Analysis of Dynamic frame Aloha with frame restart

Abstract

Abstract-This paper provides an analysis of the Dynamic frame Aloha (DFA) protocol with frame Restart. Although a previous work has numerically provided the best restarting strategy when the number of tags N is known, that strategy is represented by a table whose entries are so many to be impractical for high values of N . Here we provide a simpler set of equations that, besides the optimal strategy, lead to a very simple sub-optimal strategy whose performance is practically indistinguishable from the optimal one. Furthermore, we prove that asymptotically the Frame Restart property is useless, being the corresponding efficiency equal to e −1 , the same as the plain DFA. We investigate the strategies and performance when N is unknown, furthermore providing a procedure, called AE 2 , that is able to asymptotically reach the theoretical efficiency e −1 .

Asymptotic Analysis of Backlog Estimates for Dynamic Frame Aloha

“…In this paper we generalize the approach already exposed in [18] and, after deriving the asymptotic efficiency of the Schoute's estimate, equal to 0.311, we use it to prove that estimate proposed in [13] is asymptotically efficient, namely is able to reach e −1 .…”

“…The aim is at maximizing efficiency, defined as η(N ) = N/L(N ), being L(N ) the average number of slots needed to identify all N tags. In [12] we have proved that, when N is known, the optimal frame setting is r = n, and the asymptotic efficiency, as N → ∞, is e −1 , while in [13] we have shown that the FR procedure does not improve the DFA asymptotic efficiency. In practice N is often unknown, and it turns out that the efficiency suffers from the mismatch between N and the initial frame length r 0 , especially when N is unbounded, as it can be in future applications.…”

“…A way to reduce the number of tags transmitting in the frame, entirely respecting the EPC standard specifications, is to re-start a new frame before the exploration of the entire frame is completed. This has led to the proposal of AE 2 (Asymptotically Efficient Estimate), whose operation has been briefly anticipated in [13] and reads as follows.…”

“…In [18] we have analyzed the asymptotic efficiency of the first and simpler of the Schoute's method, and we have proved that its asymptotic efficiency is 0.311, quite below the theoretical value e −1 , when the initial frame length is any finite value. In [13] we have also proposed a simple and efficient estimate, AE 2 , when using the Frame Restart property.…”