Using Patterns of Social Dynamics in the Design of

Using Patterns of Social Dynamics in the Design of Social Networks of Sensors Marcello Tomasini and Franco Zambonelli

Ronaldo Menezes

Dipartimento di Scienze e Metodi dell’Ingengneria Universit`a di Modena e Reggio Emilia, Italy [email protected] [email protected]

BioComplex Laboratory, Computer Sciences Florida Institute of Technology, Melbourne, USA [email protected]

Abstract—Sensor networks are gaining in importance in today’s society; from air-pollution monitoring to forest-fire detection, from agriculture to battlefield communication, sensor networks are ubiquitous in many parts of the world. Furthermore, this is a world where sensors are increasingly integrated in smart phones and tablets. The use of this collection sensors as sensornetwork infrastructures (towards what we call Social Networks of Sensors”, or SNoS) may be very fruitful and economically advantageous. However, it also introduces some new research challenges, one of which relates to understanding the potential impact of social mobility patterns to the performances of sensor infrastructures. This paper delves into such issue and analyses how the presence of mobile sensors moving according to social mobility patterns can impact the performances of fixed sensor network infrastructures and their design choices. Simulation results show that such integration can lead to increased efficiency of the integrated SNoS infrastructure for both sensing coverage and data delivery.

I. I NTRODUCTION Since their introduction, sensor networks have assumed an increasing practical relevance [1], and the current number of deployed sensor-network infrastructures is considerable [2]. Additionally, according to the Internet of Things vision [3], we are moving towards a world where “smart” physical objects, enriched with computing and sensing capabilities, will be seamlessly integrated into our lives and our information networks [3]. This integration will enable us to opportunistically exploit such pervasive sensing and networking capability of objects as if such objects formed a wireless sensor network, or a “Social Network of Sensors” (SNoS); an event that will make sensor networks de facto pervasive and widely used. One aspect of SNoS that makes them much different from traditional sensor network infrastructures is that some of these sensors can be mobile without requiring any energy to achieve mobility owing to the fact that they are carried by people moving around—social dynamics. These devices include primarily mobile phones, but also tablets, smart watches, and similar devices. As a consequence of such mobility, these mobile nodes can be very effective in SNoS given that they can be dynamically patrolling and monitoring the environment (e.g., looking for chemical, biological, or radiological agents). Mobile nodes in SNoS will be extremely valuable in locations where there are no (or enough) smart objects to opportunistically exploit the environment, and where deployment of dense-enough wireless sensor nodes is not be possible

or economically feasible. The existence of mobile nodes in particular can be used to improve network efficiency or to eliminate “blind spots of coverage” caused by low availability of sensors [4]. In recent years, a considerable amount research work has been devoted to understand how some degree of mobility, typically via some mobility mechanisms embedded in sensor nodes [5], can improve the effectiveness of sensing coverage and data dissemination. From a different perspective, many researches faced the issue of exploiting humans carrying on smart phones as sensor nodes, and analysed how and to which extent they can effectively achieve sensing goals and with which effectiveness [6]. However, the issue of how network of mobile sensors integrated with fixed sensor network infrastructures can produce an overall impact on sensing performances and data delivery, and can thus impact on sensor network design, has not been deeply investigated. In this work, we evaluate the performance of an urban SNoS composed of both mobile and static sensors in order to understand the design choices that could be made in urban environments. In particular, in our model: • Mobile sensors are carried by people, and the human mobility patterns that drive their movements—extremely relevant in affecting the performance of the system—have been modeled based on the most common social mobility patterns for urban environments. • Static sensors are assumed to be deployed uniformly around the environment which is is realistic for urban environments where one uses the current infrastructure (traffic lights, light posts, etc) to install sensors. Using a number of simulation experiments, we have elucidated the relationship between detection and report time in SNoS under presence and absence of mobile sensors. This has lead us to observe that mobile sensors can decidedly help the delivery of data to specific sinks (nodes responsible for collecting events detected by the network), and that the decision on where to place sink nodes is critical to the performances of the overall SNoS. In addition, we showed the existence of a lower and a higher threshold in the percentage of mobile sensors that gives us the minimum number of mobile sensors required to achieve a good trade-off between performances and costs. The paper is organized as follows. Section II discusses the

