Modeling Mobility in Cooperative Ad Hoc Networks
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Abstract
This paper addresses issues concerned with design and managing of mobile ad hoc networks. We focus on self-organizing, cooperative and coherent networks that enable a continuous communication with a central decision unit and adopt to changes in an unknown environment to achieve a given goal. In general, it is very difficult to model a motion of nodes of a real-life ad hoc network. However, mobility modeling is a critical element that has great influence on the performance characteristics of a cooperative system. In this paper we investigate a novel approach to cooperative and fully connected networks design. We present an algorithm for efficient calculating of motion trajectories of wireless devices. Our computing scheme adopts two techniques, the concept of an artificial potential field and the concept of a particle-based mobility. The utility and efficiency of the proposed approach has been justified through simulation experiments. The results of presented case studies show a wide range of applications of our method starting from simple to more complex ad hoc networks.
Keywords
MANET Ad hoc networks Coherent networks Mobility models Potential function1 Introduction
A mobile ad hoc network (MANET) comprises a group of self-organizing wireless devices that can play the roles of routers and terminals [4,16]. Each device can run applications and participate in transferring data to recipients within its radio range. The devices can dynamically change their geographical locations in a workspce. Due to limited power of the transceiver direct communication between each pair of devices is not usually possible. In ad hoc networks no fixed network infrastructure components are required for communication, no device has a specific location assigned, and there is no central network management unit. The dynamic changes in network infrastructure allow creating unique topologies and enable the dynamic adjustment of individual nodes to the current network structure. Specific configurations are usually instantaneous and operate for a short time in order to meet the current requirements.
The objectives of many network systems are: (i) a comprehensive monitoring of a workspace, (ii) a tracking of moving objects, (iii) a providing network infrastructure to tackle emergency incidents and support evacuation and emergency systems, etc. To meet these requirements a permanent connection between data sources (network nodes) and data sink (base station) is required.
The main aim of this paper is to present a novel approach to motion planning of a set of wireless devices that form a cooperative and coherent network. Our mobility model can be implemented in indoor and outdoor scenarios. The described algorithm for motion patterns calculation is based on a concept of a potential field and a definition of an artificial potential function commonly used in robots navigation [5], and a particle-based mobility scheme [14,16].
The paper is organized as follows. In Section 3 we investigate and discuss the directions to mobility modeling for ad hoc networks and selected mobility models. In Section 3 we provide a formal statement of our model and in Section 3 we describe an algorithm of the motion patterns calculation. In Section 3 we focus on the design and development of a cooperative and well connected network using our mobility model. In Section 3, we describe potential applications of our algorithm. We conclude this paper in Section 3.
2 Introduction to mobility models
Mobility models describe the movement of actors in a workspace, i.e., how their location, velocity and acceleration change over time. The main problem addressed in many recent publications on MANETs is a high impact of the mobility of network devices on the overall network performance and connectivity [2,4,6-10]. Therefore, the mobility models should resemble the real life movements of actors. Moreover, they should be appropriately reflected in simulations, which can be used to support design and management of an ad hoc network. A number of less and more detailed and accuracy mobility models have been introduced, and adopted in the design and development of mobile ad hoc systems. The survey and discussion of the taxonomies of mobility models and main directions to mobility modeling are provided in [3] and [16]. Generally, the existing mobility models can be classified into two following categories, namely syntactic models: analytical random-motion model - a discrete implementation of Brownian-like motion with randomly generated destination point and velocity, and motion traces models that require the accurate information about mobility patters (i.e., positions of nodes in time).
Bai et al. [3] classify the mobility models based on their basic mobility characteristics into: random models, models with temporal dependency, models with spatial dependency and models with geographical restrictions. The alternative classification is proposed by Roy in [16]. He distinguishes the following groups of models: individual mobility models, group mobility models, autoregressive mobility models, non-recurrent mobility models, virtual game-driven mobility models, flocking and swarm mobility models and social-based mobility models.
The concept of a potential function is used in particle-based mobility schemes, where network node considered as a self-driven moving particle is characterized by a sum of forces, describing its desire to move to the target and avoiding collisions with other nodes and obstacles. The details concerned with mobility of particles modeling are described in [1,18].
Various forms of potential functions are introduced in literature, [5,16]. The inspiration comes from classical and quantum mechanics. Many of these functions can be computed on-line but they still suffer from one shortcoming, i.e., they often introduce oscillations into the motion patterns, and these oscillations are hard to eliminate.
3 Group mobility model for coherent and cooperative network
We have developed a group mobility model that resembles a collision-free movement of a group of mobile wireless devices. The preliminary version of this technique was described in [11]. In this section we present the formulation of our model. We start from the description of the workspace and all objects operating in this workspace.
3.1 Network system and workspace definition
Both network nodes and obstacles are solid bodies with any shape. In order to simplify the description of the system we model each network node D _{ i } and obstacle O _{ i } by a polyhedron with a set of vertices \(P^{i} = \left \{\mathbf {p}^{i}_{1},...,\mathbf {p}_{L_{i}}^{i}\right \}\). In case of the object type D _{ i } (network node) we define one additional point reference point c ^{ i }. The detailed description of the objects operating in W is provided in the next section.
