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

The combinatorial effect of an exponential backoff scheme and retransmission cutoff on the stability of frequency-hopping 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 depends 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.

[1]  Sanjiv Nanda.  Stability evaluation and design of the PRMA joint voice data system , 1994, IEEE Trans. Commun..

[2]  Raphael Rom,et al.  Multiple Access Protocols: Performance and Analysis , 1990, SIGMETRICS Perform. Evaluation Rev..

[3]  Katsumi Sakakibara,et al.  The effect of limiting the number of retransmission trials on the stability of slotted ALOHA systems , 2000, IEEE Trans. Veh. Technol..

[4]  Randolph D. Nelson,et al.  Stochastic catastrophe theory in computer performance modeling , 1987, JACM.

[5]  Sang Wu Kim.  Frequency-Hopped Spread-Spectrum Random Access with Retransmission Cutoff and Code Rate Adjustment , 1992, IEEE J. Sel. Areas Commun..

[6]  Hideo Miyahara,et al.  Analysis of Dynamic Behavior in p-Persistent CSMA/CD Using Cusp Catastrophe , 1986, Comput. Networks.

[7]  Shoichi Noguchi,et al.  On the Thrashing Cusp in Slotted Aloha Systems , 1985, IEEE Trans. Commun..

[8]  Shoichi Noguchi,et al.  Stability of a slotted ALOHA system with capture effect , 1989 .

[9]  Michael E. Woodward.  Communication and Computer Networks , 1993 .

[10]  Dipankar Raychaudhuri,et al.  Performance evaluation of slotted ALOHA with generalized retransmission backoff , 1990, IEEE Trans. Commun..

[11]  K. Sakakibara.  Performance approximation of a multi-base station slotted ALOHA for wireless LAN's , 1992 .

[12]  Katsumi Sakakibara,et al.  On the Stability of Five Types of Slotted ALOHA Systems with Capture and Multiple Packet Reception , 1998 .

[13]  Yu-Sun Liu.  Performance analysis of frequency-hop packet radio networks with generalized retransmission backoff , 2002, IEEE Trans. Wirel. Commun..

[14]  S. Wicker.  Error Control Systems for Digital Communication and Storage , 1994 .

[15]  Shoichi Noguchi,et al.  Effect of Propagation Delays on ALOHA Systems , 1986, Comput. Networks.

[16]  René Thom,et al.  Structural stability and morphogenesis , 1977, Pattern Recognit..

[17]  Sang Wu Kim.  Stabilization of Slotted ALOHA Spread-Spectrum Communication Networks , 1990, IEEE J. Sel. Areas Commun..

[18]  Martin E. Hellman,et al.  Bistable Behavior of ALOHA-Type Systems , 1975, IEEE Trans. Commun..

[19]  Brian L. Hughes,et al.  Coding and stability in frequency-hop packet radio networks , 1998, IEEE Trans. Commun..

[20]  Raphael Rom,et al.  Multiple Access Protocols: Performance and Analysis , 1990, SIGMETRICS Perform. Evaluation Rev..

[21]  Wha Sook Jeon,et al.  Performance of an exponential backoff scheme for slotted-ALOHA protocol in local wireless environment , 1995 .

[22]  David J. Aldous.  Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random access communication channels , 1987, IEEE Trans. Inf. Theory.