1800 share the same HLR, significantly outperforms a heterogeneous connection in the call incompletion probability.
However, the effects of the co-existence of dual-band and single-dual-band handsets on the carried traf-fic have not been investigated. It is clear that as the percentage of dual-band handsets increases, the system carried traffic increases. In this paper, we will show that the channel re-assignment technique can significantly increase the carried traffic even when only 25 per cent of the handsets are dual-band. The effects of the user mobility on the sys-tem carried traffic will also be studied. In addi-tion, the message overhead of the load-balancing schemes will be investigated. The paper is organized as follows. Section 2 presents dual-band PCS net-works and channel assignment schemes. Section 3 describes analytic models for the channel assignment schemes. Section 4 derives equations for evaluating the system performance. Section 5 shows the ana-lytic and simulation results. Section 6 concludes the paper.
B-band BTS A-band BTS HLR BSC VLR MSC PSTN Telephon hand set BSS
Fig. 1. The network architecture of dual-band systems.
2. Dual-Band PCS Networks and Channel Assignment
In Taiwan, dual-band GSM cellular networks have been provided by Chunghwa and Far EasTone Tele-communications. The networks consist of GSM900 and DCS1800 systems. In our study, we use A-band/B-band systems to represent dual-band PCS sys-tems. Figure 1 shows the network architecture of a dual-band system. A base station subsystem (BSS) consists of a base station controller (BSC) and two base transceiver stations (BTS): an A-band BTS and a B-band BTS. The BSC connects to a mobile switch-ing center (MSC), which connects to the switches of the public switched telephone network (PSTN) [17]. The BTS serves the calls to and from the handsets in its service area, called cells, via radio channels. The BSC assigns radio channels to serve the calls. To simplify the analytic model, we assume that an A-band cell and its overlaid B-A-band cell are of the same size and cover the same area. This configuration is a special case of the microcell/macrocell architecture where a macrocell overlays only one microcell [5, 6]. Since the A-band and B-band BTSs are located at the same site, one advantage of the overlaid architecture is cost reduction for site preparation and site rental.
A home location register (HLR) and visitor loca-tion registers (VLRs) facilitate the roaming manage-ment of handsets. One or more cells are grouped to form a registration area. The BSCs of a regis-tration area are connected to an MSC providing the call processing for all the handsets within the service area. Every registration area has a corresponding VLR which keeps a record for each handset visiting the registration area. The HLR contains the primary infor-mation of each handset, including the visited VLR of the handset. In this way, the current location of a handset can be obtained from the HLR. For the dual-band handsets, the dual-band network configura-tion can be considered as a single network where the radio spectrum has been extended from one band to two bands [16]. However, a dual-band handset tunes to only one of the BTSs. When a dual-band handset requests a channel, the BSC assigns a free chan-nel from the BTS to which the dual-band handset is tuning.
2.1. The load-balancing scheme
Since a dual-band handset can use the channels of either band. This flexibility can be utilized to balance the loads of both bands. Based on the numbers of free channels on both bands and the expected loads of both bands, the BSC selects a band to serve a call of a dual-band handset. The goal of this band-selection is to balance the loads of both bands and to minimize the probability that a call cannot be completed (either be blocked or forced to terminate for no free channels). For load-balancing, a simple, greedy algorithm for band-selection may assign the band with a greater number of free channels to serve a call request of a dual-band handset. However, this greedy algorithm may not balance the loads of both bands in the long
CR = CA + 0.5; /* all dual-band handsets use B-band */ CL = -CB − 0.5; /* all dual-band handsets use A-band */ while CR-CL>ε do /* ε is a pre-defined small value */
C1 = (CL+CR)/2;
C2 = C1 + ε1; /* ε1 is a pre-defined small value */ if Pnc(C1) > Pnc(C2) CL = C1; else CR = C2; endif endwhile Cmin = CR or CL;
Fig. 2. The pseudo code of the bisection search algorithm to determine Cmin.
C0 Pnc Cmin 0.06 0.05 0.04 0.03 0.02 0.01 0 −20 −10 0 10 20
Fig. 3. The effects of band-selection parameter C0on Pnc.
run, because the expected load of A-band (single-band) handsets and that of B-band handsets may be unequal. Our algorithm selects a serving band to balance the loads in the long term, and thus minimize the call probability that a call is incompleted.
The band-selection algorithm works as follows. Let FAdenote the number of free channels in the A-band, FB denote that of the B-band, and D D FAFB. A bisection search algorithm [18] that will be presented in Figure 2 determines a band-selection parameter C0DC C fwhere C is an integer and 0.5 < f 0.5; the numbers are used by the band-selection algo-rithm. For a call request of a dual-band handset, if D > C, A-band is selected to serve the request; If D < C, B-band is selected. If D D C, A-band is selected with probability f C 0.5 and B-band with probability 0.5 f. Note that when D D C and f D0, half of the dual-band handsets are served by the A-band. For a given C0, the call incompletion
probability (Pnc) can be obtained using an iterative algorithm described in Section 4.5, i.e., Pnc can be expressed as a function of C0. The function is a concave upward curve as shown in Figure 3. Con-sider the curve where C0< Cmin. If C0 is decreased, Pnc increases because the traffic loads in both bands become more unbalanced. This is also true when C0> Cmin and C0is increased. There exists an opti-mal value of C0 such that Pnc can be minimized. A bisection search algorithm, described in Refer-ence [18], can be used to obtain the optimal value, Cmin. The pseudo code is listed as follows. In this algorithm, CA (CB) is the channel capacity of A-band (B-band) in a cell.
