# Optimized Architecture for Efficient OFDMA Network Design
## 3 Analytical Model for OFDMA Networks
### Scheduling Policies
#### 3.3.2 Throttling Regime  
The throttling regime is proposed to model a performance metric defined in the IEEE 802.16e standard known as the Maximum Sustained Traffic Rate (MSTR). This metric specifies an upper limit on the maximum throughput that can be offered to a user. The traffic of a station is described using three parameters: MSTR, \(\overline{x}_{on}\), and \(\overline{t}_{off}\). The MSTR controls the maximum allowable peak rate for a connection. For each frame, the scheduler attempts to allocate the appropriate number of slots necessary for each active station to meet its MSTR. If a station is in a failure state, it does not receive any slots, resulting in degraded throughput. If at any time the total number of available slots (\(N_{S}\)) is insufficient to satisfy the MSTR requirements of all active users (those not in a failure state), the throughput of all users will be equally degraded. Conversely, if there are more available resources than needed, the excess slots will remain unused. 1. Departure Rate: To estimate the average departure rate \(\mu(n)\) related to the throttling method, it is necessary to define certain variables. To compensate for losses due to failures, a slightly elevated instantaneous throughput compared to the \(MSTR\) is considered, denoted as the Dynamic Bandwidth Rate (\(DBR\)):  
\[DBR=\frac{MSTR}{1-p_{0}} \tag{23}\]  
A mobile station using MCS\({}_{k}\) requires a minimum number of slots \(\overline{g}_{k}\) per frame to achieve the \(DBR\):  
\[\overline{g}_{k}=\frac{DBR.T_{F}}{m_{k}} \tag{24}\]  
Since there will be no slots reserved for a station in failure, it follows that \(\overline{g}_{0}\) = 0. Thus, the average number of slots per frame required by a mobile to meet its MSTR can be expressed as  
\[\overline{g}=\sum\
olimits_{k=1}^{K}p_{k}g_{k} \tag{25}\]  
Knowing \(\overline{g}\), the departure rate \(\mu(n)\) can be described as follows:  
\[\mu(n)=\frac{N_{s}}{\max(n\overline{g},N_{s})}n\frac{MSTR}{\overline{x_{on}}} \tag{26}\]  
In this equation, \(\frac{MSTR}{\overline{X}_{on}}\) represents the throughput that allows each of the active stations to complete their transfers, assuming there are always sufficient slots in the frame to meet the \(MSTR\). The term \(\frac{N_{s}}{max(n\overline{g},N_{s})}\) represents the ratio of the total departure rate achieved by the n active transfers. Specifically, if there are n active stations, an average of \(n\overline{g}\) slots is needed to achieve their respective \(MSTR\). If \(N_{s}\)\(\geq n\overline{g}\), they can all receive their \(MSTR\), resulting in a ratio equal to 1. Conversely, if \(N_{s}\)\(<n\overline{g}\), there will not be enough resources to meet the demands, and consequently, the mobiles will only receive a fraction of their \(MSTR\), specifically \(\frac{N_{s}}{n\overline{g}}\). 2. Performance Parameters: By substituting the departure rate \(\mu(n)\) (from Equation (26)) into the generic expression (14), the stationary probability \(\pi(n)\) can be calculated as follows: \[\pi(n)=\frac{N!}{(N-n)!}\left(\frac{\rho^{n}}{n!\prod_{i=1}^{n}\frac{N_{i}}{ max(\overline{g},N_{s})}}\right)\pi(0)\] (27) where \[\rho=\frac{\overline{x}_{on}}{MSTR\overline{t_{off}}}\] (28) The value of \(\pi(0)\) is obtained through normalization, similar to the previous derivations. The performance parameters can be derived from the stationary probabilities \(\pi(n)\).