2.1. WSNs with a static sink

In the early days, a typical WSN was composed of static sensor nodes and a static sink placed inside the observed region. In such a setup, the major energy consumer is the communication module of each node. In practice, multi-hop communication is required for sending data from sources to sink nodes. Consequently, the energy consumption depends on the communication distance. One way to reduce the communication distance is to deploy multiple static sinks [11] and to program each sensor node such that it routes data to the closest sink. This reduces the average path length from source to sink and hence results in smaller Ebar compared to the case of single static sink. On the other hand, reduction in Emax is also observed because routing load on the nodes located in the vicinity of a single sink also gets distributed among all the nodes located in the vicinity of multiple static sinks. The authors of [11,12] propose to deploy multiple static sinks. These static sinks partition the WSN into small sub-fields each with one static sink. By simulation it was shown that the proposed scheme leads to energy efficiency and better data delivery ratio compared to schemes based on a single sink.

However, a major problem with multiple static sinks is that one has to decide where to deploy them inside the monitored region so that the data relaying load can be balanced amongst the nodes. Vincze et al. consider this problem in [13] as an instance of the well-known “facility location problem” where for a given number of facilities and customers the optimal position for the placement of the facilities has to be identified so that all facilities are evenly burdened. If the positions of the static sinks are given, then the solution of this problem can be used for finding the optimal partitioning of the field. However, even if we assume location-optimal deployment of static sinks, the nodes close to a sink will deplete their energy rather rapidly. Adding some mobile sinks to a set of static sinks has been shown to improve the data delivery rate and to reduce energy dissipation of the sensor nodes [14].

2.1.1. Improvements for the static sink case

Some of the benefits of multiple static sinks for energy efficiency can also be realized with a single static sink by logically partitioning the sensor field at a single level or hierarchically. Such a partitioning can be either static or dynamic, and it can be predetermined or self-organized within the network. Besides the field partitioning, the selection of a cluster head in each partition is an important issue (see Fig. 1).

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Fig. 1

Basic cluster head strategies for sensor networks with a single static sink.

In order to avoid the “dying” of nodes close to the sink, partitioning of the field into subareas (clusters) has been investigated (e.g. [15,16]). Within each cluster, a cluster head is determined to which local nodes send their data. Cluster heads tend to have higher capacity than regular nodes and are responsible for forwarding collected data to the sink over single or multiple hops. Both the cluster formation and the selection of the cluster head is done in such a way that the energy dissipation during routing can be minimized [17]. This approach can also be extended to multilevel hierarchies [18]. Clusters and the hierarchical structures can either be determined once (statically) or can be changed dynamically [19]. To define a cluster, either a self-organizing algorithm can be used where each sensor independently determines whether it would like to be a cluster head or not, or a fixed regular structure of the clusters is given at the beginning of the entire process [20]. In the latter scenario, the clustering and routing overhead is reduced, but it has limited applicability. Using the concept of multilevel hierarchies, the lifetime of the WSN can be optimized as shown in [20], using an optimal number of master aggregators. Additionally, (application dependent) data aggregation (data fusion) can be performed at each cluster head before data is transferred to the sink in order to reduce the amount of data to be transmitted to the sink [16]. Potential interference of neighboring clusters can be eliminated by using CSMA-like protocols [21].

In order to extend the lifetime of the cluster head node, the task of being a cluster head can be rotated within a cluster [20]. The cluster head can be chosen either stochastically (e.g. [16]) or based on deterministic strategies [15].

Summarizing, existing approaches for WSNs with a single static sink differ primarily in the strategies for the partitioning of the sensor field and in the cluster head selection method.

3.1. Mobility model

Two basic types of state-of-the-art routing protocols will be discussed in this paper:

• (i)

  the SS protocol for a WSN based on a static sink placed at the center of the sensor field and on shortest path routing of data from the nodes towards the sink [8]; and

• (ii)

  the MS protocol for a WSN based on a mobile sink which moves along a fixed concentric circle around the center of the WSN in a stop-and-go fashion [4,8] and on shortest path routing of data from the nodes towards the current location of the sink.

