Modeling and Performance Evaluation of Handover ... - CiteSeerX
Modeling and Performance Evaluation of Handover Service in Wireless Networks Wenfeng Du1 , Lidong Lin2 , Weijia Jia1,2 , and Guojun Wang1 1
2
College of Information Science and Engineering, Central South University, Changsha 410083, China [email protected], [email protected] [email protected] http://sise.csu.edu.cn/cise/index.asp Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong, SAR China [email protected]
Abstract. With the development of wireless network, more and more applications require the QoS for message transmission. In order to enhance the QoS service in the dynamic changing wireless networks, this paper proposes two channel allocation schemes to improve the resource utilization of the base station, named FSC and FRC. FSC assigns the available shared channel to the handover call or the reserved channel when the shared channels are fully occupied. FRC, however, assigns the free reserved channel or the shared channel when the reserved channels are fully occupied. We use two-dimension Markov model to analysis the new call blocking probability and handover call dropping probability. Extensive numeric results show that the two schemes have strongly influence on the network resource utilization. In order to improve the performance of base station, the tradeoff between the number of services channel and the QoS of base station must be considered.
1
Introduction
Recently, with the quick development of wireless networks, more and more people begin to access the Internet by using wireless equipments [1]. It is supposed to provide services to mobile user anytime, anywhere in an uninterrupted and seamless way, and a lot of services which were provided by the wired network have been supported by the wireless equipments now. QoS guarantee for end-toend service has been the fundamental issues in wireless cellular networks. One of the key elements to provide QoS guarantee is an effective bandwidth allocation policy, which not only fully utilizes the scarce wireless bandwidth, but also guarantees call termination and call blocking probabilities. When a call
This work is supported by the National Grand Fundamental Research 973 Program of China under Grant No.2003CB317003. Research Grant Council RGC Hong Kong, SAR China (projects nos.CityU 1039/02E,CityU 1055/01E) and Strategy Grant of City University of Hong Kong under nos 7001709 and 7001587.
X. Lu and W. Zhao (Eds.): ICCNMC 2005, LNCS 3619, pp. 229–238, 2005. c Springer-Verlag Berlin Heidelberg 2005
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reaches a base station it may be accepted or rejected. When the call finishes within the coverage area of current base station, it will release the channel, or it will be handed over to another cell which the mobile equipment may move in. There are some schemes to handle the handover call in a priority way by reserved channel [7][8], but there are less discussion about the reserved channel allocation scheme. Due to the different performance of the base station with different channels allocation scheme, how to make good use of the reserved channel becomes an important issue. In this paper, we will analyze the performance of base stations from the viewpoint of the reserved channels allocation and the number of reserved channels, and give the analysis on the call termination probabilities, call blocking probabilities and the percentage of bandwidth utilization. The rest of the paper is organized as follows. Section 2 introduces the general channel allocation process and proposes of two channel allocation schemes. A two-dimension Markov process is used to analyze the new call blocking probability and the handover call dropping probability for the channel allocation schemes. Two performance metrics were provided in Section 3 to evaluate the schemes. In Section 4, some performance results are presented for base station with different channel allocation schemes and the relationship between channel allocation and the number of reserved channels is also analyzed. Section 5 concludes the paper and discusses the future research.
2
Channel Allocation Process and Model
The radio coverage of each base station is called a cell, such as Personal Communication System (PCS) [2][3]. Within each cell, there are mainly two classes of call traffic: new call and handover call. A new call is the one which initiates in the current cell, while a handover call is the one which initiates in another cell, and is transferred (handed over) to the current cell [4]. When a call enters the current cell, the unused channel will be assigned to it. If no channel is available, which depends on the channel allocation scheme, the call may be blocked in the system. If a call is assigned to a channel, it will not release the channel until the call is finished or handed over to another cell. From the viewpoint of a user, it is better to block a new call than dropping an ongoing call [6]. Since all handover calls are very sensitive to interruption and have more stringent QoS requirement, such as voice communication, the forced termination of an ongoing call should be considered to be more serious than blocking a new call attempt. Therefore, it is a good method to queue a new call and give way to handover call. Due to the scarce resource, with more traffic, the residual capacity of the cell’s size is getting smaller and smaller, which may increase the call handover frequency [5]. Therefore, it is critical to analyze the tradeoff between the QoS and number of mobile devices served. Many previous proposed approaches treat the handover calls with priority [7][8], thus the handover calls are generally given a higher priority than a new call in the proposed schemes through reserved channels [9][10]. The channels are categorized into SC (Shared channel) and RC (Reserved channel). The SCs can