related work in the area of this paper. Section III describes our model of SNoS and the design of the SNoS simulator. Section IV illustrates experimental results and our main findings. Section V summarizes this paper and provides the basis for future works. II. R ELATED W ORK The research described in this paper relates three different research areas: (i) Sensor Networks, which deals with spatially distributed sensors used to monitor physical or environmental conditions, (ii) Participatory Sensing, which deals with sensing by making use of smart phones, and (iii) Human Mobility Dynamics, which aims at modeling and understanding patterns of human movement. A. Sensor Networks Most of the works on sensor networks are on coverage, protocols, and algorithms to reposition sensors [7], [8], [9], [10]. The main difference between these works is on how the desired positions of sensors are computed. Typically, mobility is only exploited to achieve a static optimal configuration in an enlarged sensing environment, or exploiting inherent and mostly limited mobile capabilities of sensors [11]. Liu et al. [4], [12] show that sensor mobility can be exploited to effectively reduce the detection time of a stationary intruder and improve network coverage when the number of sensors is limited. The basic concept behind their work is that, given a fixed number of sensors, their coverage area is bound by the density of sensors. However, if sensors are allowed to move, the area that can be covered increases because sensors are now able to reach locations in the environment that would have never been covered under a static distribution of sensors. In any case, the mobility models they investigate are based on random movements, and nothing is said on the potential impact of more realistic mobility models. Chin et al. [5] investigate the problem of target detection and evaluate the detection latency using a mobile sensor network with uncoordinated mobility. These sensors work based on a probability function parametrized by the energy availability of the center. Our model assumes that if the event is within the radius of a sensor, the event will always be detected while Chin et al. assume it may not be detected as it depends on the energy availability in the sensor. The issue of understanding how mobility patterns affect coverage and the possibility of delivering messages has been deeply analyzed also in the context of mobile ad-hoc networks and delay-tolerant networks. Bild et al. [13] exploited the predictability of mobility patterns of people to improve the reliability and scalability of routing on Mobile AdHoc Networks (MANETs). This is quite important because most routing protocols do not scale to very large networks without traditional fixed infrastructures which are hard to be made available in certain environments (battlefields for instance). B. Participatory Sensing Participatory sensing is concerned with the possibility of using users’ personal devices to form sensor networks [6],

[14]. This is another area that recently emerged in the scientific community in which the impact of user mobility is very important. Participatory sensing rely on users holding smart phones (e.g., with sensing capabilities) to act as sensor nodes, e.g., by dynamically involving them in acquiring information about specific phenomena in an environment. Our approach tries to incorporate the best of the traditional sensor network sensing and of participatory sensing by defining a hybrid system in which humans (with devices) and fixed sensing devices cooperate to improve coverage and data distribution. In pure participatory sensing systems, the location and movement of people have a dramatic impact on the coverage of the sensed phenomena. Discovery of an event cannot be guaranteed in participatory sensing, because one cannot exert control on the position of users or on their willingness to participate. At most, based on the analysis of mobility patterns, one can reason about the sensing area and on the minimal percentage of users that must be involved to probabilistically ensure coverage of such an area. Our approach, by accounting for the existence of fixed sensor nodes, goes in the direction of a more realistic scenario, in which the opportunistic synergy of infrastructural sensing devices and of users will enable the increase sensing coverage and exploit the best of human mobility. Some recent approaches to participatory sensing propose means to increase the percentage of people participating in sensing activities or to affect their mobility patterns so as to reduce coverage problems. Many approaches rely on monetary incentives [15] to improve user participation, although some recent proposals also suggest affecting participation and mobility patterns by means of a gaming approach [16]. Although our current work does not account for the possibility to influence the mobility patterns of users, this is definitely an interesting area of future development. C. Human Mobility Models Made possible by the increased availability of location data, a number of recent studies have focused on proposing sound and realistic human mobility models. In our work, we show that these works may be used to better analyze the impact of mobility in SNoS. Gonzalez et al. [17] show that the mobility of humans is characterized by a time-independent travel distance and a significant probability to re-visit previous locations. This movement has been further studied by Song et al. [18], who explored the limits of predictability in human dynamics; they found a 93% predictability in user mobility and showed that it is independent of the distance users cover on a regular basis even if travel patterns differ considerably. These results are especially relevant because they tell us that human movements are not random thus the predictability can be exploited to increase performance and efficiency of sensor network protocols (e.g., routing data to sink nodes). Mobility models that explore location preference are able to account for the aforementioned properties. Song et al.

