We evaluate the performance of a wireless cellular system with four cells, as shown in Figure 1. Figure 1 shows as example, where we have celli\in \{1,2,3,4\},M=\left\{1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}3,\phantom{\rule{0.25em}{0ex}}4\right\}\text{,}{A}_{1}=\left\{2,\phantom{\rule{0.25em}{0ex}}3,\phantom{\rule{0.25em}{0ex}}4\right\}. Each services\in S requires *b*_{
s
}, a BBU to guarantee its QoS requirements in the cellular system. In each cell, the network capacity is 2 Mb/s, and the BBU is set to 32 kb/s based on the 3GPP-supported multimedia bearer services[16]. This implies that the capacity of each cell is{C}_{i}=62 BBUs.

We assume that two multimedia services are offered with service types that have “single mode service”, “dual mode full-rate service”, and “dual mode reduced-rate service” (i.e. ,S=\{1,2,{2}^{*}\}). The first service, i.e., *s* = 1, is a voice connection requiring 32 kb/s. Type 1 service indicates a “single mode service”. The second service, i.e., *s* = 2, is a video telephone (128 kb/s) with voice connections requiring 160 kb/s. Type 2 service indicates a “dual mode full-rate service”. The adaptive coding of a type 2 service (s=2*) is a half-quality video telephone (64 kb/s) with voice connections requiring 96 kb/s[17, 18]. Type 2* service indicates a “dual mode reduced-rate service”. The values are set according to the multimedia codec for 3GPP[19]. We assume that *b*_{1} is the bandwidth of a type 1 service, *b*_{2} is the bandwidth of a type 2 service, and{b}_{{2}^{*}} is the bandwidth of a type 2* service.

Thus, the QoS provisioning of these cells requires that *b*_{1} = 1 BBU, *b*_{2} = 5 BBUs, and *b*_{2*} = 3 BBUs. The connection duration has the means1/{v}_{1}=1/{v}_{2}=8 min. The interboundary time in each cell has the mean1/{\eta}_{i}=2 min, for users in the wireless cellular system.

### Effect of increasing the threshold of adaptive coding

Figure 2 shows the blocking probabilities of new connection requests to the two services and the dropping probabilities of handover connection requests for types 1, 2, and 2* services in cell 1 versus the adaptive coding threshold.

*σ* ranges from 0 to 62, while the arrival rates of new connection requests from services type 1 and 2 remain constant at 0.5 connection requests per minute and ψ = 50. Pb1 and Pb2 are the blocking probabilities of new connection requests of types 1 and 2 services, respectively. Pf1, Pf2, and Pf3 are the forced termination probabilities of handover connection requests of types 1, 2, and 2* services, respectively. The blocking probabilities of new connection requests and the dropping probabilities of handover connection requests of type 2 services are the highest because the connections require five times the amount of BBUs as type 1 services. In contrast, the dropping probabilities of handover connection requests of a type 2* service are higher than a type 1 service. This is because the connection requirement of a type 2* service requires three times as many BBUs as type 1 services.

In our study, we can see that in cell 1, the new call dropping probability of a type 1 service reduces from{10}^{-1.691} to{10}^{-3.366} while a type 2 service reduces from{10}^{-1.342} to{10}^{-2.702} due to *σ*. Furthermore, the handover call dropping probability for a type 1 service reduces from{10}^{-3.557} to{10}^{-6.366}, type 2 service reduces from{10}^{-2.589} to{10}^{-5.054}, and type 2* service reduces from{10}^{-2.939} to{10}^{-5.584} due to *σ*.

Previous studies[6] have demonstrated the effect of the level of guard capacity on blocking and forced termination probabilities. The blocking probabilities for new connection requests by two services increase whereas the dropping probabilities of handover connection requests by two services decrease when the guard capacity Cg changes from 0 to 48. Previous studies[6] have reduced the forced termination probability to a very low value by allowing the blocking probability to reach a higher level.

In our study, we reduced the blocking probabilities and the forced termination probabilities to lower levels but with a loss of the QoS for video telephones with a type 2 service. The curves of two services exhibited the same trend. For example, the connection-level QoS requires that the blocking probability should be under 2% while the forced termination probability should be under{10}^{-4}. If σ = 62, the blocking probabilities and the forced termination probabilities cannot satisfy the QoS requirements for both classes. However, if we retain σ = 40 exclusively for handover calls, the connection-level QoS can be guaranteed for calls of both classes. The level of σ should be determined by the connection-level QoS requirement in multi-service systems.