Modeling and Performance Evaluation of Handover Service
λN
λH
231
µE
µH
Fig. 1. The channel allocation model in wireless networks
be shared by new calls and handover calls, but RCs can be only allocated to the handover calls. There are different channel holding percentage and call blocking probability for different channel allocation scheme. When a handover call enters the coverage of current cell, it can attain the available channel in RCs or in SCs. There are two ways to offer channel to the handover call: The first way is the cell tries to allocate a SC to the handover call first. If all SCs are busy, the cell stops providing services to the coming new calls and allocate RCs to the handover call; The other way is the cell chooses the available RCs first to the handover call. When there is no RC available, the handover call will share the SCs with the new calls. The different number of RCs will make the base station runs in different performance. We propose two strategies for allocating channels to the new and handover calls and present a probability model for analysis the performance evaluation. The working process is shown in Fig. 1. Without loss of generality, we make the following assumptions and notations. There are totally N channels in each cell, including m reserved channels and N − m shared channels. Handover and new calls arrive at the cell follows Poisson processes with rates λH and λN respectively. The call end in each channel follows an exponential process with rate µE and the call that will be handed over to the neighbor cells in each channel follows an exponential process with rate µH . Two channel allocation strategies, FSC (Fistt SC) and FRC (First RC), were considered based on the arrival of handover call. 2.1
FSC (First SC) Allocation Scheme
The handover calls are first allocated with SC then allocated with RC. If there are unused SCs, the handover call shares SCs with the new call. If all SCs are fully occupied, the coming new call is blocked and the handover calls will be assigned to the RCs. Two cases are analyzed as follows: 1. SC is not fully occupied at time t: Assume that SCs have already been allocated to k calls, where 0 ≤ k ≤ N − m. The number of arrival calls during the time interval (t, t + ∆t) is (λN + λH )∆t + o(∆t) and the released channels are k(µE + µH )∆t + o(∆t),where we generically denote o(∆t) as a function of ∆t such that
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0, 0
2,0
1,0
µ
λ N + λH
λ N + λH
2µ
λH
λN + λH
N − m − 1,0
( N − m − 1) µ
N − m,0
( N − m) µ
λH
N − m,2
N − m,1
( N − m + 1) µ
λH
( N − m + 2) µ
N − m, m
Nµ
Fig. 2. Transition diagram of FSC
o(∆t) =0 ∆t Let pij (t) be the probability of the number of assigned SCs from i to j, it yields pk,k+1 (∆t) = (λN + λH )∆t + o(∆t), k < N − m pk,k−1 (∆t) = k(µE + µH )∆t + o(∆t) pk,j (∆t) = o(∆t), |k − j| ≥ 2 The call arriving rate λk,1 and the leaving rate µk are as follows. λk,1 =(λN + λH ), k = 0, 1, . . . , N − m and µk = k(µE + µH ) lim
∆t−>0
2. SC is fully occupied at time t, i.e., k ≥ N − m. The arriving rate λk,2 and the leaving rate µk are expressed as follows: λk,2 = λH , k = N − m, . . . , N and µk = k(µE + µH ) Denote s(t) as the number of occupied SCs at time t , r(t) as the number of occupied RCs at time t. Consider in the steady state, a bi-dimension process {s(t), r(t)} is a discrete-time Markov chain. According to above transition state equations, the transition diagram of FSC is shown in Fig. 2. 2.2
FRC (First RC) Allocation Scheme
The handover calls are first allocated with RC then allocated with SC. When the RCs are fully occupied, the handover call shares SCs with the new call. Assume the number of allocated RCs is j. Similar to the above discussion, two cases should be considered: 1. When j < m at time t, then the call arriving rate λj,2 and the leaving rate µj on queue of RC are shown as follows: λj,2 = λH , j = 0, 1, . . . , m − 1 and µj = j(µE + µH ) Consider at time t, the number of calls in SC is k, k ∈ [0, N − m]. Then the call arriving rate λk and the leaving rate µj on queue of SC are as follows: λk = λN , k = 0, 1, . . . , N − m and µk = k(µE + µN ) 2. When j > m, then RC is saturated, consider the number of calls in the SC is k, k ∈ [0, N − m] at time t. Then the call arriving rate λk,1 and the leaving rate µk as follows. λk,1 = λN + λH , k = 0, 1, . . . , N − m and µk = (k + m)(µE + µH ) According to the above transition state equations, we can derive a twodimensional transition diagram of FRC as shown in Fig. 3.
