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James Kay and Jeff Frolik. University of Vermont [email protected], [email protected]. Derandomization of Wireless Channel Access using Automata in Sensor.
Derandomization of Wireless Channel Access using Automata in Sensor Networks James Kay and Jeff Frolik University of Vermont [email protected], [email protected]

Abstract Low cost radio transceivers have enabled the deployment of wireless sensor networks (WSNs) using inexpensive and energy constrained nodes. Real time monitoring and control systems using WSNs often seek to maintain a given, but possibly varying spatial and/or temporal, sensing resolution. This control typically consists of both node participation and communication channel access (MAC). This paper proposes integrating both functions into a simple automaton achieving three benefits. First, control of the desired number of transmitting sensors in a given time period is maintained with small variance around the desired mean. Second, channel efficiency (60%) exceeds slotted-ALOHA without explicit synchronization of or idle listening by nodes. Third, the technique implicitly limits the channel load at the maximum supported level with no increase in collisions, and no additional overhead when the desired number of transmitting sensors exceeds the supported capacity.

1. Introduction The advent of low cost radio transceivers has enabled the realization of large-scale networks consisting of remote sensors and actuators. The promise of these distributed systems is beginning to be realized in such applications as agricultural and structural health monitoring [1]. However, barriers exist for the wide scale adoption of these wireless sensor networks (WSNs) due to a combination of constraints on the network nodes. These challenges are application dependant and require system tradeoffs between various figures of merit including energy usage, channel efficiency, data latency and data synchronization. These tradeoffs have resulted in significant work on, for example, new routing and medium access protocol designs specific to WSNs.

Key among the constraints on WSNs is energy usage, since the applications envisioned typically require nodes to be deployed remotely, without connection to an external power source. This constraint has resulted in energy being provided from batteries, or through energy harvesting from the environment both of which have significant power and energy limitations. These limitations have resulted in many proposed techniques to conserve energy in WSNs [2-6]. The majority of these techniques exploit the large difference in power usage by a node between its active communication state and its inactive state. Current electronics support these methods by designs which allow circuitry to be placed in a low power ‘sleep’ mode when its function is not required. However, when active, the energy use will be dictated by the node’s operational state; i.e., transmitting, receiving, data acquisition and idle. Of these states, the energy usage is typically greatest during communication. Many applications use communication distances resulting in equivalent receive and transmit communication costs. As such, there is a need to reduce both transmit and receive activity as much as possible to conserve energy. In addition to effectively use the radio transceiver, sensor nodes should be simple in design to allow the use of the minimal circuitry, and consequently energy. Demands on processing by network protocols should be minimal to achieve this goal. Once nodes become extremely simple it then becomes feasible to address system reliability and availability requirements by over-deploying sensor nodes resulting in additional benefits (e.g., robustness with respect to sensor loss, variable resolution). By over-deployment we mean populating a space with more than the minimal number of sensors required to meet a requisite spatial and/or temporal resolution; metrics that have been proposed as measures for WSN quality of service (QoS) [7, 8]. This measure of QoS is consistent with input requirements for classical real time monitoring and control systems which often require uniform data

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sampling rates from a number of fixed sensor positions in order to achieve the system functionality. These classical systems typically are interconnected with wires for transfer of information and power. These fixed position wired systems do not generally have the power constraints of wireless nodes, which are normally battery powered, and thus tradeoffs between power and wired channel access are feasible. However, with wireless systems it is extremely important to implement controls that conserve energy while still ensuring the required level of system performance. For example, the sensors’ access to the communication channel must be controlled to ensure data throughput with minimal packet loss (which can be considered wasted energy). Medium access controls (MACs) for the communication channel serve this purpose. Typically, wireless systems do not have the ability to trade off power for channel access efficiency, and in addition are likely to experience loss of nodes due to energy drain or the harshness of the environment in which they are deployed. As mentioned previously, over-deployment of sensing nodes is one solution to this problem. This paper integrates node participation control and MAC for over deployed wireless systems into a single simple automaton that achieves the following benefits: ƒ

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Control, with low variance, of the number of nodes participating (i.e., transmitting data) in a given time period. The variance around the mean control point is small resulting in good control of spatial and temporal resolution for randomly deployed sensing nodes. Channel efficiency, ~60%, exceeding slotted ALOHA without explicit synchronization, or idle listening. This results in low wasted energy due to collisions. Graceful handling of loads in excess of the supported capacity. The network limits the load at the maximum supported level with no increase in collisions, and no additional overhead. Collisions, even at the maximum load average less than 2% of transmissions. Energy usage less than carrier sense multiple access (CSMA) methods due to the lack of idle listening.

These benefits result from effectively ‘derandomizing’ the medium access, without the requirement for explicit synchronization between sensor nodes. The technique to be presented uses finite state automata to quickly converge on a set of transmit times in a communication frame that significantly reduce the probability of transmission

collisions over schemes that select the transmission times at random (i.e., ALOHA [9]). The motivation to attempt derandomization came from [10] which analyzed a scheduled persistence derandomization technique for CSMA systems. The technique presented in this paper differs in that we eliminate the need for carrier sense, and use automata to select transmit slots rather than a scheduled persistence technique. The remainder of this paper is organized as follows. First a description of the proposed automaton and previous work on its performance is presented. This is followed by a discussion of the development of a simple energy efficient sensor control and MAC protocol for use by the proposed WSN. We then present the performance of the proposed control technique against a baseline Bernoulli process with ALOHA MAC, and conclude by discussing future work.

