Capacity Optimizing Channel Allocation Scheme Supporting Multiple Services with Mobile Users in Cellular System

Ming Yang Network Technology Research Centre

Nanyang Technological University, Singapore mingyang@pmail.ntu.edu.sg

Peter H. J. Chong Network Technology Research Centre

Nanyang Technological University, Singapore ehjchong@ntu.edu.sg

Abstract: In this paper, we study the performance of mobile users, in terms of call blocking and dropping probabilities, with our proposed idea of channel partitioning (CP). CP is based on the fact that different services may require different signal-to-interference ratios, and thus different reuse factors. We apply this CP with fixed channel allocation (FCA) scheme called fixed channel partitioning (FCP) in cellular systems. With FCP scheme, each cell is allocated two or more sets of channels. Each set of the channels supports a service in the way that the required reuse factor for that service could be satisfied. A three-dimensional Markov chain is first developed to analyze the impact of the mobile user. Then a simpler model, which can be used to estimate the numeric results from the closed-form solution, is presented to make the analysis easy. Finally, the analytical results are verified with simulation results. The results of this paper show that, for equal voice and data call arrival rate, the proposed FCP scheme can provide about 32% capacity improvement at 1% grade of service (GoS) as compared with FCA scheme. The changing of mobile speed and GoS factor do not affect this improvement. Our proposed FCP scheme could apply in current GSM, GPRS EDGE and future cellular OFDM systems, in which reuse factor plays a very important role.

Keywords: Channel allocation scheme, multiple services, channels partitioning and mobile user.

I. INTRODUCTION Modern wireless cellular systems such as GPRS, EDGE or

cellular OFDM intend to provide good quality of service (QoS) to various types of services, such as voice, data, and video, etc. But the scarce spectrum resource limits the provision of good QoS for different service type users. Thus, efficient channel allocation scheme supporting different types of services is a very important issue of research studies [1]-[4]. In [1] and [2], high-rate-data are split into two or more parts and transmitted independently through different channels. While in [3], different kinds of networks are built to support different types of services, with each network supporting certain types of services. In all these papers, a single reuse factor is used to support these multiple services.

In the multiple traffic cellular systems, different services may require different bit error rates (BERs). For example, the required BER for speech service is 10-3; while the required BER for circuit- or packet-switched data service is 10-6 [5]. These different BERs lead to different signal-to-interference ratio (SIR) requirements. In the reuse factor based cellular systems, i.e., GSM, GPRS EDGE and cellular OFDM [6], different reuse factors could provide different SIRs. However,

if a single reuse factor is used in these systems, normally, the largest one among these services will be used to support them in order to meet the co-channel interference constraints. Since these multiple services may require different reuse factors to satisfy the different SIR requirements, using a single (normally the largest) reuse factor to support multiple services may result in wasting of the available radio resources. Thus, we should use different reuse factors to meet the different SIR requirements for different services in order to improve the system performance.

In this paper, we study the performance of Channel Partitioning (CP) [4] to support two types of services for mobile users in a cellular system. CP is based on the fact that different services require different SIRs and thus, different reuse factors. In brief, a service with higher SIR requirement might use a larger reuse factor while a service with lower SIR requirement might use a smaller reuse factor. As a result, the average reuse factor could be smaller and the capacity of the system can be improved. For simplicity, we propose to support voice and data services. We analyze the exact model of FCP with mobility with a three-dimensional Markov chain to support two types of services. Furthermore, a simpler approximate model, which can be used to obtain numeric results from a closed-form solution, is presented and analyzed. For FCP and FCA, the average blocking probability (PB,ave), dropping probability (PD,ave) and grade of service (GoS) [7] are evaluated. The analytical and simulation results show that FCP can provide a large improvement as compared with conventional FCA scheme, which uses a single reuse factor to support both services. And this improvement will depend on the traffic load ratio between services.

