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In this paper two novel mathematical methods for network-wide blocking probability evaluation of end-to-end optical burst switching (OBS) networks with heterogeneous ON-OFF traffic are presented. By heterogeneous traffic we mean that the traffic generated by different source-destination pairs might exhibit different values of offered traffic load. Unlike most previous works, which assume a Poisson arrival process for bursts and homogeneous traffic, the presented methods consider that sources generate bursts according to an ON-OFF process, with heterogeneous traffic loads. The ON period corresponds to the burst transmission time and the OFF period to the burst aggregation time. The first method consists of a set of analytical closed expressions which are simple and easy to interpret. However, its computational complexity makes it unsuitable for application to large networks. The second method, equivalent to the first, is made of a set of recurrence relations which makes it extremely fast (execution time in the order of 1 second for all the topologies studied). Because of its advantage in computation time, this paper focuses mainly on the second method. The proposed methods proved to be very accurate when compared to simulation for different network topologies, traffic loads and network capacities. Moreover, the second proposed method is more than 4 orders of magnitude faster than simulation. These features make the second proposed method very useful for network analysis under ON-OFF traffic sources, especially for: a) real world networks, which exhibit heterogeneous traffic, b) large size networks where simulation time can be prohibitively high and c) cases where the network analysis is an intermediate step in more complex procedures, like network dimensioning or topology design.