During the early days of WSNs only static sinks were used and it was recognized that the strategically best position for a static sink in a WSN is the center of the field, as this leads to minimum Ebar (details will be discussed in Section 4). On the other hand, it is also known from our discussion in Section 2 that a mobile sink can adapt different types of mobility patterns in a WSN, such as random mobility, fixed mobility or controlled mobility. The question arises which type of mobility scheme performs best. In [8,31,35], this question has been investigated for a simpler network model than the one we are considering. The authors of [8,31,35] concluded that if the deployment region of a WSN is of circular shape, then the maximum lifetime of a WSN (minimum Emax) can be achieved if the radius of a circular mobility trajectory of the sink is set to $\frac{\sqrt{2}R}{2}$, where R is the radius of the WSN area. However, the authors of [31,35] do not provide much information regarding the effect of changing the radius of the mobility trajectory of the sink on Ebar. We will investigate this aspect in Section 4.

For the MS protocol it is assumed that the sink sojourn time at predetermined locations is greater than the time that it spends in motion. This helps to avoid frequent route updates in the WSN; hence increasing energy efficiency both in terms of Emax and Ebar compared to other mobile sink based routing schemes, as mentioned in Section 2.2. One method of accomplishing such a decrease in the cost for updating routing information is by programming the sink to move only when the energy level of the nodes positioned in the vicinity of the sink falls below a certain pre-defined threshold. This threshold can be adapted dynamically every time the sink arrives in order to allow for repeated round trips of the sink. This scheme could be implemented by periodically reporting residual energy levels from these nodes to the sink. As a result, the energy spent by each node for updating the routing path will be very small compared to the sum of the energy spent by each node for relaying the data packets from upstream nodes towards the sink, for idle listening and for sensing parameters of interest. In our performance analysis we neglect the energy dissipation due to routing path updates for the MS protocol, and consequently the analysis we provide gives upper bounds for the lifetime achieved with this protocol.

3.2. Network model

We consider a network composed of N stationary, identical sensor nodes that are uniformly distributed over a disk of a given radius R. We assume a two-dimensional and stationary topology for the nodes. The sink is located within the sensor field. In order to ensure end-to-end connectivity for each node (from source to sink) during the simulation run, our simulation model assumes (for practical reasons of the simulation only) that nodes have unlimited battery and buffer capacity in order to avoid node failures or packet loss due to buffer overflow during a simulation run. It is further assumed that sensor nodes do not have any location information, but that the sink can obtain its position coordinates when desired using state-of-the-art GPS equipment.

The nodes are responsible for sensing and reporting the parameters of interest with constant time intervals. We assume low cost energy constrained sensor nodes that have simple and identical transceiver sub-systems and are equipped with omni-directional antennae having common fixed communication range. The communication range of the nodes is assumed to be (very) small compared to the radius R of the WSN. As a result, data propagation from source to sink can only be achieved via multi-hop routing, i.e., the best routing paths in terms of hop counts for each node are determined during the initialization phase which comprises the construction of routing tables, etc. The initialization costs are not accounted for.

3.3. Duty cycling

In our simulation model, (abstract) time is divided into slots of constant length, corresponding to the time between two ticks of the simulation clock. In reality, the distributed nodes need to be resynchronized from time to time in order to account for clock drifts. In the simulation we do not consider the overhead caused by necessary resynchronization [36]. The length of the time slots is defined in the simulator and is not representative for the real time. In a real world scenario the time taken by a node to transmit or receive a message can vary from a few microseconds to tens of milliseconds depending on the size of a packet, the MAC protocol, etc. In our simulation we assume that the length of a time slot is determined by the maximum amount of time needed by any of these actions, i.e., any action can be performed in a single time slot.

In some types of applications (which also motivate the investigations in this paper) sensor nodes spend a big fraction of their total lifetime in idle mode (doing nothing), for example, in sensing applications where sensing does not happen very frequently. Therefore, the concept of low duty cycling has been introduced, which achieves higher energy efficiency (i.e., reduces Emax and Ebar). In this case, particular modules of the sensor are turned off when not needed, i.e., energy can be saved by reducing the active time (or duty cycles) of various components of the node. This defines various operational modes for the sensor nodes. For example, Wang et al. proposed [6] four different operating modes for a sensor node: node on-duty (the node is in active state), sensing unit on-duty (only sensing and processing unit are on), transceiver unit on-duty (only transceiver and processing unit are on), and off-duty (sensing, processing unit and transceiver units are off, only a timer is running to switch on the node after some time interval).

In our simulation, we distinguish two operational modes for a node in every time slot: sleep (off-duty) and active (on-duty). In sleep mode a sensor node is in the state with the lowest energy consumption and does not carry out any task – it neither senses or processes any data nor transmits or receives data packets. After the sleep period, the node is woken up by a timer and changes into active mode, where it may either actively participate in data routing (transmitting or receiving a message) or it may be idle.