Modeling and Performance Evaluation of Handover Service λH
λH
0 ,0
µ
λN
µ
( m − 1) µ
λN
λH
λH
λN
µ
2µ
λN
(m − 1) µ 2µ
λN
λN
( N − m − 1) µ
N − m − 1,1
( N − m) µ
mµ
( N − m) µ
λN
λH
µ
N − m − 1, m
N − m −1, m −1
λN
N − m,1
λ N + λH
λH
( m − 1) µ
λH
2, m mµ
( N − 1) µ
( N − m − 1) µ
µ
λN
λN
λH
λH
N − m,0
λ N + λH
2, m − 1
( m − 1) µ
λN
( N − m − 1) µ
N − m − 1,0
mµ (m + 2) µ λH
2,1
µ
λN + λH
λH
1, m
λH
2,0
λN
0, m
mµ (m + 1) µ
1, m − 1
λH
( N − m) µ
µ
1,1
1,0
2µ
λH
0, m − 1
0,1
µ
233
λH
λN + λH
Nµ N − m, m
N − m,m−1
mµ
(m − 1) µ
Fig. 3. Transition diagram of FRC
3
Performance Metrics
Some previous research works analyzed the handover scheme using some simple weight functions [11]. Their goal of designing handover scheme is to reduce the Grade of Service (GoS) and to improve the channel utilization [12]. In this section, we discuss two main performance metrics which are used to evaluate our schemes: GoS and channel utilization. In order to describe the impact of terminating an ongoing call on the wireless network’s QoS, a punish factor γ was introduced to GoS. GoS = P B + γ × P D Where P B is new call blocking probability and P D is handover call dropping probability. Following the rationale discussed in [12], we set γ ∈ [5, 20]. The analysis of the performance metric in the two allocation schemes are illustrated as following: 1. FSC: According to the state-transition diagram in Fig. 2, the stationary distribution is deduced as follows: k−1
pk =
i=0 k
λi,1
i=1 N −m−1
pk =
i=0 N −m i=1
µi
k−1
λi,1 ·
µi
p0 =
i=N −m
1 · k!
λi,2
k i=N −m+1
· p0 = µi
λN + λH µE + µH
k · p0,
k ≤N −m
(λN + λH )N −m · (λH )k−(N −m) · p0 , k! · (µE + µH )k
k > N −m
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We can derive p0 of FSC as ⎡
N −m−1
k−1
λi,1 N −m ⎢ ⎢ i=0 + p0 = ⎢1 + k ⎣ k=1 µi
i=0 N −m i=1
i=1
λi,1
N
· µi
k=N −m+1
k−1 i=N −m k
⎤−1 λi,2 ⎥ ⎥ ⎥ ⎦ µi
i=N −m+1
The channel busy percentage α of FSC is described as follow. N
α=
L = N
k=1
kpk
N
The blocking probability P B that a new call arrival will find all N −m shared channels busy and will therefore be lost is P B = pN −m
N −m λN + λH 1 .p0 = (N − m)! uE + uH
The dropping probability P D that a handover call arrival will find all N − m shared channels and m reserved channels busy and will therefore be lost is P D = pN =
(λN + λH )N −m · (λH )m · p0 N ! · (µE + µH )N
2. FRC: According to state-transition diagram in Fig.3, when j ≤ m, we derive the stationary distribution of RC as follows. k−1
pk =
i=0 k
λi,2
i=1
p0,RC = µi
⎡ p0,RC
1 · k!
⎤−1
k−1
λi,2 ⎥ m ⎢ ⎥ ⎢ i=0 = ⎢1 + ⎥ k ⎦ ⎣ k=1 µi
λH µE + µH
k · p0,RC ,
k≤m
k −1 m λH 1 · = 1+ µE + µH k!
k=1
i=1
On the other hand, the stationary distribution of SC is deduced as follows. j−1
pj =
i=0 j i=1
λi p0,SC = µi
1 · j!
λN µE + µH
j · p0,SC ,
j ≤N −m
Modeling and Performance Evaluation of Handover Service
⎡ p0,SC
⎤−1
j−1
λi ⎥ N −m ⎢ ⎥ ⎢ i=0 = ⎢1 + ⎥ j ⎦ ⎣ j=1 µi
⎡ = ⎣1 +
N −m j=1
1 · j!