[19] has proposed a model for human mobility based on preferred locations, not fixed a priori, but rather emerging as a consequence of the mobility process. Their model is based on two generic mechanisms, exploration and preferential return, both unique to social human mobility and missing from the traditional random-walk (L´evy-flight or Continuous-Time Random Walk) models. The two mechanisms are as follows: Exploration: a scaling law is proposed to indicate that the tendency to explore additional/new locations decreases with time. Indeed, the longer we observe a person’s trajectory, the higher is the probability that he visited all nearby locations. Preferential Return: in contrast with random-walk-based models where people move randomly thus resulting in a uniform distribution of visits, humans show significant propensity to return to previously visited locations, such as their home or workplace. This model—even in its simplicity—is able to capture most of the characteristics of human mobility, thus we chose it as our reference human mobility model. A recent thread of research in human mobility modeling is based on using complex-network theory to represent social ties, by considering these as a primary drive of individuals’ movements. Social relations are described as a graph, where nodes represent individuals and weighted edges the strength of social connections. The main idea is that the next location chosen by the user depends on the position of people with whom the user shares social ties. For instance, the HCMM model [20] applies and extends this idea by adding a location preference and incorporating power-law distribution of the jumps. Furthermore in order to capture the periodical pattern in movements, GeSoMo [21] introduced the concept of timevarying graphs, that is, the social strength of relationships between users (i.e., the weight of the edges in the social graph) changes with time. Even though these models could lead to more accurate movements we believe that they do not modify our results, thus we do not think that is necessary to add this greater implementation complexity to our simulator. III. SN O S: M ODEL AND S IMULATION In this work we focus on how human mobility could impact an urban SNoS with both static and mobile sensors when we assume that mobile sensors are carried by humans (participatory sensing). In particular, we focus on the benchmarking of two issues in sensor networks: (i) the time tD to detect an event (source) in the environment, and (ii) the time tR to report that event to a specific location (sink) in the environment. Our main goal is to find ways to exploit both kind of sensors in an integrated way and see if this integration leads to performance improvements. A. The Model We start with a representation of the environment. We envision a mix of mobile and static sensors in an urban environment. The mobile sensors are carried by people forming a SNoS while fixed sensors are attached to the objects in city

infrastructure. Our city model consists of a square lattice of side ` (representing the urban area) divided in square patches of one unit area (representing blocks). In this environment, we deployed two types of sensors: static sensors are distributed along the regular lattice while mobile sensors are distributed based on a negative exponential probability from the center of the city—as proposed by Clark in his urban population density model [22]. We had to modify the model by truncating the exponential distribution so that all sensors are placed within the city urban area. In order to achieve this truncation we first concentrated on the Cumulative Distribution Function (CDF) of the exponential distribution given by: P (δ 6 d) = 1 − e−λd ,