Figure 3 shows the adaptive coding probability for handover connection requests of with a type 2 service versus the adaptive coding threshold (σ) of cell 1 ranging from ψ = 30 to 50. The adaptive coding probability in all three cases is approximately the same, whereas σ < 10. It tends to one if σ approaches to zero, as shown in Figure 3.

The permitted amount of new calls increases when σ is fixed and ψ increases. The remaining capacity of cell 1 also declines. The adaptive coding probability of handover connection requests with a type 2 service gradually increases while the remaining capacity of cell 1 gradually decreases.

Figure 4 shows the average peak signal-to-noise ratio (PSNR) value when varying the adaptation coding threshold. The PSNR is used as a measure of the quality of reconstruction of lossy compression, such as video compression. The signal is the original image while the noise is the error introduced by compression. PSNR is used when comparing compression codes as an approximation of the human perception of reconstruction quality, so in some cases one reconstruction may appear to be closer to the original than another, even though it has a lower PSNR. Typical values for the PSNR with lossy images and video compression are from 30 to 50 dB. Acceptable values for wireless transmission quality loss are considered to be about 20 to 25 dB[20]. Therefore, the average PSNR value in Figure 4 must be above 30 dB to produce acceptable quality values for wireless transmission video (video with a type 2 service).

The PSNR with a type 2 service is set to 33 dB while it is set to 28 dB with a type 2* service[21]. We assume that the number of the type 2 services in cell 1 is “n2” while the number of the type 2* services in cell 1 are “n3”. Let ω denote the average PSNR of both the type 2 and 2* services in cell 1. We have

\omega =\left(\frac{\text{n}2}{\left(\text{n2+n}3\right)}\right)\text{*33\hspace{0.17em}dB+}\left(\frac{\text{n}3}{\left(\text{n2+n}3\right)}\right)\text{*28\hspace{0.17em}dB}

(13)

The handover connection requests for type 2 services are easily changed into those of type 2* service if the adaptation coding threshold is decreased. At this point, the average PSNR is lower while the average video quality of a type 2 service is poorer. From the other perspective, the adaptive coding probability of handover connection requests for type 2 services becomes gradually higher when σ is fixed and ψ is increased, as shown in Figure 3. The average PSNR is lower, as shown in Figure 4, while the average video quality of a type 2 service becomes very poor.

Type 2 service does not change to a type 2* service if σ = 62. At this point, the average PSNR value is 33 dB. All handover connection requests for a type 2 service are changed into type 2* services if σ = 0. At this point, the average PSNR is 28 dB.

### Varying the call to mobility ratio

Figure 5 shows the blocking probabilities of new connection requests for types 1 and 2 services, and the dropping probabilities of handover connection requests for all services in cell 1 when the “call to mobility ratio” (CMR) of types 1 and 2 services is increased.

The CMR\left(\mathit{C}\mathit{M}\mathit{R}\mathit{=}{\lambda}_{s}/{\eta}_{i}\right) of a user is the average number of calls to a user per unit time divided by the average number of times the user changes registration areas per unit time[22–24]. We sets\in \{1,2\} andi=1. The arrival rate of new connection requests for type 1 (λ_{1}) and type 2 (λ_{2}) services are set from 0 to 1. Next, the interboundary time of each cell has a mean of1/{\eta}_{1}=2 min and a connection duration with means1/{v}_{1}=1/{v}_{2}=8 min. The CMR will increase and both λ_{1} and λ_{2} increase while the inter-boundary time in each cell is fixed. Next, the blocking probabilities of new connection requests and the dropping probabilities of handover connection requests for the two services are increased because the occupancy of cell 1 is increased, as shown in Figure 5.