λN µE + µH
j
235
⎤−1 ⎦
i=1
Similarly, we achieve the channel busy percentage α as follow. m
L = α= N
k=1
k · pk +
N −m j=1
j · pj
N
The blocking probability P B and dropping probability P D are described as follows. ⎤ ⎡ j −1
N −m N −m λ 1 λN 1 N ⎦ · . ⎣1 + PB = µ + µ j! (N − m)! uE + uH E H j=1 k −1
m m λH 1 λH 1 · . 1+ PD = µE + µH k! m! uE + uH k=1
When j > m, all channels of RCs are busy. The stationary distribution of SC is denoted as m−1
pk =
i=0 m i=1
k−1
λi,2 µi
·
i=0 k
λi,1
i=1
· p0 = µi
(λH )m · (λN + λH )k · p0 k! · m! · (µE + µH )k+m
We can derive p0 of FRC as ⎡
k−1
λi,2 m ⎢ ⎢ i=0 + p0 = ⎢1 + k ⎣ k=1 µi i=1
m−1 i=0 m i=1
λi,2 µi
·
N −m k=1
k−1 i=0 k
⎤−1 λi,1 ⎥ ⎥ ⎥ ⎦ µi
i=1
The channel busy percentage α thus can be derived, N −m
α=
L = N
k=1
k · pk + m N
The blocking probability P B and the dropping probability P D is PB = PD =
(λH )m · (λN + λH )N −m · p0 (N − m)! · m! · (µE + µH )N
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Numeral Results and Discussion
Through consideration of different arriving rates for the new calls and handover calls as well as the number of RCs in each base station, we have observed the different performance data. Initially, the parameters are set as follows. There are 10 channels in each cell; New call and handover call arriving are in Poisson process with rate 4/sec and 3/sec respectively; the residence time of call is an exponential process with rate 1.5/sec; The value of γ in GoS is 10.
Fig. 4. New call blocking probability with the number of RC
Fig. 4 shows the new call blocking probability of base station with different number of RCs. It can be seen that the new call blocking probability increases with the increment of the number of RC. When the number of RC is lower than 3, the FRC has a higher new call blocking probability than FSC. But when the number of RC is over 4, the new call blocking probability of FSC exceeds that of FRC. Since the FRC scheme allocate RC to the handover call firstly, only all channels in the RC are fully occupied, the handover call will share the channel of SC with a new call, whereas by FSC scheme, the handover call will firstly share the channel of SC with new call. Therefore FSC has higher new call blocking probability than that of FRC. Figure 5 shows the handover call dropping probability of different number of RCs. According to this figure, we can see that the handover call dropping probability decreases with the increase of RC. It also shows that the number of RC is a critical factor to determine the handover call dropping probability. The more is the number of RC, the smaller the handover call dropping probability is. Figure 6 shows the change of GoS with the number of RCs. According to this figure, we have the following observations. When the number of RC < 5, GoS of FRC > GoS of FSC. When the number of RC > 5, GoS of FSC > GoS of FRC. The figures also show that the different channel allocation schemes strongly influence the GoS value.
Modeling and Performance Evaluation of Handover Service
237
Fig. 5. Handover call dropping probability with the number of RC
Fig. 6. GoS with the number of RC
5
Conclusions
We have proposed two channel allocation schemes to improve the utilization of base station: FSC (First SC) and FRC (First RC). We also use two-dimension Markov model to analyze the new call blocking probability and handover call dropping probability. The performance metric of GoS is proposed to evaluate the two schemes. Extensive numeric results show that the two schemes strongly affect the network utilization. In order to improve the utilization of base station, it is advised that the tradeoff between the number of services channel and the QoS of base station should be considered. Furthermore, channel allocation scheme is critical for improving the network’s performance and resource utilizations to achieve low call dropping or blocking probability. This probability model has discussed in the circuit switch network in which each call will hold the channel until the call is ended or handed over to another cell. But in packet switching networks, the model is not valid and we are currently investigating the model fitting to such networks.