3.2 Network system objects definition
As previously mentioned we model D _{ i } and O _{ i } by a polyhedron in which a given object is enclosed. The points \(\mathbf {p}^{i}_{1},...,\mathbf {p}_{L_{i}}^{i}\), (p ^{ i } = [x ^{ i },y ^{ i },z ^{ i }]) in Fig. 2 denote the vertices of the polyhedron. The number of these points is arbitrary determined by the modeler. The point c ^{ i } = [x ^{ i },y ^{ i },z ^{ i }] denotes the reference point – the location of an antena or the GPS unit. This point is defined only for network nodes.
3.3 Group mobility model formulation
In the reference position of the i-th node \(d_{g}^{i} = \hat {d}_{g}^{i}\) we have an unstable equilibrium (\(V_{g}^{i} \approx 0\)). Such configuration is the optimal one with respect to all network goals.
The problem defined by the Eqs.(13)–(16) has to be solved for all devices D _{ i }, i = 1,…,N.
4 Algorithm for motion trajectory calculation
- 1.
Reference distance estimation: Estimation of the reference distances \(\hat {d}^{i}_{g}\), g = 1,…,J _{ i } between the node D _{ i } and all its goals from the set \(S_{G}^{i}\).
- 2.
Displacement calculation: Calculation of a new position of the device D _{ i } solving the optimization problem (13)–(16).
4.1 Reference distance estimation
Our objective is to develop a wireless network that enables the continuous communication with the base station. In such application the goal for each network node is to keep continuous connection with the neighboring nodes. Hence, the targets (goals defined in our model) for each node are neighboring nodes. We assume that all network nodes are equipped with the radio transceivers, and the RSSI can be used to estimate inter-node distances. To enable the communication with the base station the signal strength received by neighboring nodes should exceed a receiver sensitivity P ^{ s }. The well known in statistics Q-function may be used to determine the probability that the received signal level will exceed P ^{ s }. The Q-function is defined as follows
The value of X _{ σ } and N in (23) depend on the workspace conditions, and can be calculated using linear regression such that the difference between the measured and estimated path losses PL is minimized over a wide range of measurement locations. The values of N calculated for various environments are presented in [15]. Sample values are: free space: n = 2, urban area cellular radio: n = 2.7−3.5, shadowed urban cellular radio: n = 3−5, in building line-of-sight: n = 1.6−1.8, obstructed in building: n = 4−6.
4.2 Displacement calculation
- 1.
Displacement of the reference point c ^{ i } (step 1).
- 2.
Displacement of all points from the set P ^{ i } (step 2).
- 3.
Permitted position of the point c ^{ i } arising from the restriction on a solid body (step 3).
- Step 1: Calculate in the time step t _{ k } the new position of the reference point \(\mathbf {c}^{i}_{(k+1)}\), solving the optimization problem for the estimated value of the reference distance \(\hat {d}_{g,(k+1)}^{i}\), and under the assumption that all points from the set \(P^{i}_{(k)}\) are fixed:$$\begin{array}{@{}rcl@{}} && {} \min_{\mathbf{c}^{i}_{(k+1)}}\left[\sum_{G_{g}^{i} \in S_{G,(k)}^{i}}U_{g,(k)}^{i}\left(d_{g,(k+1)}^{i}\right) = \sum_{G_{g}^{i} \in S_{G,(k)}^{i}} \epsilon^{i}_{g,(k)}\right.\\ &&\quad\quad\left.\left(\frac{\hat{d}_{g,(k+1)}^{i}}{\left\|\mathbf{c}^{i}_{(k+1)} - \mathbf{c}^{i}_{g,(k)}\right\|} -1 \right)^{2}\right], \end{array} $$(27)$$ \forall_{O_{j},j = 1,\ldots,M} \quad \mathbf{c}^{i}_{(k+1)} \cap Vol\left(P^{j}_{(k)}\right) = \emptyset, $$(28)$$ \Delta t \cdot v^{i}_{max} \geq \left\|\mathbf{c}^{i}_{(k+1)} - \mathbf{c}^{i}_{(k)}\right\|. $$(29)The results of calculations are presented in Fig. 7.
- Step 2: Calculate in the time step t _{ k } the displacement for all points from the set \(P^{i}_{(k)}\), solving the optimization problem for the estimated value of the reference distance \(\hat {d}_{g,(k+1)}^{i}\), and under the assumption that the point \(\mathbf {c}^{i}_{(k+1)}\) calculated in step 1 is fixed:$$ \min_{P^{i}_{(k+1)}}\left[\sum_{\mathbf{p}^{i}_{a},\mathbf{p}^{i}_{b} \in P^{i},a\neq b}\left(\bar{r}_{a,b}^{i} - \left\|\mathbf{p}^{i}_{a,(k+1)} - \mathbf{p}^{i}_{b,(k+1)}\right\| \right)^{2} \right], $$(30)$$ \forall_{O_{j},j = 1,\ldots,M} \quad Vol\left(P^{i}_{(k+1)}\right) \cap Vol\left(P^{j}_{(k)}\right) = \emptyset. $$(31)The results of calculations are presented in Fig. 8.