(1)

where P (δ 6 d) represents the probability that the distance of a sensor is at most d from the center of the city (simulation environment). In our simulations we decided to experiment with a configuration in which 95% of the sensors are at the maximum distance `/2, which represents the distance from the center of the city to one of the sides (since the environment representing the city is a square of side `, as depicted in Figure III-A). The truncation occurs because 5% of the sensors would be placed outside the simulation environment if we strictly follow Equation 1. When generating the events in the simulator, if they are in the 5% outside the environment, their position is recalculated (truncation). The underlying principle here is to cover the simulation area in a very similar way as cities are organized, that is, most people are in the urbanized center while some live in the surrounding areas near the city and frequently move into the center. Now to simulate the detection and reporting of an event we have to include two special markers in the environment called the event and the sink. The event is the item we want to detect (e.g., a fire, an explosion) whereas the sink is the place to report the event (e.g., a police station). We placed the sink and the event in the environment at a distance D = 60 from each other. This value for D also corresponds to the diameter of a circle centered in the middle of the environment (city), such that approximately 80% of mobile sensors are included within this circle. By placing the event and the sink at distance D we argue that they are located in the periphery of the city (Fig. III-A). We chose this approach of fixing event and sink to remove one variable from simulations that arises in the case of random deployment of these two events. Mobile sensors move at a fixed speed of one unit per simulation tick and follow the human mobility model described by Song et al. in [19], where the jump length ∆r and the wait time ∆t follow a power-law distribution with exponential cutoffs as given in the following equations: P (∆r) = (∆r + ∆r0 )−1−α exp(−∆r/k1 )

(2)

P (∆t) = (∆t)−1−β exp(−∆t/k2 )

(3)

where α and β control the scaling of jump length and wait time respectively, k1 is the cutoff value of the jump length, k2 is the cutoff value of the wait time and ∆r0 is the minimum jump

Fig. 1. Setup of a simulation with 441 static nodes (violet triangles) and 220 mobile nodes (green people). The event is marked with a red cross and the sink with a blue flag. Symbols are just for display convenience and they do not reflect the real size of a sensor.

length. Differently from [19], we are able to exactly identify the position of each sensor so we have an ideally infinite space resolution, thus we set ∆r0 = 0. Each jump can be an exploration jump with probability Pnew = ρS −γ ,

(4)

where S is the number of distinct visited locations by the sensor, while ρ and γ are parameters that characterize human mobility, or a preferential return, with complementary probability Pret = 1 − Pnew . That means that sensors sometimes come back to a visited location i choosing it with a probability proportional to the number of visits fi made by that sensor to that location. If a new location is visited then the sensor increments S, thus reducing the probability of a new jump. The concept of “location” used must be defined: indeed Song et al. divide the environment using a Voronoi diagram and use a Voronoi patch as location, while in our case an environment square cell (block) is a location. B. The Simulation Our implementation of a simulator for SNoS is done in NetLogo [23], a multi-agent programmable modeling environment. The simulator is fully parameterized and supports many spatial distributions of sensors (e.g., lattice, uniform, exponential, normal) and different kinds of walks (e.g., Wiener, Rayleigh flight, Cauchy flight, L´evy walk, L´evy with an exponential cutoff, CTRW) thus many combinations can be explored and compared. We set ` = 200 for validation and testing of the implementation since we want to simulate a

large environment, while we used ` = 100 for experimental results to speed up simulations. A simulation starts in a given configuration and while time is passing, mobile sensors move accordingly to the specified model, exploring the environment. Eventually a sensor will detect the event. From that point the information spread to other sensors when they are within communication range. The simulation stops when one of the sensors with the information about the event finds the sink node. We assume a boolean sensor network with fixed sensor radius r both for mobile and static sensors, we can argue that an event can be detected if and only if the event is located at a distance, d 6 r. The concept of time in NetLogo simulations is discrete, so every tick sensors check if the event is in their radius. Those that have been told about the event check if there are other sensors in their radius and if so they spread the information further in a ripple effect. The order in which they check is random, so they are not synchronized, thus reflecting real behavior with greater accuracy. According to [19], the values of the parameters that best model human mobility are ρ = 0.6, γ = 0.21, α = 0.55, β = 0.8 and k1 = `/10. Due to the nature of discrete simulations, it is hard to synchronize a tick to real-world units (e.g. seconds), so the wait-time cutoff has been arbitrarily set to k2 = 5 ticks, that seems to allow to speed up simulations without impacting too much on mobility behavior. The results of our implementation show an accurate behavior in following Song et al.’s model. The number of distinct visited locations over time should follow the law S(t) ∼ tµ , with µ = β/(1 + γ); with the configuration described our implementation is rather accurate and gives µ ' 0.71 versus the theoretical result µ ' 0.66. It also exhibits the expected Zipf’s law, fk ∼ k −ξ , in the visitation frequency distribution of the k-the most visited locations, with little differences (tends to underestimate ξ exponent) to real data showed in Song’s work, possibly due to aggregation phenomena led by Voronoi diagrams or due to the different spatial resolution. However it should be noted that while testing as been done allowing a very long run time (max S(t) ' 700), simulation time in experimental results depends strictly on the initial configuration, so the resulting number of visited locations is between 10 and 30. IV. E XPERIMENTAL R ESULTS In order to benchmark the effect of mobile sensors we decided to first look a the performance of a network made of only static sensors where any node can reach any other node in the environment. Recall that we have a fixed size environment so we first calculated the minimum number of sensors necessary to cover the entire environment. This number is given by ns = k 2 , k = (`+r)/r, where r represents the radius of transmission in a square lattice of side `. If we assume r = 5 and ` = 100, then ns = 441. With this configuration in hands we run the simulator many times to get a pattern of spread of the information. The configuration here is similar to the one described for Fig. III-A where D = 60.

