Effect of exponential backoff scheme and retransmission cutoff on the stability of frequency-hopping slotted ALOHA systems

Abstract

The combinatorial effect of an exponential backoff scheme and retransmission cutoff on the stability of frequencyhopping slotted ALOHA systems with finite population is investigated in terms of the catastrophe theory. In the systems, the packet retransmission probabilities are geometrically distributed with respect to the number of experienced unsuccessful transmissions and a packet will be discarded after a certain number of unsuccessful transmissions. Expressions which should be satisfied at equilibrium points are first derived. Then, the cusp point and the bifurcation sets are numerically evaluated. Finally, we visualize how the exponential backoff scheme and retransmission cutoff effect on the bistable region. Numerical results show that the exponential backoff scheme can mitigate bistable behavior of the system with finite population. However, it is also revealed that there is asymptotically no effect of the exponential backoff scheme on the stability of the system with infinite population.

A Retransmission Cut-Off Random Access Protocol with Multi-packet Reception Capability for Wireless Networks

“…We have used Eqs. (6) and (10) to draw the Figure 6. This figure also shows that the finite number of retransmission trials improves the packet dropping probability at lower input traffic, which is a similar result as presented in [8,11,19].…”

“…Stability of frequency-hopped spread-spectrum random access (Slotted ALOHA) is studied in [10] considering the combined effect of exponential back-off and the number of retransmission trials. The stability and the maximum throughput of retransmission cut-off Slotted ALOHA can also be increased using multiple power levels [11].…”

“…All the above mentioned retransmission cut-off Slotted ALOHA protocols [1][2][3][4][5][6][7][8][9][10][11][12][13] have assumed the single packet reception capability. That is, a maximum of one packet can be received successfully per time slot in the receiving side.…”

Design and Analysis of Backoff Algorithms for Random Access Channels in UMTS-LTE and IEEE 802.16 Systems

“…It has been shown that system stability can be achieved by controlling the retry limit and the channel coding rate that affects the transmission success rate of a packet. Sakakibara et al examined the exponential backoff (EB) algorithm with retry limit in slotted (S)-ALOHA systems [4] and frequency-hopped S-ALOHA systems [5], respectively. Additionally, Liu [6] examined an EB algorithm in frequency-hopped S-ALOHA systems under a finite population with unsaturated traffic (FP/UST) model.…”

“…Similarly, Falla et al [8], Vu et al [9], and Chuck et al [10] examined window-based BEB with retry limit for an IEEE 802.16 system under FP/ST. It should be noted that the S-ALOHA system under the FP/ST model always operates in a stable but inefficient region [4], [5]. In contrast to [7]- [10] with the FP/ST model, in this paper, we examine the performance of UB and BEB algorithms with retry limit under a more realistic FP/UST model and discuss their stability.…”