The scheduled periods of activity and sleep are modeled deterministically according to the parameters p and q (0 < p, q < 1), respectively. For floor(1/q + 0.5) time slots the node is active, and this active phase is followed by a period of floor(1/p + 0.5) time slots that the node is asleep. In general, p and q can take any value between 0 and 1 independently of each other. The higher p and q, the more frequently the node transits from active to sleep mode and vice versa. In our simulations we always choose these parameters such that p + q = 1, i.e., the value of p (the “duty cycle value”) determines the fraction of time during which the node is active. For example, to achieve 10% duty cycling, i.e., the node is 10% of the time active, p and q are set to 0.1 and 0.9, respectively.

In order to handle heavy routing load, sensor nodes sometimes need to extend their active phase beyond the scheduled duration. This is accomplished by implementing the following condition: a node can transit from active to sleep mode only if its data buffer is empty. Thus, a sensor node extends its scheduled active phase (specified number of time slots) until all the data has been forwarded to one of the next-hop neighboring nodes (extended active phase). Thus, each actual active phase of a sensor can be divided into two parts: the scheduled part and the extended active phase. The number of time slots in extended active mode depends on the number of packets in the buffer and on how long it takes until a channel to a suitable forwarding node becomes available. As a result, even with low duty cycling of the nodes, data eventually gets forwarded towards the sink. However, in order to achieve energy efficiency and to switch to sleep mode as quickly as possible, a sensor node turns its sensing unit off during the extended active phase and neither senses data nor accepts relaying data. Depending on the sampling frequency, this may cause data loss in reality.

3.4. Energy model

In scheduled active mode or in extended active mode a sensor node can only be in one of the following operational modes: transmit, receive or idle. In transmitting/receiving mode the energy dissipation is due to transceiver electronics. In idle mode the energy dissipation of the node is only due to local data processing activity. In extended active mode, a node is only idle if it cannot forward any data packet from its buffer since all its neighbors are busy. In each active time slot, exactly one data packet can be transmitted or received, and we assume that sending and receiving a data packet takes the same amount of time. In summary, in a single (extended) active time slot the following actions can happen: (i) in active mode: generating/sensing plus forwarding a packet OR (ii) in active mode: receiving a packet to be relayed from a different node OR (iii) in active or extended active mode: forwarding a packet from the local buffer which has been received from a different node or from the own sensing unit in a previous time slot during the current active period.

We model the CSMA/CA (carrier sense multiple access/collision avoidance) protocol [21] at the MAC layer with the assumption that each task can be finished within a fixed time slot. Therefore, in any given time slot a pair of nodes can perform a successful communication only if none of their neighboring nodes are allowed to transmit. This MAC protocol is simulated as follows: At the start of each active time slot all the sensors can potentially transmit or receive or they are idle. In order to resolve channel contention issues, random permutations of the indices 1, 2 …, N associated with the sensor nodes are generated. Each sensor node is then examined based on the order resulting from the permutation. If a sensor node is able to transmit its data in the current time slot it is allowed to do so. However, no other node within the communication range of the transmitting/receiving node is allowed to transmit in the current time slot. Thus, at the start of each time slot transmissions are chosen randomly and fairly.

In a duty cycled sensor field many factors play a crucial role in identifying the total energy dissipation by any node in a WSN. Our model distinguishes four major energy consuming tasks as shown in Fig. 6. The energy consumed by the node to stay in idle active mode for one time slot (Eidle), the energy consumed by the node for transmitting/receiving one message (Etx/rx), the energy consumed in sleep mode per time slot (Esleep), and the energy consumed by a node to transit from sleep to active mode (Etrans). Since we assume that sensor nodes have a fixed communication range and exchange messages with fixed size, the energy dissipation during each message transmission and reception by a node is also fixed. The energy consumed in the transition from active to sleep mode is assumed to be zero. Since the energy cost of sensing the environment (sensor) is negligible compared to Etx/rx and Eidle we have ignored it in our simulations. Moreover, we do not consider the energy consumption of any local processing activities in our model. Depending on channel availability a node can generate and transmit its own packet in a single time slot. However, as mentioned above there is no sensing in sleep mode and in extended active mode. The total energy dissipation of a node is the sum of Eidle, Etx/rx, Etrans and Esleep.

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Fig. 6

Energy dissipation map of a node.