To originate a call, a dual-band handset uses the signaling channel to send the call attempt. Then, the BSC instructs the handset to use the selected serving band. Second, for call termination, the BSC asks the BTSs of both bands to page the dual-band handset. Then, the dual-dual-band handset requests an idle channel from the BSC. If the requested band is not the selected serving band, the BSC instructs the handset to switch to the other band and to request an idle channel. The detailed mes-sage flows of GSM systems are described as follows.
Figure 4 shows the message flows of call termi-nation for a dual-band handset in dual-band GSM systems [19]. This example illustrates that a handset tunes to BTS-A and switches over to BTS-B on call termination to the handset.
handset BTS-A BSC BTS-B handset
1. page re quest 2. channel request 3. immediate assignment 4. band-switching command 5. acknow ledge 6. page response 7. call se tup 8. call co nfirmed 9. alertin g 13. connect 14. connect ACK conversations extra messages
10. channel assignment command 11. channel assignment complete 12. alert
Step 1: The handset tunes to BTS-A. The BSC
sends a page request through both BTSs to the handset.
Step 2: On receiving the page request, the handset
sends a channel request to the BSC.
Step 3: After receiving the channel request
mes-sage, the BSC allocates a message communication channel (SDCCH: Stand-alone Dedicated Con-trol CHannel) and sends an immediate assignment message to the handset. The handset communi-cates with the BSC over the SDCCH until a voice channel is assigned [19].
Steps 4 & 5: The BSC sends a band-switching
command to the handset over the SDCCH. The handset sends an acknowledge back to the BSC and switches to B-band.
Step 6: The handset tunes to BTS-B. Then, it
sends a page response to the BSC.
Steps 7–14: The handset and BSC follow the
GSM protocol to set up a call connection [19]. Note that Steps 4 and 5 are the additional message exchanges for the band-switching; other steps are the message exchanges for a normal call termination. Thus, the message overhead of the band-switching on call termination to a handset is two extra messages.
In this scheme, the BSC must be capable of deter-mining the selected serving band and instructing dual-band handsets to switch over to the other dual-band on call origination and call termination. However, for a hand-off call, the dual-band handset tries to use the same band as it uses in the old cell. If no free channel is
available, it is forced to terminate. This scheme will be referred to as the Load-Balancing (LB) scheme. 2.2. The load-balancing scheme with inter-band handoff
To improve the LB scheme, the handoff calls of dual-band handsets are instructed to switch to the selected serving band. The procedures of call origination and call termination are the same as those in the LB scheme. This scheme will be referred to as the Load-Balancing scheme with Inter-band Handoff (LBIH). Figure 5 shows the message flows of an Inter-BSC handover call of a dual-band handset that switches to the selected serving band in the new cell. The example is a dual-band GSM system where the two BSCs connect to the same MSC.
Step 1: Before a dual-band call is handed over to
a new cell, the MSC requests a channel for the dual-band handset in the new cell.
Step 2: BTS-B allocates a new channel and sends
a channel request acknowledge to the MSC.
Step 3: The MSC sends a handover command
to the handset on the FACCH (Fast Associated Control CHannel). The channel ID of the han-dover command indicates that band-switching is required.
Steps 4–9: The handset and BTSs follow the
GSM protocol to hand the call over to BTS-B. Note that Step 3 combines a handover command and a band-switching command in one message.
handset MSC
BTS-B
(new cell) handset call connecting 1. channel request 2. request ACK 3. handover and band-switching command 7. handover completion resume call on the new channel
9. release ACK 8. release BSC (new cell) BSC (old cell) BTS-A (old cell) 4. handover access 5. physical information 6. handover detection
Therefore, no extra message exchange is required for this inter-band handoff.
2.3. The load-balancing with channel re-assignment
In the two schemes described above, an initial call or a handoff call of an A-band handset is blocked if there is no free channel at A-band. However, the call can be still connected if a dual-band handset using an A-band channel can be re-assigned to a free chan-nel at the B-band. The released A-band chanchan-nel can serve the request of the A-band handset. The channel re-assignment technique has been studied in Refer-ences [12, 13]. By using this channel re-assignment technique, a call of an A-band handset will be rejected only if all A-band channels are assigned to A-band handsets or there is no free channel at both bands. The same channel re-assignment technique can also be applied to B-band handsets.
The channel re-assignment procedure works as fol-lows. First, to originate a call, a single-band handset uses the signaling channel to make a call attempt. If the corresponding BTS has no free channel and some busy channels are used by the dual-band users, the BSC selects a victim from the dual-band hand-sets. The BSC then selects an idle channel from the other BTS and uses the signaling channel to inform the victim to switch to the other band. The victim releases the original channel and resumes the call on the selected channel. The BSC then uses the sig-naling channel to instruct the single-band handset to tune to the released channel. Second, for call termi-nation, the BSC asks the corresponding BTS to page the single-band handset. The BSC then selects a dual-band handset victim, re-assigns the victim to a free channel of the other BTS, and instructs the single-band handset to tune to the released channel. Last, for a handoff call, the handset initiates the handoff procedure by sending signals to the new BSC. The BSC selects a dual-band handset victim to release its channel and re-assigns a free channel from the other BTS. Then, the BSC notifies the MSC to set up a new routing path, and the single-band handset is handed over to the released channel in the new BTS. This channel re-assignment scheme will be referred to as the Load-Balancing with Channel Re-assignment (LBCR).
