Justification for Exponential Distribution for Active/Sleep

Two main approaches used for implementation of Sleep/Active power saving in WSN include software and hardware schemes [Van Dam and Langendoen, 2003],[Anastasi et al., 2009]. In the software-based scheme, the low duty cycle is represented as a periodic wake-up scheme where a node routinely switches be- tween active communication epoch and power efficient sleep state. In hardware- based approaches, pure asynchronous rendezvous schemes are employed. These approaches allow sensors to remain within the sleep state most of the time, but only waking up when probed by the neighbours. In this arrangement, nodes no longer use duty cycling but are instead equipped with a low-power wake-up re- ceiver module which continuously monitors the channel. In order to communicate with a neighbour, a node first sends a wake-up call. After successful reception and decoding of the wake-up call the wake-up receiver sends an interrupt signal to the node itself, which then fires up its primary radio to engage in efficient high speed communication with the sender. After the transmission, both nodes activate their wake-up receivers, resuming their usual activities and going back to sleep mode. Though this approach promises good energy saving in the long run, existing sensor nodes only have one radio system hence they may require hard- ware alterations, which may be expensive. The extra hardware also consumes

additional energy to run the supplementary circuitry [Gu and Stankovic,2005].

In another study [Anastasi et al., 2009], an Adaptive Staggered sLEEp Proto-

col (ASLEEP) for efficient power management in wireless sensor networks was proposed for periodic data-acquisition applications. This protocol dynamically adjusts the sleep schedules of the nodes to match the network demands even in time-varying operating conditions. Moreover, it does not require a-priori knowl- edge of the network topology or traffic pattern. The novelty of this approach is the fact that it overrides the use of fixed duty cycling and implements an adap- tive duty cycling scheme that automatically adjusts the Sleep/Wakeup periods depending on the observed operating conditions.

dependent upon the traffic intensity, an appropriate choice is necessary to regulate idling times. In addition, using ASLEEP protocol and hardware wake-up receivers is preferred for conserving node energy consumption. In the two approaches, timings for sleep/active periods are not predetermined but left to depend upon network traffic and operation dynamics.

While implementing the two schemes; hardware wake-up receivers and ASLEEP protocol, it can be observed that the distribution of sleep/active times is a con- tinuous process that follows i.i.d random variables. They do not depend upon the knowledge of the present or past sleep/active times, but their arrivals are purely dependent on present network operation dynamics. For tractability, it is possible to assume without loss of generality that both active and sleep times are expo- nentially distributed. In these study, hardware wake-up receivers and software, ASLEEP schemes are considered for modelling the distribution of sleep/active schedules. In the case of hardware, the nodes enter sleep mode after serving the last packet and wake up on arrival of a new data packet. However, for ASLEEP, sleep and active times are assumed exponentially distributed with random vari- ables having a mean values 1/α and 1/β respectively as explained above. The models developed for this study are based upon earlier studies in [Chiasserini and Garetto, 2006], [Zhang and Li, 2012]. The novelty of our model is the inclusion of the failed states and consideration of the bounded queues.

Considering the use of the two possible sleeping mechanisms; software ASLEEP and hardware wake-up- receivers, two models were developed.

1. Transition into sleep mode at the completion of last service and wake up at packet arrival. In this case, beta and alpha are not required as the arrival and service end times of the packets are used.

2. Duty cycling using ASLEEP protocol. In this scenario, beta and alpha play a major role in determining the required operation periods while in the various states.

In the first case above, nothing else is required except the distribution of inter- arrival and service times. However, in the second case, the events leading to sleep and active operation states are considered. These include:

1. Active State

While operating normaly, the CH schedules a time in the future when it will go into sleep mode. Conversely, when this period ends, the following are considered for determining the next action to take, which may either reduce or increase the value of alpha;

a. If there are no more packets to be served, then the CH transits into sleep mode

b. If there are packets left to be served, the CH enters into the reduced active state (N). In this state, the CH stops receiving incoming data packets. Nevertheless, it continues to serve the remaining data packets. As soon as the service for the last packet is completed, the CH enters sleep mode (S). During sleep mode, the CH does not involve in any activity.

c. During active operation, if the CH has no more requests in the system to serve, it will get into the idle state for a period after which it will automatically enter sleep mode if no more data packets arrive.

2. Sleep State

Each time the CH goes into sleep mode, it re-schedules a time in the future when it will transit back to active mode. The sleep time is assumed expo- nentially distributed with rate β. At the end of the sleep period, the CH checks the availability of data packets, and changes state to active mode otherwise it prolongs sleep state in order to save energy. The dynamic change of Sleep/Active periods based on traffic conditions can therefore be used to determine the parameter β.

6.3

Model Description

In order to build the models, the network scenario presented in Figure 4.1 is

considered. The queue model also remains the same as presented in section 5.3.

models are proposed as an advancement to the earlier model presented in Figure

5.1. The proposed models are presented below in line with the sleep scheduling

scheme employed.