Multicast is an efficient paradigm for transmitting data from a sender to a group of receivers. In this paper, we focus on multicast in single channel multi-access wireless local area networks (LANs) comprising several small cells. In such a system, a receiver cannot correctly receive a packet if two or more packets are sent to it at the same time, because the packets "collide." Therefore, one has to ensure that only one node sends at a time. We look at two important issues. First, we consider the problem of the sender acquiring the multi-access channel for multicast transmission. Second, for reliable multicast in each cell of the wireless LAN, we examine ARQ-based approaches. The second issue is important because the wireless link error rates can be very high.We present a new approach to overcome the problem of feedback collision in single channel multi-access wireless LANs, both for the purpose of acquiring the channel and for reliability. Our approach involves the election of one of the multicast group members (receivers) as a ''leader'' or representative for the purpose of sending feedback to the sender. For reliable multicast, on erroneous reception of a packet, the leader does not send an acknowledgement, prompting a retransmission. On erroneous reception of the packet at receivers other than the leader, our protocol allows negative acknowledgements from these receivers to collide with the acknowledgement from the leader, thus destroying the acknowledgement and prompting the sender to retransmit the packet.Using analytical models, we demonstrate that the leader-based protocol exhibits higher throughput in comparison to two other protocols which use traditional delayed feedback-based probabilistic methods. Last, we present a simple scheme for leader election. 0-7803-5417-6/99/$10.00 0 1 999 IEEE.

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g. election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios-in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying.Information can be communicated to the population directly by the campaigner (direct recruitment of individuals to spread the message). However, recruiting individuals and direct information communication comes with a cost (such as placing advertisement in the mass media). A campaigner may also provide incentives to individuals for spreading the message. Such an incentive is termed as a word-of-mouth incentive and it rewards an individual who refers a product or a piece of information to others.The campaigner possesses limited resources and is unable to communicate information to the entire population. Not only resource allocation among different strategies, but also the timing of direct recruitment of individuals and giving out word-of-mouth incentives are crucial for maximizing the information epidemic. We model the information spreading process as a Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) epidemic process with time varying information spreading rate, and formulate an optimal control problem which aims to minimize the campaign cost over a given period of time.SIS and SIR epidemic processes are suitable for modeling information epidemics due to the similarities in the ways disease spreads in a biological network and this information spreads in social networks. When susceptible and infected individuals interact, the topic of interest may come up with some probability, which will lead to transfer of information from infected to susceptible individual. This process is very similar to the way in which a communicable disease spreads in ...

Abstract-We model information dissemination as a susceptible-infected epidemic process and formulate a problem to jointly optimize seeds for the epidemic and time varying resource allocation over the period of a fixed duration campaign running on a social network with a given adjacency matrix. Individuals in the network are grouped according to their centrality measure and each group is influenced by an external control function-implemented through advertisements-during the campaign duration. The aim is to maximize an objective function which is a linear combination of the reward due to the fraction of informed individuals at the deadline, and the aggregated cost of applying controls (advertising) over the campaign duration. We also study a problem variant with a fixed budget constraint. We set up the optimality system using Pontryagin's Maximum Principle from optimal control theory and solve it numerically using the forward-backward sweep technique. Our formulation allows us to compare the performance of various centrality measures (pagerank, degree, closeness and betweenness) in maximizing the spread of a message in the optimal control framework. We find that degree-a simple and local measure-performs well on the three social networks used to demonstrate results: scientific collaboration, Slashdot and Facebook. The optimal strategy targets central nodes when the resource is scarce, but noncentral nodes are targeted when the resource is in abundance. Our framework is general and can be used in similar studies for other disease or information spread models-that can be modeled using a system of ordinary differential equations-for a network with a known adjacency matrix.

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas.We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns.

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