We consider stable open Jackson networks and study the rare events of excessive backlogs. Although, these events occur rarely they can be critical, since they can impair the functioning of the network. We attempt to estimate the probability of these events by simulations. Since, the direct simulation of rare events takes a very long time, this procedure is very costly. Instead, we devise a method for changing the network to speed up the simulation of rare events. We try to pursue this idea with the help of Large Deviation theory. This approach, under certain assumptions, results in a system of differential equations which may be difficult to solve. To circumvent this, we develop a heuristic method which gives the rule for changing the network for the purpose of simulations. We illustrate, by examples, that our method of simulations can be several orders of magnitude faster than direct simulations.
Femtocells or home base stations are a proposed solution to the problem of degraded indoor service from the macrocell base station in future 4G data networks. In this paper, we study user incentives for the adoption of femtocells and their resulting impact on network operator revenues. We model a monopolist network operator who offers the option of macrocell access or macro+femtocell access to a population of users who possess linear valuations for the data throughput. We compare the revenues from two possible spectrum schemes for femtocell deployment; the split spectrum scheme, where femtocells and macrocells operate on different frequencies and do not interfere, and, the common spectrum scheme, where they operate on the same frequencies (partially or fully) and interfere. Our results suggest that the optimal pricing scheme always charges a higher price for the femtocell service, i.e., the operator does not offer any subsidies for adoption. Yet, at the optimal prices, almost full adoption of femtocells is achieved even for many common spectrum schemes that degrade macrocell capacity. Femtocell deployments provide huge revenue gains when macrocell capacities are low. However, in this range, even common spectrum schemes that heavily degrade the macrocell capacity perform comparably to the split spectrum scheme. Some common spectrum schemes with moderate macrocell degradation yield revenues comparable or higher than the split spectrum scheme at all levels of macrocell congestion.
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