On the other hand, Khandelwal et al. [23] proposed using L opt =1.943 η×N, where η= log(H/N / log(1−1/N) and H represents the number of slots with no tag response.
Similarly, Huang [22] suggested the formula L opt =1/(1−e 2 ln2/N ).
For α=0.9,0.92,0.98, and N=8,10,…,32, we computed (widetilde {L}_{opt}) according to (10) and compared the results with the exact values of L opt.
It is worthwhile to determine the optimal frame size L opt that minimizes τ α.
On the other hand, Lee et al. [12] derived the formula L opt =1/(1−e −1/N ).
Considering the implementation mechanism of adjusting the frame size in EPC protocol, L opt should be some power of 2. Therefore, we can set L opt as follows: L_{text{opt}} = 2^{texttt{round}(log_{2} N_{text{unid}})}.
The optimal frame size L opt corresponds to the value of L that yields the smallest value of τ α.
At this time, a question naturally arises: Is it secure to use ((widetilde {L}_{opt}), (widetilde {T}_{alpha }^)) instead of (L opt, (T_{alpha }^)), with respect to the reliability constraint ({mathcal {P}}_{id}^{t} ge alpha ) in (1)?
The exact values of T α and L opt were computed using the MC method and MATLAB.
Because T α and τ α are functions of L, the second problem can be defined as determining the optimal frame size L opt that minimizes τ α.
Figures 8, 9, and 10 show comparisons of the exact values of L opt and (T_{alpha }^) with those obtained using (8) and (10) (i.e., (widetilde {L}_{opt}) and (widetilde {T}_{alpha }^)) for α=0.9,0.92,0.98, respectively (in these figures, the left y-axis represents "optimal frame sizes," while the right y-axis represents "termination time").