350 250 150 0

50

# of sensors

0

1

2

3

4

5

6

Time (ticks) Fig. 2. Each column represents 20 runs and depict the number of nodes that have received the information about the event at that time.

The spread in the simulator differs between runs because the sensors are not synchronized. Fig. 2 shows the spread under this static-only assumption. Most executions of the simulator stop when the simulator reaches tick number 5, tsim ' 5. It is very clear from Fig. 2 that the performance of a static network is very good if we consider the time it takes for the event to spread— it indeed spreads rapidly. But one has to also look at other costs. The configuration depicted assumes ns = 441. Given the nature of the square lattice, if we decrease the radius of the sensors so that r = 2.5 then tsim ' 10 ticks which is 2 times longer than the reference setup. This doubling the time does not seem particularly bad but unfortunately for the number of sensors would have to quadruple to a minimum of ns = 1681. In the real world, one is constantly faced with budget constraints which makes some of setups as depicted in Fig. 2 unrealistic. An approach to overcome issues such as budget limitations, is to exploit current infrastructures and attach sensors to mobile agents (e.g., people’s smartphones, vehicles) to achieve acceptable performances while keeping costs under control. In order to demonstrate the benefit of mobility we went back to the original model with ns = 441 but with a reduced radius r = 2.5. In this configuration the network is no longer connected because the sensors can no longer talk to each other. We then add an increasing percentage of mobile sensors (in relation to the number of static): 10% (44), 20% (88), 30% (132), 40% (176), 50% (220) and 60% (265) and measure the performance again. It is worth noting that we consider detection time the elapsed time from the beginning of the simulation until a mobile sensor finds the event. Although this may sound strange it is the only meaningful option because the detection time of static sensors is always 0 if none of

Fig. 3.

Mean detection time is proportional to tD ∼ an−b m .

them can see the event or 1 if at least one can see the event. The simulator was run 500 times for each percentage used. We provide the mean of each of the values and the standard error of the mean (SE) that quantifies the variance in the performance of the sensor network that may arise due to the stochastic nature of sensors deployment and movements. The analysis in a mixed environment is more complex since we must distinguish between static nodes ns and mobile nodes nm . If we focus on mobile sensors (Table I), we see that detection time follows a law of the kind tD (nm ) = an−b m where a and b are constants. If we add less than 10% of mobile sensors then the sensor density becomes too low and the space is not well covered. This leads to a very high detection time. As we add more sensors the detection time sharply drops but after we have 30% of mobile sensors the gain may not be so prominent (Fig. 3). Table I also reports the gain for the report time, tR (nm ), which is also defined by an equation similar to tD (nm ). TABLE I P ERFORMANCES OF A MIXED NETWORK FOR THE TIME OF DETECTION OF AN EVENT tD AND REPORTING AN EVENT TO THE SINK GIVEN BY tR

nm

tD

SEtD

tR

SEtR

44 88 132 176 220 265

535.94 166.31 79.24 54.92 35.47 27.47

43.75 11.35 6.48 4.59 2.63 2.46

667.77 303.69 208.32 154.13 127.14 106.40

36.01 11.05 7.71 3.41 2.77 1.91

Another way to look at the performance of a hybrid sensor network is using normalized values. Table II normalizes all the