2. Previous work Herein, we build upon the ACK strategy proposed in [8] and analyzed in [11, 12] for control of the number of active sensors in a single-hop cluster. This strategy implements the sensor nodes as finite state automata. In the following description we denote the total number of sensor nodes by N, the desired number of transmitting sensors by Q0 and the number of possible node automaton states by G. An example of the automaton used in this technique is shown in Fig. 1 for the case G=4. REWARD

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Figure 1. ACK feedback automaton In this technique one sensor is designated as a clusterhead and receives information from all other sensors in the network. Each of the remaining sensor nodes implements a finite state automaton (Fig. 1) which controls when the node becomes active and transmits. This decision is based upon a transmit probability, Ti, assigned to each automaton state and a random number between 0 and 1 generated independently by each sensor every epoch. If the random number generated by a sensor is less than the transmit probability for its current state, Ti, the node

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3. Performance and special cases [12] showed the ability of this technique to provide robust control of the desired number of active sensors with very little variance. This control does not require a priori knowledge of the desired number of active sensors, Q0, and the network was shown to be robust with respect to the loss or addition of sensors, as well as the control point Q0. This control methodology was compared to the limiting case of a single state automaton, G=1, with transmit probability T1=Q0/N, and was shown to have significantly lower variance around the control point. Note that in this G=1 case the network would require a priori knowledge of N, which may not be known in general and may change as sensors die off or are added to the network. This special case is a Bernoulli process consisting of Binomial trials and can be shown to approach [13] a Poisson process with arrival rate λ= Q0/N, as the number of sensors, N, becomes large. This case is of interest because many classical MAC analyses (e.g., ALOHA) and network theory assume a Poisson arrival process. Fig. 2 presents analytic results for the probability density function, pdf, for the number of nodes active

in an epoch. In this example, N=7, with Q0=4. We compare the ACK strategy with equivalent Bernoulli and Poisson processes. For this example, the ACK protocol utilizes G=3 automaton states, and the probability of transmission for each state is T1=0.00014, T2=0.7350, T3=0.999999. Fig. 2 was generated from the analytic models presented in [11, 12] and the well know pdfs for Bernoulli and Poisson processes. 1 Automaton Bernoulli Poisson

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becomes active and transmits. Otherwise the node remains in the low power idle state or sleeps until the next epoch. The clusterhead acknowledges only the transmitting sensors once each epoch with a common reward/punish command. The decision to reward/punish is determined at the clusterhead. Should the desired performance be less than Q0, the common command is a reward; otherwise, it is a punish. With a reward command, transmitting nodes will transition their state to the right in Fig. 1. With a punish, they the transition to the left. Note that sensors that did not transmit in an epoch do not change their state, do not need to listen for an acknowledgement/command, and thus may remain in a low power state. Also note the clusterhead has no knowledge of any node’s state. Nodes are assumed identical in regards to the amount and rate they supply data to the clusterhead, and that the system over deploys sensor nodes so that only a fraction need be active at a given time to achieve the desired spatial or temporal resolution. For the methods presented herein, we also assume that the communication channel allows perfect reception of transmitted messages. Finally, while each sensor node is assumed to have a local clock, these clocks do not need to be synchronized with one another.

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Figure 2. Comparison of pdf for the number of transmitting sensors for the ACK protocol vs. Bernoulli and Poisson processes for N=7 and Q0=4. Note that the ACK protocol has a very high probability of Q0 sensors transmitting, and correspondingly has very little variance around the control point. Specifically, the variance around the control point is 0.0040 for the ACK protocol, 1.714 for the Bernoulli process and 4.0 for the Poisson process. The importance of this result is to illustrate that the ACK protocol presents a different traffic load pattern in comparison to traditional systems that assume a Poisson pattern. The underlying phenomenon for the ACK system is that the network presents data at a uniform rate which is representative of how many sensor systems will be expected to operate. We contend the requirement of many control systems is to receive data at a uniform rate rather than the less uniform and more random data rates as expected in a computer network serving multiple users. An example of an application utilizing a uniform data rate is a structural health monitoring system where a number of strain sensors are sampled at a uniform rate to provide information on the state of a structure. Fig. 3 illustrates the dynamic performance of the ACK technique under large changes in N. Note that although there is a transient during the step changes in N, the network quickly returns to the commanded value. Again this performance is achieved without the clusterhead or the nodes needing to know the value of

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N. This is not true for the Bernoulli case, where some means would be required to communicate the value of Q0/N to all nodes each time N changed. This requirement is particular constraining in comparison to the ACK protocol where non-transmitting sensors can be in a truly low power state with no requirement to listen for the clusterhead.

In the following sections we will develop an appropriate MAC for the ACK protocol that addresses the assumptions and limitations listed above. Although addressing these issues degrades the variance somewhat, the underlying structure is shown to allow derandomization of the channel access, providing significant channel efficiency and energy usage benefits.

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Figure 3. The expected value of the number of transmitting sensors E(Q), vs. Epoch during step changes in N for: Q0=40, G=5, T1=0.045, T2=0.76, T3=0.95, T4=0.999, T5=0.99999 While these results are promising, they do not fully represent practical cases because of the following assumptions and limitations: ƒ The analysis assumed that there were no collisions (i.e. messages whose time of transmission overlap) between messages transmitted by the various nodes. This approximation only holds for low channel utilization (e.g.