The overhead of a channel re-assignment is to force a dual-band handset to switch over to the other BTS of the same cell. This band-switching procedure is the same as an inter-BTS handoff procedure in a
single-band system. The message flows of an inter-BTS handoff can be found in References [20, 21]. 2.4. Reduce the overhead
Band-switching on call origination and call termina-tion for a dual-band handset requires extra message exchanges, which may result in congestion on the sig-nal channels. The message overhead can be reduced if fewer band-switchings are performed. For example, when the system traffic load is low, a band-switching is unnecessary because there are many free channels at both bands. Therefore, we can reduce the message overhead if band-switching is performed only when the traffic load is larger than a threshold t. The old t will be referred to as the band-switching thresh-old. On the other hand, since the band-switching of a dual-band handover call requires no message over-head, this band-switching is always performed.
3. Analytic Models
In this section, an analytic model using a four-dimensional Markov chain is developed to evaluate the load-balancing schemes [14, 22]. We assume that A-band and B-band BTS are co-siting. This setup is actually exercised in GSM networks in Taiwan. An A-band cell and its overlay B-band cell are assumed to be of the same size and cover the same area. Furthermore, we assumed cells in the system are homogeneous, i.e., all cells have the same traffic load.
The terms and parameters used in our model are described as follows:
ž A (B, db): the call arrival rate of A-band hand-sets (B-band handhand-sets, dual-band handhand-sets) in a cell; the call arrivals are assumed to be a Poisson process.
ž 1/: the mean call holding time. We assume that the call holding time has a negative exponential distribution with mean 1/ as suggested in Refer-ences [22, 23].
ž 1/: the mean cell residence time of a handset at a cell. We assume that the cell residence time has a negative exponential distribution with mean 1/. ž A h (B h, db h): the handoff call arrival rate
of A-band handsets (B-band handsets, dual-band handsets) to a cell; the handoff call arrivals of A-band and B-A-band handsets are assumed to be a Poisson process.
ž db h A (db h B): the handoff call arrival rate to a cell for the dual-band users connecting an A-band (B-band) channel in the previous cell; the handoff call arrivals are assumed to be a Poisson process. ž db A (db B): The call arrival rate of dual-band
handsets tuning to A-band (B-band); the call arrivals are assumed to be a Poisson process. ž Si, j, k, l: the state of a cell, where i represents
the number of active A-band handsets, j represents the number of active B-band handsets, k represents the number of dual-band handsets using A-band channels, and l represents the number of dual-band handsets using B-band channels in the cell. 3.1. State transitions of the LB scheme
Figure 6 depicts the state transitions around Si, j, k, l for the LB scheme. Note that a legal state Si, j, k, l must satisfy 0 i C k CA and 0 j C l CB. The state transitions can be summa-rized as follows.
(1) When an A-band user (B-band user) initiates a call with rate A (B) or an A-band user (B-band user) handoff call arrives with rate A h (B h), the state parameter i j is incremented by 1, i.e., a free channel of A-band (B-band) is assigned to serve the call.
(2) When an A-band (B-band) call terminates with rate or leaves the cell with rate , the state parameter i j is decremented by 1, i.e., a free channel of A-band (B-band) is released.
(3) When a dual-band user initiates a call with rate db and D > C (D < C), the state parameter k
l is incremented by 1. If D D C, A-band is selected with probability f C 0.5 and B-band is selected with probability 0.5 f. On the other hand, when a dual-band handoff call using an A-band (B-A-band) channel arrives with rate db h A (db h B), the state parameter k l is incre-mented by 1 because handoff calls always use the same band. Let DA[i, j, k, l] be the tran-sition rate from Si, j, k, l to Si, j, k C 1, l and DB[i, j, k, l] be the transition rate from Si, j, k, l to Si, j, k, l C 1. The state transi-tions can be expressed as follows,
DA[i, j, k, l] D dbCdb h A, if D > C db h A, if D < C dbCdb hf C0.5 if D D C DB[i, j, k, l] D dbCdb h B, if D < C db h B, if D > C dbCdb h0.5 f if D D C
(4) When a dual-band call using an A-band (B-band) channel terminates with rate or leaves the cell with rate , the state parameter k l is decremented by 1.
3.2. State transitions of the LBIH scheme The state transition diagram of the LBIH scheme is similar to that of the LB scheme. The difference between them is the channel assignment for the hand-off calls of dual-band handsets. For a handhand-off call of a dual-band handset, the LBIH scheme assigns a chan-nel from the selected serving band to the call; the LB scheme assigns a channel from the same band serving the call in the old cell.
(i+1)(µ + η) (2) i,j,k,l+1 i, j, k, l i,j,k+1,l i,j+1,k,l I(µ + η) (4) i(µ + η) (2) (k+1)(µ + η) (4) (l+1)(µ + η) (4) j(µ + η) (2) (j+1)(µ + η) (2) k(µ + η) (4) i,j,k, I−1 i,j,k−1,I i,j−1,k,I i−1,j,k,I λA + λA_h (1) λA + λA_h (1) λB + λB_h (1) λB + λB_h (1) i+1,j,k,l DB[i,j,k,I−1] (3) DB[i,j,k,I] (3) DA[i,j,k,I] (3) DA [i,j,k−1,l] (3) i+1+k ≤ CA i+1+k ≤ CA j+1+l ≤ CB j+1+l ≤ CB l−1≥0 k−1≥0 j−1≥0 i−1≥0
(1) The state transitions corresponding to single-band user events are the same as those in the LB scheme.