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References 1. C. Lindemann and A. Thmmler. Performance analysis of the General Packet Radio Service. IEEE International Conference on Distribute Computing Systems, pp.673680, 2001. 2. Y. Fang, I. Chlamtac, and Y. B. Lin, Call performance for a PCS net-work, IEEE J. Select. Areas Commu, vol. 15, pp. 1568-1581, Oct.1997. 3. Y. B. Lin, S. Mohan, and A. Noerpel, Queueing priority channel assign-ment strategies for PCS hand-off and initial access, IEEE Trans. Veh.Technol., vol. 43, pp. 704-712, Aug. 1994. 4. I. C. Panoutsopoulos and S. Kotsopoulos, Handover and new call admission policy optimization for G3G systems. ACM Wireless Networks, vol. 8, pp. 381-389, July.2002. 5. Y. B. Lin, A. Noerpel and D. J. Harasty. The sub-rating channel assignment strategy for PCS hand-offs. IEEE Trans on Veh Technol, vol.45, no. 1, pp. 122-130, Feb.1996. 6. S. Tekinay. Handover & Channel Assignment in Mobile Cellular Networks. IEEE Commu Mag, Novem.1991. 7. M.-H. Chiu and Mostafa A. Bassioni, Predictive Schemes for Handoff Prioritization in Cellular Networks Based on Mobile Positioning, IEEE on Selected Areas in Comm, vol. 18, no. 3, pp.510-522, March. 2000. 8. L. Ortigoza-Guerrero and A. H. Aghvami, A Prioritized Handoff Dynamic Channel Allocation Strategy for PCS, IEEE Trans on Veh Technol, vol. 48, no. 4, pp.12031215, July. 1999. 9. Hang Chen, Qing-An Zeng, and Dharma, A Novel Analytical Modeling for Optimal Channel Partitioning in the Next Generation Integrated Wireless and Mobile Networks, Proceedings of the 5th ACM international workshop on Modeling analysis and simulation of wireless and mobile systems, pp.120-127, Sept. 2002. 10. W. Li, X. Chao, Modeling and Performance Evaluation of a Cellular Mobile Network, IEEE/ACM Trans on Networking, vol.2, no. 1, pp. 131-145, Feb. 2004. 11. R. Ramjee, D. Towsley, R. Nagarajan, On optimal call admission control in cellular networks, Wireless Networks, no 3, pp. 29-41, 1997. 12. J.Moreira, Nelson, E.A. de, Comparison of Handoff Resource Allocation Strategies through the State-Dependent Rejection Scheme, 17th International Teletraffic Congress, pp.323-334, 2001.
2
College of Information Science and Engineering, Central South University, Changsha 410083, China [email protected], [email protected] [email protected] http://sise.csu.edu.cn/cise/index.asp Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong, SAR China [email protected]
Abstract. With the development of wireless network, more and more applications require the QoS for message transmission. In order to enhance the QoS service in the dynamic changing wireless networks, this paper proposes two channel allocation schemes to improve the resource utilization of the base station, named FSC and FRC. FSC assigns the available shared channel to the handover call or the reserved channel when the shared channels are fully occupied. FRC, however, assigns the free reserved channel or the shared channel when the reserved channels are fully occupied. We use two-dimension Markov model to analysis the new call blocking probability and handover call dropping probability. Extensive numeric results show that the two schemes have strongly influence on the network resource utilization. In order to improve the performance of base station, the tradeoff between the number of services channel and the QoS of base station must be considered.
1
Introduction
Recently, with the quick development of wireless networks, more and more people begin to access the Internet by using wireless equipments [1]. It is supposed to provide services to mobile user anytime, anywhere in an uninterrupted and seamless way, and a lot of services which were provided by the wired network have been supported by the wireless equipments now. QoS guarantee for end-toend service has been the fundamental issues in wireless cellular networks. One of the key elements to provide QoS guarantee is an effective bandwidth allocation policy, which not only fully utilizes the scarce wireless bandwidth, but also guarantees call termination and call blocking probabilities. When a call
This work is supported by the National Grand Fundamental Research 973 Program of China under Grant No.2003CB317003. Research Grant Council RGC Hong Kong, SAR China (projects nos.CityU 1039/02E,CityU 1055/01E) and Strategy Grant of City University of Hong Kong under nos 7001709 and 7001587.
X. Lu and W. Zhao (Eds.): ICCNMC 2005, LNCS 3619, pp. 229–238, 2005. c Springer-Verlag Berlin Heidelberg 2005
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W. Du et al.
reaches a base station it may be accepted or rejected. When the call finishes within the coverage area of current base station, it will release the channel, or it will be handed over to another cell which the mobile equipment may move in. There are some schemes to handle the handover call in a priority way by reserved channel [7][8], but there are less discussion about the reserved channel allocation scheme. Due to the different performance of the base station with different channels allocation scheme, how to make good use of the reserved channel becomes an important issue. In this paper, we will analyze the performance of base stations from the viewpoint of the reserved channels allocation and the number of reserved channels, and give the analysis on the call termination probabilities, call blocking probabilities and the percentage of bandwidth utilization. The rest of the paper is organized as follows. Section 2 introduces the general channel allocation process and proposes of two channel allocation schemes. A two-dimension Markov process is used to analyze the new call blocking probability and the handover call dropping probability for the channel allocation schemes. Two performance metrics were provided in Section 3 to evaluate the schemes. In Section 4, some performance results are presented for base station with different channel allocation schemes and the relationship between channel allocation and the number of reserved channels is also analyzed. Section 5 concludes the paper and discusses the future research.
