Formas de interrumpir la prescripción de la acción cambiaria

The quality of wireless links can change significantly and unpredictably over time and space [Eckhardt and Steenkiste, 1996]. Errors are burst like in nature due to attenuation, fading or interference radiating sources [Eckhardt and Steenkiste, 1998]. In the presence of burst errors, immediate attempts to retransmit a failed packet will result in a another failure [Willig et al., 2002]. CSMA style channel access protocols attempt to resend the packet immediately or after a slight pause based on the exponential back-off process, FIFO ordering of the packet queue is maintained. Typically an IEEE 802.11 transceiver will attempt seven retries before dropping the packet. In doing so the queue of packets for transmission is blocked leading to jitter combined with slow and variable transfer rates resulting in poor use of the channel capacity.

reactionary protocol which faced with burst errors to dynamically alter the transmission schedule in an effort to maximise throughput of packets. Each link may be considered statistically independent, since in a mobile wireless multi user environment propagation effects seriously impact on the quality of the signal received thus the signal received at any two stations is likely to be different even if they are in close proximity. Multi-path fading may result in zero signal at one location only for a different station to have a good quality signal a matter of meters away thus the definition that each point to point link is independent is reasonable. To overcome a bursty error situation the transmission queue may be reorded dynamically producing a new schedule at runtime [Balasubramanian et al., 2006] or implement a queuing strategy based on service requirements [Bhagwat et al., 1997].

As a TDMA channel access system is employed, contention and collisions can no longer be considered as causes of packet loss. When a packet loss is detected, its loss must be attributed to propagation conditions of the medium.

2.2.2.1 Characterisation of the Bursty Channel

Basic telecommunication theory is developed on the assumption that noise on communi- cation channels is additive white Gaussian noise [Haykin, 2001, Berber, 2003], bit errors are independent and the channel has no memory of previous errors. The consequence of this assumption is that there is no statistical dependence between succeeding transmitted bits [Berber, 2003].

However Kanal et al [Kanal and Sastry, 1978] states that the channel has memory, due to the impact of time varying propagation effects and suggests the use of Markov chains to model the wireless network. A Markov chain determines the state transition probabilities, based on the current state of the channel. The channel therefore has memory and the success or failure of a transmission is dependent on prior attempt outcomes. Error bursts are infrequent occurrences, a bursty channel is constant and reliable with relatively little bad bursts [Wang et al., 2007].

The use of a Markov chain to model the wireless channel and in particular the two state Markov chain model known as the Gilbert and Elliot model [Elliott, 1963] is widely accepted as modeling the wireless channel with sufficient accuracy. Others propose the use of more complex analysis with large numbers of states such as the N state Fritchman model [Fritchman, 1967], or Aldridge et al [Aldridge and Ghanbari, 1995] who adopt a three state model.

2.2.2.2 Gilbert/Elliot Channel Model

The Gilbert/Elliot Channel Model [Elliott, 1963] is a simple two state model, in which the channel is either in a good or bad state, where the bad state indicates a packet upon reception will have one or more erroneous bits. Probabilities classify the probability of moving from one state to another given the state of the previous packet e.g. probability of transition to bad given last packet was good,Pgb. Immediately before each packet is

sent the channel state is determined.

Good Bad

P_bb P_bg

P_gb P_gg

Fig. 2.3: Gilbert/Elliot Channel Model

This simplistic but useful model hides some of the detail such as the number of erroneous bits and the point at which they occur within a frame, Willig et al [Willig et al., 2002]. Figure 2.3 shows the state transition diagram of the Gilbert/Elliot Channel Model, the probabilities of transitions of the model can be described as follows:

Pgg Probability given last packet was not effected by error that the next packet received

will also be error free, good good.

Pbb Given the last packet was effected by error, probability that the channel will remain

erroneous, bad bad.

Pgb Probability given last packet was not effected by error that the next packet received

will be, good to bad.

Pbg Probability given last packet was by effected error that the next packet received

will not, bad to good.