(2) The state transitions for dual-band user events including terminating a call and leaving a cell are the same as those in the LB scheme. (3) When a dual-band user initializes a call with
rate db or a dual-band call is handed over with rate db h ACdb h B, the state parameter k l is incremented by 1, if D > C (D < C). If D D C, A-band is selected with probability f C0.5 and B-band is selected with probabil-ity 0.5 f. Transition rates DA[i, j, k, l] and
DB[i, j, k, l] shown in Figure 7 can be expressed as follows, DA[i, j, k, l] D dbCdb h, if D > C 0, if D < C dbCdb hf C0.5 if D D C DB[i, j, k, l] D dbCdb h, if D < C 0, if D > C dbCdb h0.5 f if D D C
3.3. State transitions of the LBCR scheme The Markov chain of the LBCR scheme can be simplified to a three-dimensional model as shown
i+1,j,k,l i,j,k+1,l (i+1)(µ + η) (1) l(µ + η) (2) k (µ + η) (2) i (µ + η) (1) (l+1)(µ + η) (2) (j+1)(µ + η) (1) (k+1)(µ + η) (2) j (µ + η) (1) i,j,l −1 i−1,j,k,l i,j,k,l+1 i,j+1,k,l i, j, k, l i,j−1,k,l i,j,k−1,l λB + λB_h (1) λA + λA_h (1) DB[i,j,k,l−1] (3) DB[i,j,k,l] (3) DA[i,j,k−1,l] (3) DA[i,j,k,l] (3) λA + λA_h (1) λB + λB_h (1) i+1+k ≤CA i+1+k ≤CA i+1+l ≤CB j+1+l ≤CB l−1≥0 k−1≥0 j−1≥0 i−1≥0
Fig. 7. State transitions around Si, j, k, l for the LBIH scheme.
i, j, k i+1,j,k i−1,j,k i,j+1,k i,j,k+1 (i+1)(µ + η) (2) k (µ + η) (4) j (µ + η) (2) (k+1)(µ + η) (4) (j+1)(µ + η) (2) i (µ + η) (2) i,j,k−1 i,j−1,k λdb + λdb_h (3) λB + λB_h (1) λA + λA_h (1) λA + λA_h (1) λdb + λdb_h (3) λB + λB_h (1) i+1≤CA j+1≤CB i+j +k +1≤CA +CB i−1≥0 k−1≥0 j−1≥0
in Figure 8. Si, j, k denotes the state for a cell, where i represents the number of active A-band handsets, j represents the number of active B-band handsets, and k represents the number of active dual-band handsets. Figure 8 depicts the state transitions around Si, j, k. Note that a legal state Si, j, k must satisfy 0 i CA, 0 j CB and 0 i C j C k CACCB. The state transitions can be described as follows.
(1) When an A-band user (B-band user) initiates a call with rate A (B) or an A-band user (B-band user) handoff call arrives with rate A h (B h), the state parameter i j is incremented by 1. (2) When an A-band (B-band) call terminates with
rate or leaves the cell with rate , the state parameter i j is decremented by 1.
(3) When a dual-band user initiates a call with rate db, the state parameter k is incremented by 1. (4) When a dual-band call terminates with rate or
leaves the cell with rate , the state parameter k is decremented by 1.
4. Performance Analysis
To evaluate the system performance, the following terms are defined.
ž i,j,k,l: the steady state probability of the state Si, j, k, l.
ž Routi, j, k, l Rini, j, k, l: the net outgoing (incoming) flow rate of state Si, j, k, l.
ž P0: the probability that a new call is blocked (the average of A-band, B-band and dual-band handsets).
ž PA 0(PB 0, Pdb 0): the new call blocking probabil-ity of A-band (B-band, dual-band) handsets. ž Pf: the probability that a call is forced to terminate. ž PA f (PB f, Pdb f): the forced termination
proba-bility of A-band (B-band, dual-band) handsets. ž Pnc: the probability that a call is not completed
(either blocked or forced to terminate).
ž PA nc(PB nc, Pdb nc): the call-incompletion proba-bility of A-band (B-band, dual-band) users. ž Pbs(Rbs): the probability (rate) that on call
origina-tion or call terminaorigina-tion, a dual-band handset needs to switch to the band with more free channels. ž Phs (Rhs): the probability (rate) that a handoff call
of a dual-band handset needs to switch to the band with more free channels.
ž Pfs(Rfs): the probability (rate) that call origination or call termination of a single-band handset forces a dual-band call to switch to the other band. Since the sum of the all steady state probabilities is equal to 1, we have
i,j,k,l
i,j,k,l D1 1
Since the system is in a steady state, the net outgoing flow rate and the net incoming flow rate are equal for all states. We have
Routi, j, k, l D Rini, j, k, l, for all legal states
Si, j, k, l. 2
From the balanced Equations (1) and (2), we can derive the steady state probabilities of all states i,j,k,l.