TABLE III S PEEDUP RELATIVE THE SLOWEST CONFIGURATION WITH 10% OF MOBILE SENSORS . nm /ns

SD = tD−1 /tD

SR = tR−1 /tR

Sp

1 3.2225 2.0987 1.4428 1.5486 1.2911

1 2.1989 1.4578 1.3515 1.2123 1.1949

1 2.5611 1.6345 1.3755 1.2857 1.2146

10% 20% 30% 40% 50% 60%

TABLE IV P ERFORMANCES OF A NETWORK WITH ONLY MOBILE SENSORS VERSUS A MIXED NETWORK

Fig. 4.

mobile (ns = 0)

mixed (ns = 441)

nm

tD

tR

tD

tR

44 265 706

630 48 12

1038 172 64

536 27 —

668 106 —

Mean report time is proportional to tR ∼ cn−d m .

TABLE II P ERFORMANCES OF THE NETWORK NORMALIZED AGAINST tR10% . nm /ns

tD /tD10%

tR /tR10%

tR /(tD + tR )

10% 20% 30% 40% 50% 60%

1 0.3103 0.1479 0.1025 0.0662 0.0513

1 0.4548 0.3120 0.2308 0.1904 0.1593

0.5548 0.6462 0.7244 0.7373 0.7819 0.7948

values according to the worst-case with (tD10% and tR10% ) representing the scenario where only 10% of mobile sensors are present. The normalized values clearly show that detection time drops very quickly to a little fraction of tD10% , while report time improves but more slowly. This leads to another observation that detection time becomes less relevant with the increase in the number of mobile sensors and the bottleneck is the time to report the event to the sink; this behavior is strongly influenced by the mobility model. In our implementation, movements are conditioned by the preferential return pattern that may lead to an asymmetry between detection time and report time. Since the probability of exploration jumps decreases over time (eq. 4), most sensors offer a better (more uniform) coverage initially, while they will visit just a finite set of locations as they age. If the sink is not one of these locations or it is not on the path to reach them, then it could take quite a long time before the event is reported to the sink. Moreover, if the sink is placed in the periphery of the city, where the probability to find mobile sensors is smaller, then the performances of the network degrade. The same applies for the deployment of the event, but in a lesser degree for what explained before. If we look at performances relative to the previous step

(table III) we can make another interesting observation: when engineers design sensor networks, they usually have to conform to minimum requirements such as finding events within a time tDmin and reporting it within a time tRmin . Taking these together, we can set a lower bound as tmin = tDmin + tRmin that must be respected. These numbers are generally used to decide the initial number of mobile sensors required. However when they look for a performance improvements they look for the speedup SD , SR relative to current performance, or in other words, how much faster does the network become as we add more sensors. From Table II we can extract the weights ωD = 1 − ωR and ωR = tR /(tD + tR ) of tD and tR to calculate the general speedup as Sp = ωD SD + ωR SR . As seen earlier, static nodes are very important to the performances of the network because they maximize the chance of a mobile sensor to be informed about an event—they work as gateways between mobile sensors. But how good is the contribution of the static sensors? To look into this question we could envision a scenario where all nodes are mobile. If the sensor density is too low the inter-contact time could be relevant thus the performances of the network degrade. Table IV shows that with a limited amount of mobile sensors the mixed configuration is faster, but if we consider a mobile configuration with the same amount of sensors of the mixed configuration with ns = 441 and nm = 265, that is a mobile sensor network with 706 mobile sensors, then in this case the mobile-only configuration is able to outperform the mixed network thanks to the greater sensor density, so inter-contact time is no longer relevant. Lower detection time is also a consequence of the better coverage of the periphery and the high sensor density allows a quick spreading of the event till the sink. This result is fully coherent with our model and previous observations. Last we look at the coverage by the mobile sensors. As

