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Physical activity, including less vigorous forms of physical activity such as walking and cycling, reduce the risk of cardiovascular disease (CVD).1 Despite the knowledge of its benefits, levels of activity are still low in many countries.2 With increasingly sedentary occupations and busy lives, many people have little time for leisure time physical activity. Activity as part of a journey, such as the commute or for transport in general, offers a comparatively easy way to integrate exercise into daily life.3
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During our first hour on the road, Elijah rifled through hundreds of stickers I had brought along to keep him busy in the car. He feverishly peeled them and pasted them onto a large piece of cardboard like a small machine with his strict and narrow concentration. In the rear-view mirror, I saw the waxy paper backings of the stickers piling up in the back seat like fluffy patches of snow surrounding him. When he had peeled the very last sticker from its paper he let out a screech. Quickly, I popped the Pinocchio soundtrack into the tape player to redirect him, but to my dismay, I had forgotten to rewind it.
In this work, we focus on file distributing networks, and on the harmful effect caused by peers that enter the system and begin the file downloading process but leave before finishing it or just after finishing their own download. Hence, resources can be assigned to a peer that is not staying long enough in the network to cooperate with the rest of the users, that is, leading to a waste.
BitTorrent is a P2P application used to facilitate the download of popular files. The main idea is to divide the files into several pieces called chunks. To download a file, peers exchange these chunks following some rules.
The BitTorrent protocol differentiates two types of peers: leeches, which are peers that have a part of the file or not data at all, and seeds, which are those peers having downloaded the complete file and remaining in the system to share their resources. Both leeches and seeds cooperate to upload the file to other leeches. Whenever a peer joins the system with the objective of downloading the file, it contacts a particular node called tracker which has the compete list of peers that have part or the complete file. Then, the tracker returns a random list of potential peers that might share the file with the arriving peer. At this point, the downloading peer contacts the peers on the list and establishes which chunks it is willing to download from each peer it is connected with. The decision of which peers to upload to depends basically on how much chunks have downloaded the peers in question. Hence, the peers that have downloaded the most are the ones that have priority over the peers that do not share their chunks, discouraging the free riders (peers that only download but do not share their data).
We built our priority model based on , and using also [3, 4, 13]. Unlike these works, we consider a two-population model. Additionally, a priority mechanism is proposed and studied by means of a fluid simplification and a Markov chain. Fluid models as the one in , allow simple analytical discussions. We complete the analysis with a Markov chain model such as the one presented in  to get better insight into the performance of the system. In , two classes of users are considered, namely: high bandwidth users and low bandwidth users. This is done in order to approximate a real system where different users have different hardware characteristics. Unlike , we focus on the behavior of the different peers during the downloading procedure rather than the different bandwidth capacities that can be encountered in a real network. Moreover, an event simulator is implemented to study a managed P2P network where the transfer rates are considered to be constant. This model can no longer be studied using neither the Markov chain nor the Fluid model.
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New peers arrive to the system according to a Poisson process having rate λ and are labeled as leeches. All peers have the same uploading rate μ and the same downloading rate c, c>μ. A single file download is considered. At any given time there is at least one seed in the system. All peers have complete knowledge of the system, i.e., all peers know which chunks has any other peer and peers always cooperate to upload data if they have available bandwidth. As such, if the number of leeches and seeds is sufficiently high, all leeches download the file at the maximum download rate c. However, when there are not enough peers in the system, the leeches download at rate μ(x+y), where x is the instantaneous number of leeches and y is the instantaneous number of seeds. With respect to , we simplify the model by assuming that the efficiency η defined in that paper is 1. From the previous description, the evolution with time x and y satisfies:
For the two population model, the behavior of two types of users is considered: cooperative leeches (also called high tolerance leeches) and defeat leeches (also called low tolerance leeches). For the former, they are peers that arrive to the system and usually stay throughout the entire download procedure. In other words, they have a high tolerance for download latency. Therefore, their departure rate (θc) is lower than the download rate at the maximum capacity, i.e., c>θc. For the latter, they are peers that arrive to the system and have very little tolerance to download latency. Hence, even if their departure rate is lower than the download rate at the maximum capacity, it is just lower. In view of this, we consider the next set of values: θc=θ and θd=0.9c. Cooperative leeches arrive with rate λc and defeat leeches arrive with rate λd.
As such, the simulations are performed as close as possible to both the Markov and Fluid models but without some important assumptions. Specifically, the aforementioned models consider that all the peers, from the moment of the arrival of the peer to the moment of the peer departure, always cooperate to share the file in the system. Conversely, the simulation considers that the peers can only share the file once it has downloaded the file. A more detailed simulation, considered for future work would consider the sharing of the file once it has downloaded at least some chunks of the file.
The pseudo-code of the event simulator is presented in Algorithm 1. Four types of events are considered: Arrival of a new peer, End of the download of the file, Departure of a Leech, and Departure of a Seed. Each arriving peer is assigned an individual and particular identifier id. Hence, in the pseudo-code, the identifier of the peer that is being attended according to the different events is referred as id. And the identifier of the peer that is uploading the file is referred as idupload.
In the peer arrival event, the new peer looks for an idle peer, i.e., a peer that is not uploading the file to any other peer. Indeed, since a peer that shares the file uploads at the upload rate μ it cannot upload to any other peer. And the new arriving peer continues to look for other peers until the download capacity is fulfilled. For each peer that shares the file, it is marked as busy as an indicator that it cannot upload the file to another peer. When the file is downloaded, these uploading peers are marked as idle and they can now attend other peers. Also, the peer that finished the download is converted to a seed and is also marked as idle. Since a new peer programs its departure of the system, whenever an End Download event occurs, all the events related to the peer id have to be removed from the event list. This is also the case of the Departure Leech event. However, for the Departure Seed event, this is not necessary since a Seed only has this event on the event list. Finally, the expo instruction corresponds to the generation of an exponential distributed random variable.
An additional advantage of this event simulator is that it allows the use of different distributions for the time variables. In particular, we want to investigate the system when the transfer rates are constant. The interest of fixing the download and upload rates to constant values, is that it models one important aspect of managed P2P networks. As such, it is possible to evaluate the impact of the priority schemes on these systems. Indeed, in a managed P2P network, the service providers use their own devices which typically have the same upload and download rates. This is an important difference compared to the case of a more general P2P system, where users typically use their PCs or mobile devices (laptops, smart phones, etc.). It is clear that these devices have very different capabilities for both hardware and software. Also note that the Markov model and Fluid model are no longer valid in this case. Finally, the implementation of the constant model in the simulator is straightforward.
In this second scheme, the peers that are statistically more likely to remain in the system longer once they have downloaded the file are served first over the peers that defeat once they become seeds. For this model, the number of cooperative and defeat seeds have to be considered separately. Therefore, the two population model presented before has to be extended accordingly. It is important to emphasize the difference between this priority scheme and the priority scheme for cooperative leeches. In the later, each peer is studied regarding their behavior as a leech and the leeches that are statistically more likely to rest in the system are classified as cooperative peers. These peers who have a high probability of staying in the system throughout the download procedure are served first in case of penury. For the former, each peer is studied regarding their behavior as seed and the ones that are statistically more likely to remain in the system as seeds are classified as cooperative peers.