The dual-band handoff rate db h can be derived using the iterative algorithm described in Section 4.5. We can calculate db h Aand db h Busing the follow-ing equations. db h ADdb h CA iD0 CB jD0 CAi kD0 CBj lD0,kCl6D0 k k C li,j,k,l 1 CA iD0 CB jD0 i,j,0,0 db h BDdb h CA iD0 CB jD0 CAi kD0 CBj lD0,kCl6D0 l k C li,j,k,l 1 CA iD0 CB jD0 i,j,0,0 3
Since the number of the dual-band handsets tuning to A-band (B-band) is proportional to the number of the dual-band handsets using A-band (B-band) channel. Therefore, the call arrival rates db A and db B can be expressed as db ADdb CA iD0 CB jD0 CAi kD0 CBj lD0,kCl6D0 k k C li,j,k,l 1 CA iD0 CB jD0 i,j,0,0 db BDdb CA iD0 CB jD0 CAi kD0 CBj lD0,kCl6D0 l k C li,j,k,l 1 CA iD0 CB jD0 i,j,0,0 4
4.1. The LB scheme
In the LB scheme, an A-band user call is blocked or forced to terminate if no free A-band channel is available. We have
PA0 DPA fD j,l,iCkDCA
i,j,k,l
Similarly, the new call blocking and forced termina-tion probabilities of B-band users can be expressed as
PB 0DPB fD i,k,jClDCB
i,j,k,l
A dual-band user call request is blocked if no avail-able A-band or B-band channel. The new call block-ing probability of dual-band user can be expressed as
Pdb 0D
iCkDCAand jClDCB
i,j,k,l
The new call blocking probability can be expressed as P0D A ACBCdb PA 0C B ACBCdb PB 0 C db ACBCdb Pdb 0 5
A handoff call of a dual-band user using an A-band channel (B-band channel) is forced to terminate if no free A-band channel (B-band channel) in the cell where the call is handed over. We have
Pdb A fD j,l,iCkDCA i,j,k,l Pdb B fD i,k,jClDCB i,j,k,l
The forced termination probability of dual-band users can be expressed as Pdb fD db h A db h j,l,iCkDCA i,j,k,lC db h B db h i,k,jClDCB i,j,k,l
The forced termination probability of all users can be written as PfD A h A hCB hCdb h PA f C B h A hCB hCdb h PB f C db h A hCB hCdb h Pdb f 6
We can obtain the call-incompletion probability Pnc using the equation developed in Reference [24],
PncDP0C h Pf, 7 where D ACBCdb and hDA hCB hC db h.
4.2. The LBIH scheme
In the LBIH scheme, an A-band (B-band) user call is blocked or forced to terminate if no free A-band (B-band) channel is available. We have
PA 0DPA fD j,l,iCkDCA i,j,k,l PB 0DPB f D i,k,jClDCB i,j,k,l
A dual-band user call request is blocked or forced to terminate if there is no available A-band or B-band channel. We have
Pdb0DPdb fD
iCkDCAand jClDCB
i,j,k,l
The new call blocking, forced termination, and call-incompletion probabilities can be obtained from Equations (5), (6), and (7).
4.3. The LBCR scheme
In the LBCR scheme, an A-band (B-band) user call is blocked or forced to terminate if no free A-band (B-band) channel is available or no free A-band or B-band channel is available. We have
PA 0DPA fD iDCAor iCjCkDCACCB i,j,k PB 0DPB fD jDCBor iCjCkDCACCB i,j,k
A dual-band user call request is blocked or forced to terminate if no available A-band or B-band channel. We have
Pdb0DPdb fD
iCjCkDCACCB
i,j,k
The new call blocking, forced termination, and call-incompletion probabilities can be obtained from Equations (5), (6), and (7).
4.4. The overhead
If D > C, a dual-band handset tuning to B-band needs to switch to A-band on call origination or call termination. Pbs and Rbs can be expressed as
PbsD db A db CAikCBjl<C i,j,k,l C db B db CAikCBjl>C i,j,k,l Rbs Ddb A CAikCBjl<C i,j,k,l Cdb B CAikCBjl>C i,j,k,l
On the channel request of a single-band handset, if there is no free channel in the requested band, an active dual-band handset tuning to the band is selected and forced to switch to the other band. Pfs and Rfs can be expressed as
PfsD ACA h ACBCA hCB h ð iCkDCA,jCl<CB,k>0 i,j,k,l C BCB h ACBCA hCB h ð jClDCB,iCk<CA,l>0 i,j,k,l Rfs DACA h iCkDCA,jCl<CB,k>0 i,j,k,l CBCB h jClDCB,iCk<CA,l>0 i,j,k,l Using the band-switching threshold described in Section 2.4, we can reduce the number of band-switchings performed on call origination and call ter-mination of dual-band handsets. For a band-switching threshold t, band-switching is performed when the load of a BTS is large than t. The probability Pbsand the rate Rbs can be expressed as
PbsD db A db ð
iCk>tand CAikCBjl<C i,j,k,l C db B db ð jCl>tand CAikCBjl>C i,j,k,l Rbs Ddb A ð
iCk>tand CAikCBjl<C i,j,k,l Cdb B ð jCl>tand CAikCBjl>C i,j,k,l 4.5. An iterative algorithm
We can use an iterative algorithm, proposed by Hong and Rappaport [23], to calculate new call blocking and forced termination probabilities. Let Pn0 be the probability that a new call at the cell is not completed before the handset moves out of the cell, and Pnh be the probability that a handoff call at a cell is not completed before the handset moves out of the cell. We have Pn0DPnh D 1 tD0 1 tcDt etetcdt cdt D C 8 Consider the LB scheme, the handoff rate of A-band handsets can be expressed as
A hDA1 PA 0Pn0CA h1 PA fPnh 9 Equation (9) indicates that handoff calls of A-band handsets occur in two cases:
ž A new call of A-band handsets is not blocked with rate A1 PA 0. In addition, the call is not completed before it moves out of the cell with probability Pn0.
