## 4 Reader Collision
When the number of readers is low, the probability of an empty slot is high, and as the number of readers increases, the probability of an empty slot decreases. Therefore, throughput of the system also increases, however large number of readers initiates collision slots. According to the proposed algorithm, the throughput of the system is much higher than conventional one since the average value of contention window and waiting time are modified. With four readers working together in the system, the throughput reached 2165 queries/s for the existing method and 2509 queries/s for the proposed one. As the number of readers increases, communication duration between reader and tag becomes shorter. As a result, the overall utilization of the system reached nearly 92% for the proposed protocol, which is 15.2% higher than the existing protocol. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Denotation** & **Value** \\ \hline CW & Contention Window & 32 \\ \(T_{bi}\) & Beacon Interval & 5000 \(\mathrm{\SIUnitSymbolMicro s}\) \\ \(T_{min}\) & Minimum waiting time & \(3\times T_{bi}\) \\ \(T_{max}\) & Maximum waiting time & \(2\times T_{min}\) \\ \(T_{read}\) & Reading time & \(4\mathrm{s}\) \\ \(T_{collision}\) & Collision beacon decrement interval & \(2\times T_{bi}\) \\ \(T_{success}\) & Successful beacon decrement interval & \(T_{read}+T_{max}+T_{bi}\) \\ \(Tempty\) & Empty beacon decrement interval & \(1\times T_{bi}\) \\ \(l_{b}\) & Query transmission time & 265 \(\mathrm{\SIUnitSymbolMicro s}\) \\ \(l_{q}\) & Beacon transmission time & 341 \(\mathrm{\SIUnitSymbolMicro s}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. ```
/* Initialize parameters */ Random back_off \(()\)\(\rightarrow\) r Backoff_timer \(()\)\(\rightarrow\) bt Waiting_timer \(()\)\(\rightarrow\) wt Reading_timer \(()\)\(\rightarrow\) rt Paused time \(()\)\(\rightarrow\)\(\Delta\)t ifState_value = = 1; /* state is idle*/ wt \(\rightarrow\)\(T_{min}\) elseifState_value = 0 && State = \"Contend\" while while _control channel is busy bt \(\rightarrow\)\(\Delta\)t endwhile while _control channel is idle bt \(\rightarrow\) bt+\(\Delta\)bt endwhile elseifState_value \(\
otin\) {0,1} /* state is waiting*/ whiule _bt \(>\)  bt \(\rightarrow\) bt \(-\Delta\)bt while _bt \(\leq\) 0 bt\(\rightarrow\) r endwhile endif whilecontrol channel is idle Beacon is transmitting over control channel State = \"Reading\" endwhile Whilert \(\leq\) 0 ifState = \"Successful\" cancel all timer else ifState = \"Waiting\" resetting state after reading wt\(=\)\(T_{max}\) endwhile endif endif endif endif
```  
**Algorithm 1**Queue Delay Calibration (0)  
The execution time analysis is depicted in Figure 10 to define the computational complexity of the proposed Modified Pulse Protocol. Three main parameters are considered for determining the computational complexity. (i) Contention window as it determines the average back-off time for each reader. (ii) Collision of probability to notify that how many retransmissions are required. (iii) Adaptive Beacon Interval (ABI) as it supervises the duration cycle. Readers are varied from 1 to 20 and execution time is evaluated for each reader. It is observed from the Figure 10 that execution time is increases in a piece-wise linear manner as number of readers are increased. The maximum execution time is 0.008 s for 20 readers. Therefore, the selection of our contention window as triangle distribution function reduced execution time and established computational efficiency. Further, memory depends primarily on number of readers and execution time. Therefore, proposed algorithm runs within O(n) complexity. That signify linear memory usage. Figure 8: System throughput of conventional and proposed algorithm. Figure 10: The execution time analysis of Modified Pulse protocol. Figure 9: System utilization of conventional and proposed algorithm.