**2.1.2 Analytical modeling**

Table 3 lists the notations used for analytical modeling.


Table 3. Notations used in Analytical Modeling.

Throughput modeling is described below. For the purpose of brevity bandwidth allocation is explained for the three types of users for eRTPS service flow. Similar equations can be derived for the other service flows.

BS allots bandwidth to the high-priority eRTPS service flows as per eqn 1.

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Once bandwidth is allotted to a high-priority eRTPS service flow, the leftover bandwidth is calculated as per eqn 2.

$$\begin{aligned} \text{avol\\_bw} &= \text{tot\\_bw} - \left(\sum\_{j=1}^{x} \text{ertps\\_pri\\_bw\\_alloc\\_allot\\_j}\right) \\ &\ge \text{m}\_i \end{aligned} \tag{2}$$

After all the high-priority eRTPS service flows are allotted bandwidth, bandwidth is allotted to the regular eRTPS service flows as per eqn 3.

\_ \_ \_ () \_ \_ \_ () \_ \_ \_ () \_ \_ \_ \_ () \_ \_ \_ () \_ \_ \_ () \_ \_ \_ \_ \_ \_ () \_ *ertps reg bw req p if ertps reg bw req p tr and ertps reg bw req p avl bw tr if tr ertps reg bw req p ertps reg bw allot p and ertps reg bw req p avl bw avl bw if avl bw ertps reg bw req p and avl bw tr tr oth erwise* (3)

After allocating bandwidth to a regular eRTPS service flow, leftover bandwidth is calculated as per eqn. 4

$$\begin{aligned} \text{avl\\_bw} &= \text{avl\\_bw} - \left(\sum\_{j=1}^{\infty} \text{ertps\\_reg\\_bw\\_alloc\\_allot\\_j}\right) \\ &\ge \text{in}\_t \end{aligned} \tag{4}$$

Once we are through with the regular eRTPS service flows, bandwidth is allotted to the lowpriority eRTPS service flows as per eqn. 5.

Throughput modeling is described below. For the purpose of brevity bandwidth allocation is explained for the three types of users for eRTPS service flow. Similar equations can be

\_ \_ \_ () \_ \_ \_ () \_ \_ \_ () \_

Once bandwidth is allotted to a high-priority eRTPS service flow, the leftover bandwidth is

1 \_ \_ \_ \_ \_ ()

After all the high-priority eRTPS service flows are allotted bandwidth, bandwidth is allotted

\_ \_ \_ () \_ \_ \_ () \_ \_ \_ () \_

*erwise*

After allocating bandwidth to a regular eRTPS service flow, leftover bandwidth is calculated

1 \_ \_ \_ \_ \_ ()

Once we are through with the regular eRTPS service flows, bandwidth is allotted to the low-

*x*

*j avl bw avl bw ertps reg bw allot j*

*tr if tr ertps reg bw req p ertps reg bw allot p and ertps reg bw req p avl bw*

*tr oth*

  *x*

*j avl bw tot bw ertps pri bw allot j*

,

,

*x n*

priority eRTPS service flows as per eqn. 5.

*x m*

to the regular eRTPS service flows as per eqn 3.

*tr if tr ertps pri bw req p ertps pri bw allot p and ertps pri bw req p avl bw*

*tr oth*

\_ \_ \_ ()

*ertps pri bw req p*

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*ertps reg bw req p*

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*if ertps reg bw req p tr*

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*and ertps reg bw req p avl bw*

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*and ertps pri bw req p avl bw*

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(2)

(1)

(3)

(4)

BS allots bandwidth to the high-priority eRTPS service flows as per eqn 1.

 

derived for the other service flows.

calculated as per eqn 2.

as per eqn. 4

$$\text{rents\\_npr\\_pur\\_law\\_req(p)} = \begin{cases} \text{ertps\\_npr\\_tw\\_req(p)} \\ \quad \text{if } \text{ertps\\_npr\\_tw\\_req(p)} < \text{tw} \\ \quad \text{and } \text{ertps\\_npr\\_bw\\_req(p)} < \text{val\\_bw} \\ \quad \text{if } \text{tr\\_sertps\\_npr\\_bw\\_req(p)} \\ \quad \text{and } \text{ertps\\_npr\\_bw\\_req(p)} < \text{val\\_bw} \\ \quad \text{and } \text{\\_bw} \le \text{ertps\\_npr\\_bw\\_req} \\ \quad \text{and } \text{val\\_bw} \le \text{tr} \\ \quad \text{otherwise} \end{cases} \tag{5}$$

After allotting bandwidth to the jth low-priority eRTPS service flow, leftover bandwidth is calculated as per eqn. 6

$$\begin{aligned} \text{avol\\_bw} &= \text{avol\\_bw} - \left(\sum\_{j=1}^{\infty} \text{ertps\\_npr\\_bw\\_alolot\\_j}\right) \\ &\ge \sigma\_2 \end{aligned} \tag{6}$$

At this point bandwidth has been allotted to all the eRTPS connections. The above method of bandwidth allocation is repeated for RTPS, nRTPS and BE. This ensures that for each service flow, bandwidth is allotted to high-priority users first followed by regular users and finally the low-priority users.

#### **2.1.3 Simulation results**

In order to evaluate DBAM, simulations were carried out on NS-2. Light WiMAX module (LWX) (Chen 2008) was used to simulate the WiMAX environment in NS-2. Strict priority bandwidth allocation algorithm of LWX was modified to accommodate DBAM algorithm. Simulations were carried out with the parameters from table 4.


Table 4. Simulation parameters for DBAM.

Simulation network was setup such that at any point in time, 33% of the SS are priority SS, next 33% are regular SS and the final 1/3rd are low-priority SS. Each SS generates only eRTPS traffic. Uplink data is generated at the rate of 1Mbps. Downlink ftp traffic was also added. Downlink data is generated at the rate of 1Mbps.

Simulation results for throughput are shown in Fig. 4.

Fig. 4. Simulation results for throughput for the three types of SS.

When the number of MS is 9 each MS has sufficient bandwidth to transmit its data. But, when the number of SS is more than 9, there isn't sufficient bandwidth to support all SS. DBAM provides bandwidth to high-priroity SS first then regular SS and the leftover bandwidth is shared by low-priority SS. When the number of SS crosses 13, bandwidth for regular SS keeps reducing. Theoretical Results are shown in Figure 5.

Fig. 5. Theoretical results for DBAM.

High Priority SS Regular SS Low Priority SS

0 5 10 15 20 25 **Number of SS**

Theoretical High Priority SS Theoretical Regular SS

0 5 10 15 20 25 30 **Number of SS**

When the number of MS is 9 each MS has sufficient bandwidth to transmit its data. But, when the number of SS is more than 9, there isn't sufficient bandwidth to support all SS. DBAM provides bandwidth to high-priroity SS first then regular SS and the leftover bandwidth is shared by low-priority SS. When the number of SS crosses 13, bandwidth for

Fig. 4. Simulation results for throughput for the three types of SS.

regular SS keeps reducing. Theoretical Results are shown in Figure 5.

Theoretical Low Priority SS

0

Fig. 5. Theoretical results for DBAM.

**Average Throughput (Kbps)**

200

400

600

**Average Throughput (Kbps)**

800

1000

1200

Comparing figure 4 and figure 5 we see that the simulation results closely follow the theoretical results.

By introducing DBAM we can provide graded quality of service to the users. This is a winwin situation for both users and operators. The users win because their data gets prioritized and hence they get a better quality of service. The service providers stand to gain because they get higher revenue for the same amount of data being transmitted. Its just that the order of bandwidth allocation is modified.