ž A handoff call of A-band handsets is not forced to terminate with rate A h1 PA f. In addition, the call is not completed before it moves out of the cell with probability Pnh.
From Equations (8) and (9), we have A hD
A1 PA 0 C PA f
Similarly, the handoff rate of B-band handsets can be written as B hD B1 PB 0 C PB f 11 Consider the handoff rate of dual-band handsets con-necting A-band channels in the previous cell. We have
db h ADdb1 Pdb0Pn0
Cdb h A1 Pdb A fPnh 12 From Equations (8) and (12), we obtain
db h AD db1 Pdb0 C Pdb A f 13 Similarly, we have db h BD db1 Pdb0 C Pdb B f 14 From Equations (13) and (14), we obtain
db hD db1 Pdb0 C Pdb A f Cdb1 Pdb0 C Pdb B f 15 For the LBIH and LBCR schemes, the handoff rates of A-band and B-band handsets can also be calculated using Equations (10) and (11). The handoff rate of dual-band handsets can be expressed as
db hDdb1 Pdb 0Pn0Cdb h1 Pdb fPnh 16 From Equations (8) and (16), we can get
db hD
db1 Pdb0 C Pdb f
17 We can calculate new call blocking and forced ter-mination probabilities, using the following iterative algorithm.
Step 1. Select initial values for A h, B h, and db h.
Step 2. Compute PA 0, PB 0, Pdb0, PA f, PB f, and Pdb fusing equations derived in the previous sections.
Step 3. Let A h,old A h, B h,old B h, and db h,old db h
Step 4. Compute the handoff rates A h, B h, and db hby using Equations (10), (11), (15), and (17).
Step 5. Let υ is a pre-defined small value.
If jA hA h,oldj> υA h or jB hB h,oldj>
υB h or jdbhdb h,oldj> υdb h, then go to Step 2.
Step 6. The values of A h, B h, and db h con-verge.
5. Analytic and Simulation Results
Computer simulations have been conducted to verify the analytic results. To ensure simulation results are converged, 200 000 calls are simulated in each simu-lation. Figure 9 shows that the simulation results and the analytic results are consistent. In the experiments, 1/ D 3 min, D 0.2 or 2, and A: B: dbD 1 : 1 : 2. The total traffic load D ACBCdb/ varies from 20 to 30. The capacities of A-band chan-nels and B-band chanchan-nels are CADCBD20. The results indicate that the LBCR scheme significantly outperforms the other two schemes when the traf-fic load is high. For a low user mobility ( D 0.2 in the example), the LB and LBIH schemes have about the same performance. For a high user mobil-ity ( D 2), the LB scheme provides significantly higher call incompletion probabilities than the LBIH scheme. The results imply that inter-band handoff for load-balancing is important to PCS systems with high user mobility.
5.1. The effects of dual-band handset percentage and user mobility
Figure 10 shows the effects of dual-band handset per-centage (˛) and user mobility on the call incompletion probability. The traffic loads in the experiments are 26 and 30; ˛ of the traffic load is dual-band handsets, 1 ˛/2 of the traffic load A-band handsets, and the remaining B-band handsets. In all schemes, Pnc increases for a high user mobility ( D 2 in this example). On the other hand, the call incompletion probability Pnc decreases as the percentage of dual-band handsets increases. However, Pnc drops more rapidly in the LBCR scheme; it drops near to the low-est value when the percentage of dual-band handsets is as low as 25%. For the LBIH scheme, this hap-pens only when the percentage of dual-band handset is as high as 75%. The results imply that channel re-assignment is an effective technique to balance the loads of both bands. For the LB scheme with a high user mobility, Pnc is much higher than that of the other two schemes even for the case where all hand-sets are dual-band (˛ D 100%). This is because for a high user mobility, a handset experiences more hand-offs; however, a handoff call is restricted to use the
0 1 2 3 4 5 6 7 8 9 10 20 22 24 26 28 30 ρ (traffic load) Pnc (%) η=0.2µ LB LB analytic results simulation results LBIH LBCR 0 1 2 3 4 5 6 7 8 9 10 20 22 24 26 28 30 ρ (traffic load) Pnc (%) η=2µ analytic results simulation results LBIH LBCR
Fig. 9. The call-incompletion probability with 50% dual-band load ( D 1/3, A: B : dbD1 : 1 : 2.
