Simulative Analysis of Saturation Condition in a Pedestrian Ad-hoc Network Andrea Gorrieri Wireless Ad-hoc Sensor Network Laboratory Department of Information Engineering University of Parma, I-43124, Parma, Italy Email: andrea.gorrieri@gmail.com Gianluigi Ferrari Wireless Ad-hoc Sensor Network Laboratory Department of Information Engineering University of Parma, I-43124, Parma, Italy Email: gianluigi.ferrari@unipr.it Abstract—In this paper, we consider a particular type of wireless ad-hoc networks, namely Pedestrian Ad-hoc NETworks (PANETs), where all nodes in the network are sources and desti- nations of information. In particular, we refer to an application where nodes report their presence by broadcasting an hello message to all other nodes in both IEEE 802.11 monodimensional and bidimensional scenarios. The system performance, in terms of throughput and delay, is analyzed using a recently proposed broadcasting protocol, namely Irresponsible Forwarding (IF) and its extension, denoted as Silencing IF (SIF). The proposed framework allows to determine a critical hello generation rate below which multi-source broadcasting is efficient. Keywords—Ad-hoc networks; broadcast protocols; saturation conditions. I. I NTRODUCTION In general, in ad-hoc networks nodes share and distribute information by rebroadcasting. Typically, rebroadcasting re- sults in redundant retransmissions of the same information packet, thus leading to a useless occupation of the radio chan- nel, and depleting the available network resources. Minimizing the redundancy, while still guaranteeing complete reachability throughput the network, is one of the main objectives in multi-hop broadcasting [1][2]. In recent years, many multicast protocols for ad hoc networks have been proposed by the research community mostly related to single source scenario [3][4]. In [5], multiple sources communicate using a cluster- based multicast protocol. In this work, we focus on IEEE 802.11 Pedestrian Ad- hoc NETworks (PANETs), where users in network report their presence by sending a very small information data to all others. In this setting, the main design goal is to make information fast and to reach the largest number of users in network. Note that presence information should be sent periodically with a relatively long period (because of the low speed of the considered terminals). This is representative for opportunistic ad-hoc networks of smartphone or tablets in which node acts as source, re- broadcaster, and receiver. In order to propagate the generated information, the nodes make use of a probabilistic multihop broadcast protocol, denoted as Irresponsible Forwarding (IF) [6], and a possibile extension, denoted as silencing IF (SIF) [7], which make use of the concept of silencing. Two different types of scenario are considered: monodimensional and bidi- mensional. The efficiency of these protocols is evaluated in terms of throughput and propagation delay. The structure of the paper is the following. In Section II, the IF and SIF protocols are defined. In Section III is carried out the performance analysis of the two protocol in monodimensional and bidimensional scenarios. In Section IV the results obtained by IF and SIF are summarized and compared. Finally, conclusions are drawn in Section V. II. IF AND SIF The IF protocol is probabilistic in the sense that a node decides to retransmit or not a received packet in a probabilistic manner. Considering a monodimensional scenario, if d ij is the distance between the source i and a potential rebroad- caster node j , the probability of retransmission is computed according to a certain Probability Assignment Function (PAF), defined as follows: p = exp  - ρ s (z - d ij ) c  . (1) Note that with the probability assignment in (1), the node spatial density ρ s (dimension:[nodes/m 2 ]) is also taken into account. When the network is sparse, the overall retransmis- sion probability should be high (e.g., even if the receiving node is close to the transmitter) in order to ensure complete connectivity. In addition, the coefficient c (adimensional) is also effective at shaping the rebroadcast probability, as the overall rebroadcast probability can be increased by increasing the value of c [8]. In order to explain the concept of silencing, we first in- troduce the concept of Transmission Domain (TD). The initial transmission of a new packet from a source is denoted as the 0-th hop transmission, while the source itself identifies the so- called 0-th transmission domain. After the source transmission, the packet is then received by the N z = ρ s z source neighbors, that are the potential rebroadcasters at the 1-st hop. Hence, their ensemble constitutes the 1-st TD. Each node in the 1-st TD decides to forward the packet according to (1). With IF, it is possible that many nodes in a TD decide to rebroadcast the packet, and this can leads to inefficiencies due to a too large number of retransmissions and, therefore, potential collisions. A more efficient probabilistic broadcast protocol, regardless of the expression of the PAF, can be obtained by imposing that 978-1-4673-2480-9/13/$31.00 c  2013 IEEE 978-1-4673-2480-9/13/$31.00 ©2013 IEEE 189