II. FCP SCHEME WITH MOBILE USERS

A. System Model In our model, we assume to support two types of services:

service type 1 (S1) and service type 2 (S2) with the required reuse factor of N1 and N2, respectively. And without loss of generality, we assume that N1 is smaller than N2. S1 call can be considered as a traditional voice service that requires lower reuse factor and longer call duration time. S2 call can be considered as a data service. The fraction of call arrival rate for S1 and S2 is assumed to be γ1 and γ2, respectively. Calls are assumed to be uniformly distributed over the service area and they are activated (requiring service from the system) according to a Poisson process with a per cell call arrival rate

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of λ = λ1+ λ2, where λ1 and λ2 is per cell call arrival rate for S1 and S2 calls respectively, therefore

i iλ γ λ= × for i =1 or 2. (1) Call durations are exponentially distributed for S1 and S2

calls with a mean of 1/µ1 and 1/µ2 respectively. The offered traffic load (in Erlang) to S1 and S2 calls of a cell is defined as ρ1 and ρ2. Therefore, we have

/i i iρ λ µ= , for i = 1 or 2. (2)

And the total traffic load per cell is given by

1 2 1 1 2 2/ /ρ ρ ρ λ µ λ µ= + = + . (3)

The Poisson data arrival rate and exponential transmission time have been used to analyze the data traffic [8].

Let C1 and C2 be the number of channels supporting S1 and S2 calls respectively in each cell (as traffic1 or traffic2 channels) and Cfcp = C1+C2 be the total number of channels per cell. If the total number of available channels of the system is m, it must satisfy

1 1 2 2N C N C m+ ≤ . (4)

In FCP, we use two reuse factors instead of the highest reuse factor, N2, for channel allocation as used in the conventional FCA. Thus, Cfcp is larger than the number, Cfca, of channel per cell in FCA, i.e., 2/fcaC m N= .

To study the effect of mobility, we define the residual time as the time that a mobile station (MS) stays in its current cell. And from [9], we can obtain that the residual time is exponentially distributed with mean of 1/µh where µh is the handoff rate and is given by

[ ]h

E V LA

µπ

= (5)

where E[V] is the average mobile user speed, L is the length of the perimeter of the cell and A is the area of the cell. In the hexagonal cell, L and A are given by L = 6R and A= 23 3 / 2R , respectively. Since S1 and S2 have the same traveling area, we can obtain µh1 = µh 2 = µh where µh1 and µh 2 are the S1 and S2 handoff rates respectively.

In our model, for simplicity, we assume that there are no reserved channels for S1 and S2 handoff calls. So the handoff call will be dropped if there is no free channel when it handoffs to the other cell. But in the practical system, we may reserve some channels for the handoff calls to be used because dropping of an on-going call will be more annoying than blocking a new-coming call.

In this paper, we use GoS as defined in [7] to evaluate the system performance. The GoS is given by

GoS = (1-α)PB,ave+αPD,ave (6)

where [0,1]α ∈ is the GoS factor to indicate the relative importance of PB,ave and PD,ave in a particular system.

B. Performance Analysis of FCP with Mobility Channel partitioning (CP) is first introduced and studied in

[4] with stationary users. And in this paper, we analyze the performance of CP with FCA for mobile users. When a new or handoff S1 call arrives at the system, it is first assigned to an unused traffic1 channel. If all traffic1 channels are busy, then the overflow technique will be used. The overflow technique is that the new or handoff call is allowed to assign to an unused traffic2 channel because S1 calls using traffic2 channels will not violate the co-channel constraints. If there is still no unused traffic2 channel found, this S1 call is blocked or dropped. The new or handoff S2 calls can only use traffic2 channels. If no traffic2 channel is found, the S2 call is blocked or dropped. The reverse overflow, i.e., S2 calls to use traffic1 channels, is not allowed due to co-channel interference constraints.

The above FCP scheme with mobile users scheme can be modeled by a three-dimensional Markov chain. And one of the example with the C1 = 2 and C2 = 3 is shown in Fig. 1.

Figure 1. An example of transition rate of FCP with mobile users with C1=2 and C2=3.

In Fig.1, all the transition state, Q, is given by

1 2 2 2{( , , ) | 0 ,0 ,0 , }Q x y z x C y C z C y z C= ≤ ≤ ≤ ≤ ≤ ≤ + ≤ (7)

where x means the number of S1 calls using traffic1 channels (x type calls); y means the number of S1 calls using traffic2 channels (y type calls); z means the number of S2 calls using traffic2 channels (z type calls). The handoff arrival rates, λhx, λhy and λhz, are for x, y, and z type calls respectively, i.e.,

[ ]hx hE Xλ µ= , [ ]hy hE Yλ µ= and [ ]hz hE Zλ µ= (8)

where E[X], E[Y] and E[Z] are the average number of x, y, z type calls respectively. They are given by

( , , )[ ] ( , , )

x y z QE J jP x y z

∈= ∑ j = x, y, z (9)

Three handoff arrival rate parameters, λhx, λhy and λhz, are initially unknown. They can be obtained from the iteration procedure. First, an initial value of βλ, e.g., β = 0.1, is assigned to handoff arrival rates, λhx, λhy and λhz, for each type of calls.