Figure 6 shows the effect of the CMR on the adaptive coding probability. λ_{1} and λ_{2} are set from 0 to 1 new connection requests per minute. Next, we set1/{\eta}_{1}=2min, ψ = 50, and σ from 35 to 62. λ_{1}, λ_{2}, and the occupancy of cell 1 are very low, while\mathit{C}\mathit{M}\mathit{R}\le 0.5 and1/{\eta}_{1} is fixed. Thus, the probability of meeting the adaptive coding condition\left(\sum _{{s}^{\text{'}}\in S}{m}_{{i}_{{s}^{\text{'}}}}{b}_{{s}^{\text{'}}}+{b}_{2}>\sigma \right) is very low. At this point, the effect of the adjustment of σ on the adaptive coding probability is not significant. In other words, as the amount of new calls decreases, the adaptive coding probabilities of the four cases are close to zero when\mathit{C}\mathit{M}\mathit{R}\le 0.5. The dropping probabilities of handover connection requests for services will be increased when CMR increases, as shown in Figure 5. This indicates that the occupancy of cell 1 becomes higher and the probability of meeting the adaptive coding condition\left(\sum _{{s}^{\text{'}}\in S}{m}_{{i}_{{s}^{\text{'}}}}{b}_{{s}^{\text{'}}}+{b}_{2}>\sigma \right) is higher. At this point, the adaptive coding probabilities of handover connection requests for type 2 services are higher, as shown in Figure 6. However, Figure 6 also shows that the adaptive coding probability increases when CMR and ψ are fixed, but σ is decreased, which is the same relationship as that shown in Figure 3.

Figure 7 shows the average PSNR of handover connection requests for type 2 services after the CMR of types 1 and 2 services is increased. The adaptive coding probability of handover connection requests for type 2 services will increase when the CMR increases, as shown in Figure 6. The average PSNR of handover connection requests for type 2 services is decreased when the adaptive coding probability is increased, as shown in Figure 4. Therefore, the average PSNR is gradually decreased while the CMR is gradually increased. In contrast, the average PSNR declines if σ is lower, as shown in Figure 4. Thus, we can obtain show that the average PSNR becomes significantly lower if σ is lower and CMR is fixed.

Figures 8 and9 show the blocking and forced termination probabilities of connection requests for type 1 services versus the CMR, respectively. The difference in the dropping probabilities of handover connection requests for type 1 services between σ = 62 and 55 is very large, as shown in Figure 9. The occupancy of cell 1 decreases while type 2 service connections are changed into type 2* services at the point of handover. Next, the dropping probabilities of handover connection requests for types 1 and 2 services become lower, especially for type 1 services. This is because the bandwidth of type 1 service handover connection requests is lower than that of type 2 services.

Figures 10 and11 show the blocking and forced termination probabilities of type 2 service connection requests versus the CMR, respectively. Figure 12 shows the forced termination probabilities of type 2* service connection requests versus the CMR. σ ranges from 35 to 62, while ψ is fixed at 50. As shown in these figures, the CMR has a significant impact on the blocking and forced termination probabilities. As the CMR increases, there is a rapid increase in both probabilities. As the CMR approaches 2, the blocking probabilities of both services are close to 0.1, and the forced termination probability is around 1 × 10^{–3}. The occupancy of cell 1 becomes lower and the blocking and forced termination probabilities are reduced due to the adaptive coding of type 2 services. Thus, user mobility can seriously affect the connection-level QoS, as shown in Figures 8,9,10,11, and12.

### Varying arrival rate service type 2 (λ_{2})

Figure 13 shows the connection-level QoS for the blocking and forced termination probabilities of both classes of calls versus the arrival rate of new calls for type 2 services (λ_{2}). The new connection request threshold (ψ) is 50 and the adaptive coding threshold (σ) is 35. The parameters1/{v}_{1}=1/{v}_{2}=8 min and1/{\eta}_{i}=2 min are used. The arrival rate of new connection requests from type 1 services (λ_{1}) remains constant at 0.5 connection requests per minute. λ_{2} ranges from 0.1 to 1. The blocking and forced termination probabilities are very sensitive to the arrival rate when the arrival rate is below a certain threshold (light load region).

This indicates the effectiveness of ψ and σ in providing a better connection-level QoS for more important handover calls.

Figures 14 and15 show the blocking and forced termination probabilities of type 2 service connection requests versus λ_{2}, respectively. As σ decreases, we can see that both probabilities decrease. More type 2 service connection requests of are easily changed to type 2* service connection requests when σ is lower. The goal of cell capacity saving can be met and the blocking and forced termination probabilities are reduced.