Numerous works, Jiao et al [Jiao et al., 2002], Wang et al [Wang et al., 2007] Zorzi et al [Zorzi, 1998] and others, have expanded on the works of [Fritchman, 1967] and [Elliott, 1963]. Errors occur in bursts, errors occur due to phenomena related to dynamic real- world events, channel fading due to stations and other objects moving causing the signal strength to vary.

Aldridge et al [Aldridge and Ghanbari, 1995] identifies the need to model single bit errors in a different manner to which burst errors are modeled. A three state Markov model is proposed, this being a simple Fritchman model with error states for both the single bit error case as well as the burst error condition. A Poisson distribution is suggested to model the bursty channel condition, which for a low average λ e.g. 1 or less has a long tailed distribution which has been shown to represent the real world experience as noted by others [Otani et al., 1981, Willig et al., 2002]. An analysis is presented which requires knowledge of the average overall mean bit error rate, the mean gap between errors and the mean error burst length.

Communication is a two way process, in the case of acknowledged transmissions the loss of the data packet or the acknowledgment are treated the same as a result of lack of global knowledge, Wang et al [Wang et al., 2007] discusses the issues which arise when a transmission requires handshaking e.g. the 4 way DCF handshake in IEEE 802.11, using

a two state Markov model to represent channel conditions. While a detailed analysis is presented the values chosen to represent the channel probabilities and burst lengths are not linked to any real world experience.

2.2.2.3 Channel State Dependent Scheduling

Ci et al [Ci and Sharif, 2000] employ a simple adaptive approach to overcome packet loss by halving the fragmentation threshold upon failure to receive an acknowledgment frame. While this reduces the probability of a single bit error by sending smaller packets. The process does not overcome bursty errors, which are transient effects possibly effecting several packet transmissions. While the papers title suggests it addresses the bursty channel issue the approach adopted appears to target an environment with a high bit error rate.

Willig et al [Willig et al., 2002] performs a low level evaluation of packet loss in an industrial context. A very useful outcome is the validation of the non independence of transmissions under failure conditions, for the conditional probability of a packet loss given the previous packet was lost, Pr[packetn+1 lost|packetn lost] results in value

of 0.7179, which highlights that the use of instant retransmission of failed packets is suboptimal. The converse probability,Pr[packetn+1 success|packetn success] results in

a value of 0.9804.

Willig [Willig et al., 2002] proposes that a better understanding of the statistical properties of the errors encountered at the bit level can provide a better MAC layer. Due to the detailed analysis of the errors encountered at the physical layer, the MAC layer can be conditioned to react appropriately to channel conditions, since the presence of certain error types or patterns informs us of conditions that allow appropriate reaction - as to opposed to the typical single assumption of a collision.

Bhagwat [Bhagwat et al., 1997] argues that the typical approach of multiple retries is a poor solution when faced with bursty channel error conditions, since further transmis- sions to that station will continue to fail in the short term. This results in the blocking

of other transmissions and in poor utilisation of the bandwidth. Transmissions to other hosts are not effected, by virtue of the statistical independence of the communications link to individual hosts. A transmission queue can be implemented for each host and if a transmission fails, that queue can be marked as error prone for an interval, and packets from other queues can be sent instead. As a result, head of queue blocking is avoided.

Balasubramanian et al [Balasubramanian et al., 2006] propose a combination of three techniques to provide a real-time communication system with high reliability. A TDMA structure is combined with the ability for nodes to exchange groups of slots as to allow a host to make a retransmission attempt in the future to allow for any busrty error condition to subside and the ability to retransmit small percentages of packets if needed. This results in a robust approach with several levels of recovery, however, the schedule is managed by a master node. Stations submit requests through a contention-based access approach to obtain slots. Some flexibility and performance is lost, since a precondition exists that all messages will be available at the start of the TDMA cycle and have a deadline that expires after the end of the cycle to eliminate scheduling concerns and allow the slot exchange between stations to be undertaken without real-time deadline concerns.