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Then from Markov chain in Fig. 1, we can numerically [10] obtain and estimate of the state probability, i.e., P(x, y, z). Following this, we use Eqs. (8) and (9) to estimate λhx,est, λhy,est and λhz,est. Compared with the initial βλ1 value, we obtain the difference between these values. Then, we use the new estimated values, λhx,est, λhy,est and λhz,est, as the new handoff rates to obtain new estimates of P(x, y, z). The iteration procedure will go on until the difference between the estimated values and the resulting values is lower than a predefined desired accuracy, ε.

Refer to Fig. 1, when all the traffic1 channels are busy, i.e., x = C1, the new S1 calls (no matter whether it is new call or handoff call) will use traffic2 channels. So, there is a transition rate of λ1+λhx+λhy from (C1, y, z) to (C1, y+1, z). This is not true when there is still some free traffic1 channels, i.e., x ≤ C1. No transition rate is from (x, y, z) to (x, y+1, z) for x ≤ C1 because traffic1 channels have higher priority for S1 to be used.

The above three-dimensional Markov chain can be solved to obtain the probability of each state P(x, y, z) [10]. And the blocking probability for S1 is the states that all the traffic1 and traffic2 channels are busy and is given by

2

1 1 20

( , , )C

by

P P C y C y=

= −∑ (10)

And the blocking probability for S2 is the states that all the traffic2 channels are busy and is given by

1 2

2 20 0

( , , )C C

bx y

P P x y C y= =

= −∑∑ (11)

The average blocking probability of the system is given by

, 1 1 2 2B ave b bP P Pγ γ= + (12)

The call dropping probability, Pd, is the probability that a non-blocked call is dropped because of handoff failure. Thus, the average probability that a non-blocked call is dropped at the first handoff is given by

1 1 1 2 2 2(1)d h b h bP P P P Pγ γ= + (13)

where Ph1 and Ph2 is the probability that the handoff occurs before a call completion for S1 and S2. They are given by

hhi

h i

Pµ

µ µ=

+ i = 1 or 2 (14)

Consequently, the average probability that a non-blocked call is dropped at the mth (m ≥ 1) handoff is given by

1 11 1 1 1 1 2 2 2 2 2( ) ( (1 )) ( (1 ))m m

d h b h b h b h bP m P P P P P P P Pγ γ− −= − + − (15)

Thus, the average call dropping probability is given by

1 1 1 2 2 2,

1 1 1 2 2

( )1 (1 ) 1 (1 )

h b h bD ave d

m h b h b

P P P PP P m

P P P Pγ γ∞

== = +

− − − −∑ (16)

C. An Approximate Model for FCP with Mobility In the above part, the steady-state probabilities, i.e.,

P(x, y, z), for the two service model are obtained by solving

three-dimensional Markov chain numerically. Because of the iteration process to estimate the values of λhx ,λhy and λhz, the computational time could become very long as the number of states increases. In this section, we present an approximate model for analyzing the performance of the FCP with mobility. This model allows the state probabilities to be expressed with a closed-form solution.

Figure 2. The Markov chain of the approximate model.

The two-dimensional Markov chain as shown in Fig. 2 can represent the approximate model to analyze the FCP scheme. In Fig. 2, a represents the number of S1 calls in the system no matter whether it is using traffic1 or traffic2 channels; b represents the number of S2 calls in the system using traffic2 channels. As shown in the figure, the maximum number of channels that can be used by S1 is C1 + C2 = C, whereas the maximum number of channels for S2 calls is C2. The parameters λh1 and λh2 are handoff call arrival rates for S1 and S2 calls respectively and they are given by 1 [ ]h a hE Nλ µ= and

2 [ ]h b hE Nλ µ= respectively, where Na and Nb is the number of S1 and S2 users in the system. The λh1 and λh2 are obtained by using the iterative procedure similar to that used in Section II B.

This method is not an exact model of FCP with mobility system. This is because when a S1 call using traffic1 channel releases its traffic1 channel, this approximate model will automatically switch a S1 call currently using a traffic2 channel to this just released traffic1 channel. In the exact model, no such kind of switching occurs. But in order to meet such switching criterion in the approximate model, the following situation must be met: 1) one S1 call leaves the system; 2) all the traffic1 channels are occupied and 3) one or more S1 calls are using traffic2 channel. Thus, the chance to perform such switching in the approximate model is quite low. So this approximate model can still provide a fairly good estimation for FCP with mobility as shown in the Section III. And from the above reason, the blocking and dropping probabilities for the approximate model are slightly lower than those for the exact model because the approximate model will perform switching to free the traffic1 channel for future S1 new or handoff call.