2
Channel Allocation Process and Model
The radio coverage of each base station is called a cell, such as Personal Communication System (PCS) [2][3]. Within each cell, there are mainly two classes of call traffic: new call and handover call. A new call is the one which initiates in the current cell, while a handover call is the one which initiates in another cell, and is transferred (handed over) to the current cell [4]. When a call enters the current cell, the unused channel will be assigned to it. If no channel is available, which depends on the channel allocation scheme, the call may be blocked in the system. If a call is assigned to a channel, it will not release the channel until the call is finished or handed over to another cell. From the viewpoint of a user, it is better to block a new call than dropping an ongoing call [6]. Since all handover calls are very sensitive to interruption and have more stringent QoS requirement, such as voice communication, the forced termination of an ongoing call should be considered to be more serious than blocking a new call attempt. Therefore, it is a good method to queue a new call and give way to handover call. Due to the scarce resource, with more traffic, the residual capacity of the cell’s size is getting smaller and smaller, which may increase the call handover frequency [5]. Therefore, it is critical to analyze the tradeoff between the QoS and number of mobile devices served. Many previous proposed approaches treat the handover calls with priority [7][8], thus the handover calls are generally given a higher priority than a new call in the proposed schemes through reserved channels [9][10]. The channels are categorized into SC (Shared channel) and RC (Reserved channel). The SCs can
Modeling and Performance Evaluation of Handover Service
λN
λH
231
µE
µH
Fig. 1. The channel allocation model in wireless networks
be shared by new calls and handover calls, but RCs can be only allocated to the handover calls. There are different channel holding percentage and call blocking probability for different channel allocation scheme. When a handover call enters the coverage of current cell, it can attain the available channel in RCs or in SCs. There are two ways to offer channel to the handover call: The first way is the cell tries to allocate a SC to the handover call first. If all SCs are busy, the cell stops providing services to the coming new calls and allocate RCs to the handover call; The other way is the cell chooses the available RCs first to the handover call. When there is no RC available, the handover call will share the SCs with the new calls. The different number of RCs will make the base station runs in different performance. We propose two strategies for allocating channels to the new and handover calls and present a probability model for analysis the performance evaluation. The working process is shown in Fig. 1. Without loss of generality, we make the following assumptions and notations. There are totally N channels in each cell, including m reserved channels and N − m shared channels. Handover and new calls arrive at the cell follows Poisson processes with rates λH and λN respectively. The call end in each channel follows an exponential process with rate µE and the call that will be handed over to the neighbor cells in each channel follows an exponential process with rate µH . Two channel allocation strategies, FSC (Fistt SC) and FRC (First RC), were considered based on the arrival of handover call. 2.1
FSC (First SC) Allocation Scheme
The handover calls are first allocated with SC then allocated with RC. If there are unused SCs, the handover call shares SCs with the new call. If all SCs are fully occupied, the coming new call is blocked and the handover calls will be assigned to the RCs. Two cases are analyzed as follows: 1. SC is not fully occupied at time t: Assume that SCs have already been allocated to k calls, where 0 ≤ k ≤ N − m. The number of arrival calls during the time interval (t, t + ∆t) is (λN + λH )∆t + o(∆t) and the released channels are k(µE + µH )∆t + o(∆t),where we generically denote o(∆t) as a function of ∆t such that
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W. Du et al. λN + λH
0, 0
2,0
1,0
µ
λ N + λH
λ N + λH
2µ
λH
λN + λH
N − m − 1,0
( N − m − 1) µ
N − m,0
( N − m) µ
λH
N − m,2
N − m,1
( N − m + 1) µ
λH
( N − m + 2) µ
N − m, m
Nµ
Fig. 2. Transition diagram of FSC
o(∆t) =0 ∆t Let pij (t) be the probability of the number of assigned SCs from i to j, it yields pk,k+1 (∆t) = (λN + λH )∆t + o(∆t), k < N − m pk,k−1 (∆t) = k(µE + µH )∆t + o(∆t) pk,j (∆t) = o(∆t), |k − j| ≥ 2 The call arriving rate λk,1 and the leaving rate µk are as follows. λk,1 =(λN + λH ), k = 0, 1, . . . , N − m and µk = k(µE + µH ) lim
∆t−>0
2. SC is fully occupied at time t, i.e., k ≥ N − m. The arriving rate λk,2 and the leaving rate µk are expressed as follows: λk,2 = λH , k = N − m, . . . , N and µk = k(µE + µH ) Denote s(t) as the number of occupied SCs at time t , r(t) as the number of occupied RCs at time t. Consider in the steady state, a bi-dimension process {s(t), r(t)} is a discrete-time Markov chain. According to above transition state equations, the transition diagram of FSC is shown in Fig. 2. 2.2
FRC (First RC) Allocation Scheme
The handover calls are first allocated with RC then allocated with SC. When the RCs are fully occupied, the handover call shares SCs with the new call. Assume the number of allocated RCs is j. Similar to the above discussion, two cases should be considered: 1. When j < m at time t, then the call arriving rate λj,2 and the leaving rate µj on queue of RC are shown as follows: λj,2 = λH , j = 0, 1, . . . , m − 1 and µj = j(µE + µH ) Consider at time t, the number of calls in SC is k, k ∈ [0, N − m]. Then the call arriving rate λk and the leaving rate µj on queue of SC are as follows: λk = λN , k = 0, 1, . . . , N − m and µk = k(µE + µN ) 2. When j > m, then RC is saturated, consider the number of calls in the SC is k, k ∈ [0, N − m] at time t. Then the call arriving rate λk,1 and the leaving rate µk as follows. λk,1 = λN + λH , k = 0, 1, . . . , N − m and µk = (k + m)(µE + µH ) According to the above transition state equations, we can derive a twodimensional transition diagram of FRC as shown in Fig. 3.