0 2 4 6 8 10 12 14 16 0% 25% 50% 75% 100% Pnc (%) 10% η=0.2µ ρ=30 ρ=26 LB LBIH LBCR
α (percentage of dualband handsets)
0 2 4 6 8 10 12 14 16 0% 25% 50% 75% 100% Pnc (%) 10% η=2µ ρ=30 ρ=26 LB LBIH LBCR
α (percentage of dualband handsets) Fig. 10. The effects of dual-band traffic load ( D 1/3, A: BD1 : 1).
same band in the LB scheme. As a result, the call is more likely to be forced to terminate. The results imply that if the percentage of dual-band handset is low, the LBCR scheme should be used. If the percent-age of dual-band handsets is high, the LBIH scheme can be used to reduce the overhead of channel re-assignment.
Table 1 shows the maximum carried load when the system is engineered to operate at Pnc2%. Note that the improvement of the LBCR over the LB is
significant when the percentage of dual-band handsets is low or the user mobility is high. The improvement could be as high as 15% for the case where D 2 and ˛ D 25%.
5.2. The comparison between single-band and dual-band users
Figure 11 shows the call-incompletion probabilities of single-band and dual-band users. The
call-incom-pletion probabilities of single-band handsets are sig-nificantly higher than those of dual-band handsets in the LB and LBIH schemes. The Pnc of the dual-band handsets with high mobility in the LB scheme is clearly higher than that with low mobility. This is because the handoff calls cannot switch between bands. On the other hand, for the LBCR scheme, the call incompletion probabilities of single-band and dual-band handsets converge when the percentage of dual-band handsets is larger than 25%. This is true for both low user mobility and high mobility. The results indicate that the channel re-assignment scheme pro-vides fairness in channel assignment to both single-band and dual-single-band handsets.
5.3. The overhead of band-switching and forced band-switching
Figure 12 shows the effects of the percentage of dual-band handsets and user mobility on the dual-
band-switch-Table 1. The carried load when the system is engineered at PncD2%. Mobility Percentage of dual-band traffic load (˛) LB LBIH LBCR D2 25% dual-band 24.03 25.72 27.65 50% dual-band 24.96 27.08 28.03 75% dual-band 25.78 27.70 28.03 D0.2 25% dual-band 28.00 28.32 30.14 50% dual-band 29.24 29.55 30.44 75% dual-band 29.88 30.12 30.44
ing rate Rbs and probability Pbs. The traffic load () is 30. On call origination or call termination of a dual-band handset, the handset is instructed to switch to the selected band if it does not tune to the band. It is clear that Rbs increases as the percentage of dual-band handsets increases. However, the band-switching probabilities Pbs decreases as the percentage of dual-band handsets increases, because more dual-band handsets lead to a higher probability that the loads of two bands are balanced. For the LB scheme, Rbs and Pbs of the users with high mobility are significantly larger than those with low mobility, when ˛ is large. This can be explained as follows. The calls with high mobility experience more handoffs. Since handoff calls do not perform band-switching in the LB scheme, more handoff calls result in a higher probability that the loads of two bands are unequal. As a result, Rbs and Pbs increase as user mobility increases. For the LBIH and LBCR schemes, the user mobility has no effects on Rbs and Pbs, because handoff calls can perform band-switching for load-balancing in both schemes.
Figure 13 shows the effects of user mobility and traffic load on the forced band-switching rate Rfs and probability Pfs in the LBCR scheme. On the channel request of a single-band handset, if there is no free channel in the requested band, an active dual-band handset tuning to the band is selected and forced to switch to the other band. Figure 13(a) shows that Rfs increases as the user mobility or the traffic load increases. Since high user mobility leads to more handoffs, the forced band-switching rate Rfs
0 1 2 3 4 5 6 0% 25% 50% 75% 100% Pnc (%) 0 1 2 3 4 5 6 Pnc (%) single-band η=0.2µ 10% dual-band LB LBIH LBCR single-band η=2µ dual-band LB LBIH LBCR
α (percentage of dualband handsets)
0%10%25% 50% 75% 100%
α (percentage of dualband handsets)
30% 32% 34% 36% 38% 40% 42% 44% 46% 48% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 25 50 75 100 Rbs Pbs α(%) η=0.2µ η=2µ LB LB LBIH LBCR η=0.2µ η=2µ LBIH LBCR (a) Rbs with ρ=30 0 25 50 75 100 α(%) (b) Pbs with ρ=30
Fig. 12. The effects of the percentage of dual-band handsets and user mobility on Rbsand Pbs( D 1/3, A: BD1 : 1).
0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 25 50 75 100 Rfs Pfs α(%) η=0.2µ η=2µ load=26 load=30 η=0.2µ η=2µ load=26 load=30 (a) Rfs in LBCR scheme 0 25 50 75 100 α(%) (b) Pfs in LBCR scheme
Fig. 13. The effects of user mobility and traffic load on Rfsand Pfs( D 1/3, A: BD1 : 1).
increases as increases. In addition, Rfs and Pfs increase as the traffic load increases, because higher traffic load results in a higher probability that all channels in a band are occupied. The effects of the percentage of dual-band handsets on Rfs and Pfs are mixed. For small ˛, Rfs and Pfs increases as ˛ increases, because the probability of finding a band victim increases as the number of active dual-band handsets increases. For large ˛, Rfs and Pfs
decrease as ˛ increases, because the probability that the number of free channels in A-band is equal to that in B-band increases.