The Markov chain as shown in Fig. 2 is a standard two-dimensional Markov chain that has a closed-form solution [11]. And the probability for each state (a, b) is given by

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1

1 2

1 2

( , )

! !( , )

! !

a b

x y

x y Q

a bP a b

x y

ρ ρ

ρ ρ∈

=∑

(17)

where Q1 is all the allowable states and is given by

1 2{( , ) | 0 , min{ , }}Q a b a C b C a C= ≤ ≤ ≤ −

and ρ1 and ρ2 are the traffic loads for S1 and S2 calls respectively. They are given by 1 1 1 1( ) /( )h hρ λ λ µ µ= + + and

2 2 2 2( ) /( )h hρ λ λ µ µ= + + . The using of the closed-form solution makes the computational time much shorter.

From Fig. 2, we can obtain that the new call blocking probability for S1 calls is when all the traffic1 and traffic2 channels are busy and is given by

1

1 ( , )C

bi C

P P i C i=

= −∑ (18)

Similarly, the new S2 call blocking probability is given by

1

1

1

2 20

( , ) ( , )CC

bi C j

P P i C i P j C−

= == − +∑ ∑ (19)

And the average new call blocking probability is still given by (12) and the average call dropping probability is given by (16). Particularly, for the stationary user, we could set λh1=λh2=0 and µh=0 and use the same Markov chain to represent the system. The analysis results with stationary user agree with the results in [4]

III. ANALYTICAL AND SIMULATION RESULTS A 49-cell area with wrap-around technique is used in the

simulation. We assume that a very large population of mobiles are in the system so that the call activation rate is independent of the number of calls in progress. The mean value of the average call duration time for S1 and S2 is 100 and 50s, respectively. The reuse factor for S1 and S2 is assumed to be 4 and 7, respectively. The S1 call can be considered as a traditional voice service that requires lower reuse factor and longer call duration time. The S2 call can be considered as a data service. A total of m = 210 channels are available in the system. So, the number of channel per cell for FCA is 30. To achieve the best results, different channel combination, i.e., C(C1, C2), is simulated in FCP scheme. We use a simple mobility model in [9] where all the mobiles move in the straight line without changing their speed and direction. For simplicity, there is no reserved channel in FCP and FCA schemes. Connection call blocking probability, handoff call dropping probability and grade of service (GoS) are considered in our analysis and simulation results. The desired accuracy, ε, is set to be 10-6 in our analysis. We assume the GoS factor α = 0.5. For all the simulation results, the 95% confidence intervals within 5%± of the average values are observed.

Fig. 3 shows the results of PB,ave and PD,ave values for two services with the call arrival rate ratio of γ1:γ2 = 1:1 (corresponding to the traffic load ratio of ρ1:ρ2=2:1). For the FCA system, each cell has 30 channels based on a reuse factor

of 7 to support both service types. The PB,ave for FCA system is obtained by using Erlang B formula. For FCP system, a few combinations of channel allocation, C(C1, C2), to each traffic channel have been considered and the best combination is shown in the figure. Under the arrival rate ratio of γ1:γ2 = 1:1, the channel combination, C(21:18), gives the best performance compared with other channel combination at the GoS of 1%. In Fig. 3, it can be seen that the FCP with C(21:18) for mobile users can provide about 32% capacity improvement as compared with FCA for 1% blocking probability and 33% capacity improvement for 1% dropping probability. This is because some of the S1 users use the reuse factor of 4 for channel allocation and thus, the average reuse factor of the FCP system is lower than the FCA system. Therefore, the system improvement can be achieved.

Fig. 4 shows the GoS results for two services with the call arrival rate ratio of γ1:γ2 = 1:1 (corresponding to the traffic load ratio of ρ1:ρ2=2:1) and α = 0.5. The GoS results of both FCA and FCP are obtained by Eq. (6). The improvement of FCP over FCA is about 32% at GoS = 1%. In Fig. 3 and Fig. 4, we can see that the analytical results are very close to the simulation results, which validates the correctness of the analytical model. In these two figures, we can also see that although the analytical results using approximate model is slightly lower than the exact model, the discrepance between them is acceptable. This observation agrees with our expectation as stated in Section II. But by using the approximate model, the computational time is much shorter than exact model.