Modeling and Performance Evaluation of Handover Service λH
λH
0 ,0
µ
λN
µ
( m − 1) µ
λN
λH
λH
λN
µ
2µ
λN
(m − 1) µ 2µ
λN
λN
( N − m − 1) µ
N − m − 1,1
( N − m) µ
mµ
( N − m) µ
λN
λH
µ
N − m − 1, m
N − m −1, m −1
λN
N − m,1
λ N + λH
λH
( m − 1) µ
λH
2, m mµ
( N − 1) µ
( N − m − 1) µ
µ
λN
λN
λH
λH
N − m,0
λ N + λH
2, m − 1
( m − 1) µ
λN
( N − m − 1) µ
N − m − 1,0
mµ (m + 2) µ λH
2,1
µ
λN + λH
λH
1, m
λH
2,0
λN
0, m
mµ (m + 1) µ
1, m − 1
λH
( N − m) µ
µ
1,1
1,0
2µ
λH
0, m − 1
0,1
µ
233
λH
λN + λH
Nµ N − m, m
N − m,m−1
mµ
(m − 1) µ
Fig. 3. Transition diagram of FRC
3
Performance Metrics
Some previous research works analyzed the handover scheme using some simple weight functions [11]. Their goal of designing handover scheme is to reduce the Grade of Service (GoS) and to improve the channel utilization [12]. In this section, we discuss two main performance metrics which are used to evaluate our schemes: GoS and channel utilization. In order to describe the impact of terminating an ongoing call on the wireless network’s QoS, a punish factor γ was introduced to GoS. GoS = P B + γ × P D Where P B is new call blocking probability and P D is handover call dropping probability. Following the rationale discussed in [12], we set γ ∈ [5, 20]. The analysis of the performance metric in the two allocation schemes are illustrated as following: 1. FSC: According to the state-transition diagram in Fig. 2, the stationary distribution is deduced as follows: k−1
pk =
i=0 k
λi,1
i=1 N −m−1
pk =
i=0 N −m i=1
µi
k−1
λi,1 ·
µi
p0 =
i=N −m
1 · k!
λi,2
k i=N −m+1
· p0 = µi
λN + λH µE + µH
k · p0,
k ≤N −m
(λN + λH )N −m · (λH )k−(N −m) · p0 , k! · (µE + µH )k
k > N −m
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We can derive p0 of FSC as ⎡
N −m−1
k−1
λi,1 N −m ⎢ ⎢ i=0 + p0 = ⎢1 + k ⎣ k=1 µi
i=0 N −m i=1
i=1
λi,1
N
· µi
k=N −m+1
k−1 i=N −m k
⎤−1 λi,2 ⎥ ⎥ ⎥ ⎦ µi
i=N −m+1
The channel busy percentage α of FSC is described as follow. N
α=
L = N
k=1
kpk
N
The blocking probability P B that a new call arrival will find all N −m shared channels busy and will therefore be lost is P B = pN −m
N −m λN + λH 1 .p0 = (N − m)! uE + uH
The dropping probability P D that a handover call arrival will find all N − m shared channels and m reserved channels busy and will therefore be lost is P D = pN =
(λN + λH )N −m · (λH )m · p0 N ! · (µE + µH )N
2. FRC: According to state-transition diagram in Fig.3, when j ≤ m, we derive the stationary distribution of RC as follows. k−1
pk =
i=0 k
λi,2
i=1
p0,RC = µi
⎡ p0,RC
1 · k!