Fig. 5. Maximum fraction of covered area versus nm . It remains practically constant, indeed the linear fitting has a slope of ' 0.0005.

they move, they are able to “see” areas of the environment that would not otherwise be seen. This accounts for a fraction of the area visited/covered by the mobile sensors. Fig. 5 shows the fraction of the area covered at the end of the simulation, tsim , as we increase the number of mobile sensors. At first glance, it looks surprising that the coverage increases slowly. However this is a consequence of the goal we have in our simulation which is to detect an event and report it to a sink node. With this in mind the total time of the simulation, tsim = tD + tR , decreases rapidly, as shown in Figs. 3 and 4, which tells us that adding more mobile sensors may not help after some saturation point. Finally, it should be noted that the performances both of a fully mobile or a mixed network cannot be compared to an ideal fully connected static network because a fully connected network is fast (although expensive). In a mixed network if we add 100% of mobile nodes, detection time is tD ' 12 and report time is tR ' 75. But even if we have a high enough number of mobile sensors it is still impossible to match the performance of a fully connected network (e.g 1681 mobile sensors are able of tD ' 2, tR ' 23). Moreover a fully connected sensor network covers the whole area at all times with little overlapping and high reliability [24]. V. C ONCLUSION AND F UTURE W ORK As shown by our experimental results, there are many ways to exploit the setup of sensor networks to improve both performance and cost. Moreover, even if not showed in this work, we have data on sensing overlapping that will be used in future for comparisons against other models. First, since most of mobile sensors are near the center of the city, it is worthless to have static sensors in that place because it is already well covered. This approach could lead

to cost savings if we choose not to deploy static sensors or in performance and coverage improvement if we move the static sensors in the periphery. The result is likely to be a connected network which virtually eliminates detection time. Another technique could consist in building short paths from the periphery to the center so that if they are hit by a sensor that knows about the event, it immediately propagates where the density of mobile sensors is greater thus greatly reducing report time. Second, due to the urban population density distribution and the greater relevance of report time over detection time, to maximize performances the best sink deployment is in the center of the city. This also leads to more uniform distance from event to sink in case the event is placed randomly in the space thus reducing the variance of tD and tR . However the model for urban population density is quite simplistic and does not take in account multi-centered cities [25]. Third, there are two thresholds. A lower-bound threshold that ensures that mobile sensors achieve a high enough density and a higher-bound threshold over which it is not worth the addition of more mobile sensors because they do not provide a significant improvement in the performance. Of course these thresholds could vary as a function of the cost of mobile sensors, that is, there still exists a tradeoff between cost and performance. In this paper sensor faults are not considered but we intend to perform this work in the near future. Last, even if not quantified in this paper, the human mobility model may not be the best to patrol an area; this is because the preferential return should lead to a strong overlapping of areas, which in a real environment is only partially mitigated by the different locations different users visit. This is explained by the fact that in a real city there is a finite amount of “hot” locations that are visited by many users (e.g., malls, discos & pubs, post offices), so that a sort of correlation between users is introduced. The human mobility model we used does not take overlap into account since user locations are independently chosen. Given the great flexibility of our simulator future works will focus on different mobility models and spatial distributions that could lead to better performances. We also need to find scenarios where these combinations can be applied so that it is possible to get some real-world benefits. A common scenario could be a forest or a sea where we attach sensors to animals, that move accordingly to L´evy walk, and we try to monitor the chemicals and physical parameters of those environments. Another scenario could be a battlefield where sensors are airdropped randomly and then they move following a Wiener process. Moreover while in a multi-center city the ideal location of a static sink should be arguably in one of the “hot spots”, in case of multiple mobile targets/events the displacement of sink (or sinks) offers an even more challenging problem because the target mobility model and their spatial distribution must be taken in account. In the model we described here, sensors communicate with all others in their communication range. This could be inefficient for the sensors since the information

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