- Step 3: Recalculate the position of \(\mathbf {c}^{i}_{(k+1)}\) to satisfy the constraint on a solid body, and under the assumption that all points from the set \(P^{i}_{(k+1)}\) calculated in step 2 are fixed:$$ \min_{c^{i}_{(k+1)}}\left[\sum_{\mathbf{p}^{i}_{a} \in P^{i},\mathbf{c}^{i} \in P^{i}}\left(\bar{r}_{0,a}^{i} - \left\|\mathbf{p}^{i}_{a,(k+1)} - \mathbf{c}^{i}_{(k+1)}\right\| \right)^{2} \right], $$(32)$$ \forall_{O_{j},j = 1,\ldots,M} \quad \mathbf{c}^{i}_{(k+1)} \cap Vol\left(P^{j}_{(k)}\right) = \emptyset, $$(33)The results of calculations are presented in Fig. 9.
The method of steepest descent is used to solve all above optimization problems. Finally, the device D _{ i } is moved to the designated location, which is recalculated again after the time interval Δ t.
5 Motion pattern computing for coherent network
To managing the mobility of a whole network and meet the requirements for providing continuous connectivity with a base station we propose two-level scheme for motion trajectories computing for all network nodes. Hence, calculations are carried out by two types of units, i.e., a base station (central unit in the system) and network nodes. The base station initiates the calculation process using the algorithm COHERENT_NET.
- L1
The central station determines the initial position of each node in a network system based on the measurements from GPS or other localization systems described in [13]. Next, the messages with initial goals are distributed among nodes. Due to dynamic changes in a workspace the goals can change over time. In case of any changes new target points are transmitted to given nodes of a network.
- L2
In the time step t _{ k } every mobile device (network node) computes its new position in the workspace using algorithm NETWORK_NODE, and next move to the designated location. The calculations are repeated every time interval Δ t due to changes in communication conditions and a workspace.
- step 1:
Read the data from the base station (current position and current goals).
- step 2:
Calculate \(\hat {d}^{i}_{g,(k+1)}\), g = 1,…,J _{ i } – the distances between a node i and each its goal \(G_{g}^{i}\) expected after network transformation (in t _{ k+1} = t _{ k }+Δ t) due to the formula (23).
- step 3:
Calculate the displacements for points c ^{ i }, and \(\mathbf {p}^{i}_{l}\), l = 1,…,L _{ i } solving in sequence three optimization problems: (27)–(29), (30)–(31) and (32)–(33).
- step 4:
Move points c ^{ i } and \(\mathbf {p}^{i}_{l}\), l = 1,…,L _{ i } to the new positions using results of step 3.
- step 5:
Broadcast the new position of D _{ i }, update the time step (t _{ k } = t _{ k }+Δ t), and return to step 1.
6 Case study results
We evaluated our mobility model through simulations. All experiments were performed using the software system for ad hoc network simulation on multiprocessor machines, described in [12,17]. In this paper we present and discuss the usage of our mobility model to design three ad hoc systems, starting from simple synthetic networks to more complex and realistic ones.
6.1 The design of coherent network
6.2 Re-establishing the communication infrastructure
6.3 Emergency situation awareness
Simulation results
Time | Average node degree | Average inter-node distance | Sum of energy |
---|---|---|---|
0 | 21.0 | 9.45 | 5936.73 |
20 | 16.0 | 17.71 | 799.14 |
40 | 12.0 | 19.13 | 398.37 |
60 | 8.64 | 19.66 | 189.07 |
80 | 7.55 | 20.46 | 133.55 |
100 | 7.09 | 20.44 | 131.64 |
120 | 6.73 | 21.23 | 119.97 |
140 | 5.55 | 20.65 | 106.94 |
160 | 6.0 | 20.86 | 113.98 |
180 | 5.55 | 20.83 | 111.57 |
200 | 5.27 | 21.16 | 96.83 |
7 Conclusion
In this paper, we focused on mobility modeling in indor and outdoor scenarios and proposed a novel approach to cooperative mobile network design. Our approach combines techniques based on the potential field and the particle-based scheme for the motion paths computation. We defined the artificial potential function that is used in calculation of the optimal inter-node distances in a cooperative network. The main result of our research is the algorithm for designing and managing the mobility of ad hoc networks. The algorithm was implemented in our simulation platform and verified in many tests. In our opinion the presented mobility model is a good compromise between accuracy of the mobility modeling and computational burden. The presented case studies show that the COHERENT_NET algorithm can be successfully applied to design self-configuring, cooperative and coherent real life networks. In the future work, we plan to evaluate the performance of the COHERENT_NET algorithm in the testbed of middle-size ad hoc network in our laboratory.
Notes
Acknowledgments
This work was partially supported by National Science Centre grant NN514 672940.
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