Fig. 5 shows the influence of speed of the mobile to the improvement of FCP over FCA with different traffic load ratios between two services. It can be seen that the improvement increases as the traffic of S1 increases. Besides, we could see that although the speed of the mobile changes, the improvement of FCP over FCA does not change much. The same conclusion can be drawn with different GoS factors as shown in Fig. 6. The above two results indicate the speed or the GoS factor does not decrease the effectiveness of our FCP scheme. And this conclusion is very important for our channel assignment scheme.

IV. CONCLUSIONS AND FUTURE WORK In this paper, we present an idea of channel partitioning and

apply it with FCA for the mobile users. An exact model using three-dimensional Markov chain is first proposed and analyzed. Then, an approximate model is presented to reduce the computational complexity. The analytical results show that our approximate model can well represent the exact model for FCP with mobile users and at the same time, reduce the computational time greatly. We also study the impact of different traffic ratios, mobile speeds and GoS factors. The simulation and analytical results show that with the increasing of the traffic ratio of S1 service, FCP can gain more throughputs as compared with FCA scheme. The mobile speed and the GoS factor do not decrease the effectiveness of our scheme. Our proposed scheme could work for the reuse factor based systems such as GSM, GPRS, EDGE or cellular OFDM.

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In this FCP with mobile users system, the optimum number of channels allocated to each service is pre-defined based on the traffic load for each service. This may not be feasible in practice because the optimum channel combination may vary with the traffic variation. Our future work will consider a pure and flexible dynamic channel allocation scheme that no channels are pre-allocated to each type of service. In other words, any channel in principle can be used by any service call and no pre-defined channel allocation for each service is required.

REFERENCES [1] J. Choi and J. A. Silvester, “A Fair-Optimal Channel Borrowing Scheme

in Multiservice Cellular Networks with Reuse Partitioning,” in Proc. of IEEE ICUPC '98, vol.1, pp. 261-265,1998.

[2] D. Zhao, X. Shen and J. W. Mark, “Performance Analysis for Cellular Systems Supporting Heterogeneous Services,” in Proc. of IEEE ICC, vol.5, pp. 3351-3355, May 2002.

[3] S.-H. Lee and J.-S. Lim, “Performance Analysis of Channel Allocation Schemes for Supporting Multimedia Traffic in Hierarchical Cellular systems,” IEICE Trans. Commun., vol. E86-B, March 2003.

[4] M. Yang and Peter H. J. Chong, “Capacity optimizing channel allocation schemes for multi-service cellular systems”, Int. J. of Commun. Systems, Vol. 17, pp. 575-590, Aug. 2004.

[5] H. Holma and A. Toshala, WCDMA for UMTS, 2nd Ed. John Wiley & Sons, 2002.

[6] Z. Wang and R. A. Striling-Gallacher, “Frequency Reuse Scheme for Cellular OFDM Systems,” IEE Elect. Lett. Vol. 8, No. 8, pp. 387-388, 11th April 2002.

[7] D. Hong and S. Rappaport, “Traffic Model and Performance Analysis for Cellular Mobile Radio Telephone Systems with Prioritized and Nonprioritized Handoff Procedures,” IEEE Trans. Veh. Tech., Vol. 35, No. 3, pp. 77-92, Aug. 1986.

[8] W. Y. Chen, J-L C, Wu and L-L Lu, “Performance Comparison of Dynamic Resource Allocation with/without Channel De-Allocation in GSM/GPRS Networks,” IEEE Commun. Lett., Vol. 7, No. 1, pp. 10-12, Jan. 2003

[9] R. Thomas, H. Gilbert and G. Mazziotto, “Influence of the Movement of the Mobile Station on the Performance of a Radio Cellular Network.” In Proc. 3rd Nordic Seminar, Paper 9.4, Copenhagen, Sept. 1988.

[10] L. Kleinrock, Queueing Systems, vol. 1: Theory. New York: John Wiley & Sons, 1975.

[11] D. Bertsekas and R. Gallager, Data Networks, 2nd ed. Prentice Hall, New Jersey, 1992.

Figure 3. Average call blocking and dropping probabilities with traffic load ratio ρ1:ρ2=2:1 (λ1:λ2=1:1) for FCA and FCP with C(21,18).

Figure 4. GoS results with traffic load ratio ρ1:ρ2=2:1 (λ1:λ2=1:1). Channel combination: C(21,18)

Figure 5. GoS =1% improvement VS. different traffic load ratio under different speed

Figure 6. GoS =1% improvement VS. different traffic load ratio under different GoS factor

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