5.4. The effects of the band-switching threshold Figure 14 shows the effects of the band-switching threshold (to activate load-balancing band-selection) on Rbs and Pnc for the LBIH scheme. In the
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 25 50 75 100 Rbs Pnc t=0 t=15 t=16 t=17 t=18 t=19 t=20 α(%) 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% t=0 t=15 t=16 t=17 t=18 t=19 t=20
(a) The effects of t on Rbs
0 25 50 75 100
α(%)
(a) The effects of t on Pnc
Fig. 14. The Rbsand Pnc with t D 0, 15–20 for the LBIH scheme ( D 1/3, A: BD1 : 1, D 26).
experiment, the system traffic load is 26, the user mobility is D 0.2, and the band-switching threshold t varies as 0 and 15–20. For t D 0, it is the original LBIH scheme. It is clear that Rbs decreases as the band-switching threshold increases, because fewer band-switchings are performed. However, this reduction on band-switching overhead is obtained at the cost of a higher call incompletion probability Pnc as shown in Figure 14(b); Pnc increases as the band-switching threshold increases. Compare the results of the cases where t D 0 and t D 16. It is interesting to note that Rbs decreases significantly while Pnc increases only modestly, especially when ˛ is large. The results indicate that the band-switching threshold can be carefully selected such that the band-switching overhead is significantly reduced at the cost of increasing the call incompletion probability by a small amount. Although the experiment results are not presented in this paper, the band-switching threshold has the same effects on reducing the signal overhead of the LB and LBCR schemes.
5.5. The effects of cell residence time and call holding time variances
We investigated the effects of the variances of cell residence time and call holding time on Pnc. Gamma distribution is used to generate the cell residence time and call holding time. In the computer simulation experiments, the mean values of the cell residence time and call holding time were fixed, but their
variances changed. The probability density function of a Gamma distribution is
fx D ˛ ˛x
1e˛x
, for x > 0
The mean of the distribution is /˛, the variance is /˛2, and the coefficient of variation is v D 1/p˛. The results in Figure 15(a) show that for the high mobility case ( D 2), as the cell residence time variance increases, Pnc increases. This is because when cell residence time variance is large, handsets may experience a large number of handoffs and thus are more likely to be forced to terminate. For the low mobility case, the cell residence time variance has insignificant effect on Pnc. This is because the handset mobility is so low that most calls experience no handoff. The results in Figure 15(b) show that for the high mobility, as the call holding time variance increases, Pnc decreases. This is because when call holding time variance is large, handsets may experi-ence a large number of short calls and less handoffs, and thus are more likely to complete the calls. For the low mobility, the call holding time variance has an insignificant effect on Pnc. This is because the hand-set mobility is so low that most calls (especially for short calls) experience no handoff.
6. Conclusion
This paper studied the channel assignment problem of dual-band PCS systems where single-band and
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 0 1 2 3 4 Pnc Pnc v LB LBIH LBCR η=2µ η=0.2µ LB LBIH LBCR η=2µ η=0.2µ 0% 1% 2% 3% 4% 5% 6% 7% 8% 0 1 2 3 4 v (a) (b)
Fig. 15. Effects on (a) the cell residence time and (b) the call holding time variances on Pnc.
dual-band handsets co-exist. Three load-balancing channel assignment schemes were proposed in this paper. Analytic models and computer simulation are developed to evaluate the channel assignment schemes. Our experiments show the following results. ž Both the load-balancing and channel re-assignment strategies are effective in increasing the system carried traffic. If the percentage of dual-band hand-sets is low (˛ < 50%), both strategies should be applied, i.e., the LBCR scheme should be used. If the percentage is high (˛ > 75%), the LBIH scheme, which applies the load-balancing tech-nique only, can be used.
ž The LBCR scheme provides fairness in channel assignment to single-band and dual-band handsets when ˛ is larger than 25%. In this case, both single-band and dual-single-band handsets experience about the same call incompletion probability.
ž The band-switching overhead increases as the per-centage of dual-band handsets and the traffic load increase. The experiment results show that the switching threshold can reduce the band-switching overhead at the cost of increasing the call incompletion probability by a small amount. ž The system performance of the dual-band system
is affected by the variances of the cell residence time and the call holding time. The experiment results show that when the cell residence time vari-ance is small or the call holding time varivari-ance is large, the system provides a low call incompletion probability.
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Authors’ Biographies
Ming-Feng Chang received the
Ph.D. degree in computer science from the University of illinois at Urbana-Champaign in 1991. He is currently an Associate Professor in the Department of Computer Science and Information Engineer-ing, Chiao-Tung University, Tai-wan, Republic of China. His rese-arch interests include Internet com-munication, mobile computing and VLSI system design. Current research projects include VoIP for wireless networks, interworking of VoIP protocols and cache model for WAP applications.
Long-Sheng Li was born in Taiwan,
R.O.C., in 1964. He received the M.S. degree from National Chiao Tung University, Hsinchu, Taiwan, in 1991. Currently, he is lecturer in the Institute of Computer Sci-ence and Information Engineering, National Chaiyi University, Chai-Yi, Taiwan, and working toward the Ph.D. degree with the Department of Computer Science and Information Engineering, National Chiao Tung University. His current research interests include personal communication systems and mobile computing.
![Figure 4 shows the message flows of call termi- termi-nation for a dual-band handset in dual-band GSM systems [19]](https://thumb-ap.123doks.com/thumbv2/9libinfo/7665243.140787/4.892.193.690.755.1077/figure-shows-message-flows-termi-nation-handset-systems.webp)