⎤−1
k−1
λi,2 ⎥ m ⎢ ⎥ ⎢ i=0 = ⎢1 + ⎥ k ⎦ ⎣ k=1 µi
λH µE + µH
k · p0,RC ,
k≤m
k −1 m λH 1 · = 1+ µE + µH k!
k=1
i=1
On the other hand, the stationary distribution of SC is deduced as follows. j−1
pj =
i=0 j i=1
λi p0,SC = µi
1 · j!
λN µE + µH
j · p0,SC ,
j ≤N −m
Modeling and Performance Evaluation of Handover Service
⎡ p0,SC
⎤−1
j−1
λi ⎥ N −m ⎢ ⎥ ⎢ i=0 = ⎢1 + ⎥ j ⎦ ⎣ j=1 µi
⎡ = ⎣1 +
N −m j=1
1 · j!
λN µE + µH
j
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⎤−1 ⎦
i=1
Similarly, we achieve the channel busy percentage α as follow. m
L = α= N
k=1
k · pk +
N −m j=1
j · pj
N
The blocking probability P B and dropping probability P D are described as follows. ⎤ ⎡ j −1
N −m N −m λ 1 λN 1 N ⎦ · . ⎣1 + PB = µ + µ j! (N − m)! uE + uH E H j=1 k −1
m m λH 1 λH 1 · . 1+ PD = µE + µH k! m! uE + uH k=1
When j > m, all channels of RCs are busy. The stationary distribution of SC is denoted as m−1
pk =
i=0 m i=1
k−1
λi,2 µi
·
i=0 k
λi,1
i=1
· p0 = µi
(λH )m · (λN + λH )k · p0 k! · m! · (µE + µH )k+m
We can derive p0 of FRC as ⎡
k−1
λi,2 m ⎢ ⎢ i=0 + p0 = ⎢1 + k ⎣ k=1 µi i=1
m−1 i=0 m i=1
λi,2 µi
·
N −m k=1
k−1 i=0 k
⎤−1 λi,1 ⎥ ⎥ ⎥ ⎦ µi
i=1
The channel busy percentage α thus can be derived, N −m
α=
L = N
k=1
k · pk + m N
The blocking probability P B and the dropping probability P D is PB = PD =
(λH )m · (λN + λH )N −m · p0 (N − m)! · m! · (µE + µH )N
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Numeral Results and Discussion
Through consideration of different arriving rates for the new calls and handover calls as well as the number of RCs in each base station, we have observed the different performance data. Initially, the parameters are set as follows. There are 10 channels in each cell; New call and handover call arriving are in Poisson process with rate 4/sec and 3/sec respectively; the residence time of call is an exponential process with rate 1.5/sec; The value of γ in GoS is 10.
Fig. 4. New call blocking probability with the number of RC
Fig. 4 shows the new call blocking probability of base station with different number of RCs. It can be seen that the new call blocking probability increases with the increment of the number of RC. When the number of RC is lower than 3, the FRC has a higher new call blocking probability than FSC. But when the number of RC is over 4, the new call blocking probability of FSC exceeds that of FRC. Since the FRC scheme allocate RC to the handover call firstly, only all channels in the RC are fully occupied, the handover call will share the channel of SC with a new call, whereas by FSC scheme, the handover call will firstly share the channel of SC with new call. Therefore FSC has higher new call blocking probability than that of FRC. Figure 5 shows the handover call dropping probability of different number of RCs. According to this figure, we can see that the handover call dropping probability decreases with the increase of RC. It also shows that the number of RC is a critical factor to determine the handover call dropping probability. The more is the number of RC, the smaller the handover call dropping probability is. Figure 6 shows the change of GoS with the number of RCs. According to this figure, we have the following observations. When the number of RC < 5, GoS of FRC > GoS of FSC. When the number of RC > 5, GoS of FSC > GoS of FRC. The figures also show that the different channel allocation schemes strongly influence the GoS value.
Modeling and Performance Evaluation of Handover Service
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Fig. 5. Handover call dropping probability with the number of RC
Fig. 6. GoS with the number of RC
5
Conclusions
We have proposed two channel allocation schemes to improve the utilization of base station: FSC (First SC) and FRC (First RC). We also use two-dimension Markov model to analyze the new call blocking probability and handover call dropping probability. The performance metric of GoS is proposed to evaluate the two schemes. Extensive numeric results show that the two schemes strongly affect the network utilization. In order to improve the utilization of base station, it is advised that the tradeoff between the number of services channel and the QoS of base station should be considered. Furthermore, channel allocation scheme is critical for improving the network’s performance and resource utilizations to achieve low call dropping or blocking probability. This probability model has discussed in the circuit switch network in which each call will hold the channel until the call is ended or handed over to another cell. But in packet switching networks, the model is not valid and we are currently investigating the model fitting to such networks.
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