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SUMMARYWe propose an efficient message-flooding scheme that aims to reduce the number of messages transmitted over the network. The proposed method involves the prior conversion of two-way links into single-way links (in this paper we refer to this as the link-cut technique); by avoiding message link collisions we aim to reduce the number of messages transmitted and by incorporating a time-out transaction, we are able to realize a 50 percent reduction in the number of messages as compared to standard flooding methods while maintaining a delivery success rate of 100 percent. In addition, we show in simulations that by making use of information regarding the number of outgoing links for each node (the number of adjacent nodes), we are able to reduce the number of messages sent while constraining the growth in the message transmission times.

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We propose a technique for reducing the number of message duplicates during message flooding in wired networks.The key feature of our proposal is that each node keeps the partial information of shortest path trees whose roots are in its neighborhood. When receiving the flooding message, each node generates its duplicates and forwards them to a subset of neighbors, which are on the partial shortest path tree rooted at the message source. The partial information on shortest path trees is stored in message forwarding table of each node. We show that the partial shortest path tree can be constructed in a fully-distributed manner by simply using dummy message flooding. Our proposal can largely reduce the number of message duplicates while it guarantees the full reachability and keeps the time to reach the same as that in the full flooding. Duplicate reduction effect of our proposal is theoretically evaluated and numerically examined by simulation experiments.

We propose a new finite population model for cellular mobile systems with traveling users. In this model, mobile users arrive according to a Poisson process from outside the system, independently travel in the system, and leave the system in due time. A mobile user is either in call (active) or out of call (inactive). We find that if two minor modifications are made to the model, the joint distribution of the number of calls in progress in each cell has the product form. Making the two modifications is referred to as product-form approximation in this paper. Under the product-form approximation, the probability that channels are fully occupied in a cell is given by the Erlangloss formula. We evaluate the accuracy of the product-form approximation through several simulation experiments, and find that the Erlang-loss formula remains applicable to the performance evaluation and channel provisioning of cellular mobile systems.Keywords: Telecommunication, mathematical modeling, cellular mobile systems, Erlang-loss formula, insensitivity IntroductionInvestigating the performance characteristics of cellular mobile networks has been the focus of considerable research reported in literature. The performance of cellular mobile systems is often described in terms of the probability of call blocking or that of hand-off blocking. Thus, it is crucial to find a simple method to evaluate these performance indices in order to design cellular mobile networks.In traditional wired telephone networks, the Erlang-loss formula has been used to evaluate the call blocking probability. The Erlang-loss formula holds when new calls are generated according to a Poisson process. In wired telephone networks, calls are generated by users, the number of which is much larger than the number of available channels, and thus the call arrival rate does not depend on the number of calls in progress. Under such infinite population models, the use of the Poisson-arrival assumption is appropriate. However, the infinite population model may not be applicable to cellular mobile systems because the number of mobile users (mobile units) in a small cell cannot be regarded as "infinite" compared with that of available channels. In this sense, the finite population model would suite cellular mobile systems. Note that, due to user mobility, the number of mobile users within a cell should fluctuate over time. Most existing formulas based on finite population models like the Engset formula, however, do not take the fluctuation of the population over time into account.Recently, Machihara proposed a finite population model for cellular mobile systems [7]. In Machihara's model, mobile users arrive according to a Poisson process from outside the system, travel independently within the system, and leave the system in due time. He found that, in this model with a certain modification, the call blocking or hand-off blocking probability is given by the Erlang-loss formula. In addition, he showed that an insensitive property holds; the stationary