4.1. General considerations – a gedankenexperiment

Let us first focus on the influence of the mobility radius of the sink. Since we consider shortest path routing to the sink, all data to be transferred from a certain sector of the field has to pass through a critical area around the center of the sensor field independently of the position of the sink (see Fig. 8). For a fixed critical region at the center, we expect its load to increase when the sink is positioned closer to the center and to decrease when the sink moves away from the center. On the other hand, moving the sink away from the center will increase the load to be handled by some nodes in the vicinity of the sink, as explained in the following.

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Fig. 8

Geometrical model for analyzing the influence of the mobility radius on energy dissipation.

When the sink has a larger mobility radius, the path length which the data has to travel until it reaches the sink varies more – for the data originating from nodes between the sink and the closest boundary the path length decreases, whereas for the data originating from nodes on the other side of the center of the network the path length increases. On a longer path data has a higher probability for encountering congestion, which may cause more extended active periods in the nodes and thus lead to a higher total energy dissipation of the affected nodes. Moreover, a larger mobility radius leads to a stronger funneling effect, i.e., the area in the neighborhood of the sink through which data from far away has to pass becomes smaller for larger mobility radius, because the corresponding angle becomes narrower. Once the sink moves away too far from the center, much more load comes from the central area than from the periphery, which also results in more congestion and increased energy dissipation along the longer paths.

Nevertheless, sink mobility and a larger mobility radius also have a positive influence on the energy dissipation. A mobile sink collects data at several locations, and the increased congestion is effectively divided by the number of stops of the sink since the mobile sink remains at each position for a shorter time than the static sink at the center. Moreover, as mentioned before, the larger the mobility radius, the less relaying load we expect in a fixed region around the center of the WSN.

So far, we have summarized some basic considerations. Next, we investigate the situation more formally with a simple geometrical model in order to verify this basic understanding of the influence of the sink’s mobility radius on the energy consumption.

4.2. Geometrical model

Let us assume that the sink is positioned at a point P₁ at a distance y = αR from the center of the sensor field with radius R. We consider a circle of radius z around the sink representing the neighboring nodes of the sink and a circle of radius x = βR around the center of the sensor field representing the critical central region (see Fig. 8) with α, β  ∈  (0, 1). All data in the corresponding sector from the opposite side of the sensor field has to pass through this circle around the center.

The area A(P₁ P₂ P₃) can be computed by summing the area of the sector with angle $\gamma =360-2\text{arccos}\beta -2\text{arccos}\frac{\beta }{\alpha }$ and twice the area of the triangle formed by P₁, P₃ and the center of the sensor field: $A=R^2\pi \frac{y}{360}+R^2\beta [\sqrt{1-{\beta }^2}+\sqrt{{\alpha }^2-{\beta }^2}]$. The corresponding arc c of the circle around P₁ is given as $c=\frac{2\pi z}{180}\text{arcsin}\frac{\beta }{\alpha }$.

With these quantities, we can quantify the data load which has to pass on average through one node along the arc c as a function of the distance α of the sink from the center of the sensor field:

For given R, β, and z this load per node increases monotonically and superlinearly with the distance α of the sink from the center of the sensor field. Moreover, the load $\overline{A}$ going through the critical region around the center of the sensor field is given by summing the area to the right of the critical region and the area of the critical region itself:

For given R and β, the load $\overline{A}$ going through the critical region decreases monotonically for increasing α. This decrease is stronger for small α and becomes weaker as α increases.

Summarizing, the geometrical model leads to the following observations:

• (i)

  On the one hand, the load per node in the close neighborhood of the sink increases monotonically with increasing mobility radius of the sink. From this fact, we expect more congestion close to the sink and thus higher Emax for larger mobility radius of the sink.

• (ii)

  On the other hand, the load to be handled by the region around the center of the sensor field decreases monotonically with increasing mobility radius of the sink. From this fact, we expect less congestion close to the center of the field and thus lower Emax for larger mobility radius of the sink.

The investigations so far clearly demonstrate that the duty cycling value and the mobility radius of the sink have a very strong influence on the contention and thus on the energy dissipation of the WSN. Since some of the effects work in opposite directions, it remains to be explored which of them are stronger. Moreover, we want to quantify the energy dissipation of the WSN for various combinations of duty cycling value and mobility radius of the sink. For this purpose, we summarize and discuss the results of corresponding simulation experiments in the following and compare them to the analytical insights from this section.

This work was partially supported by the Austrian Science Fund (FWF): S10608 (NFN SISE).