Performance analysis of MAC protocols in wireless line networks using statistical mechanics

Abstract

Abstract-In this paper we consider the application of the Ising model from statistical mechanics to model interactions among interfering stations in a wireless network with a line topology. Each station employs a medium access control (MAC) protocol such that it decides to transmit or not depending on the states of its nearest neighbors and itself in the previous time slot. We use the Ising model to demonstrate how the interactions between neighboring stations affect the one-hop throughput of the network and to optimize the underlying MAC protocol. Both the cases of single-packet and multipacket reception are considered. For single-packet reception, the throughput achieved by an optimized protocol is shown to be 15.8% better than that achieved by slotted ALOHA. In the multipacket reception case, the MAC protocol achieves the same throughput as TDMA, which doubles the throughput of slotted ALOHA.

Medium access control via nearest-neighbor interactions for regular wireless networks

“…Therefore, it may be necessary to assume each station can only be in one of the two states: 'transmit' or 'idle.' In this aspect, it has been recognized in [1] and [2] that the resulting interactions among stations are similar to that found in the Ising model in statistical mechanics [3], [4]. Using the Ising model, we design a MAC protocol that can achieve a throughput of 3/4 in square networks.…”

“…Following similar arguments as in the proof of Theorem 2, these are the only recurrent configurations, and the stationary distribution resulting from these dynamics is also given by (2).…”

“…Each spin can be in 'up' or 'down' state, which is affected by the external magnetic field acting on it and its interactions with neighboring spins. We can use the Ising model to model regular wireless networks, such that the spins represent the stations, and E = {+1, −1}, where +1 means transmitting or 'up', and −1 means idle or 'down' [2].…”

“…2 Stations then choose their current states based only on the previous states of their neighbors and themselves. Precisely, we are interested in MAC protocols for which X = {X(t)} t∈N is a Markov Chain of Markov Fields (MCMF) [5], i.e., a process for which…”

Exploiting peer-to-peer state exchange for distributed medium access control

“…For one-and two-dimensional regular networks with links between nearest neighbors only, distributed, adaptive, selfstabilizing MAC protocols are introduced in [4] and [5], respectively. The technique is to divide time into periodic cycles, where each cycle is divided into slots.…”