In this paper, bandwidth acquisition and allocation problem of a telecommunications Bandwidth Broker (BB) is analyzed under uncertain end-user capacity requests and pay-per-byte (volume) based pricing policy. Furthermore, related objective function coefficients such as revenue and costs are modeled as fuzzy numbers in order to cope with vague market conditions. By integrating fuzzy mathematical programming and two-stage stochastic programming techniques, deterministic equivalent of single objective profit maximization problem of BB is obtained solved to optimality. In addition, infrastructure related performance measures such as delay and jitter amounts in the network are modelled via stochastic parameters that obey some known probability distributions. Two performance statistics namely fuzzy Expected Value of Perfect Information (EVPI) and fuzzy Value of Stochastic Solution (VSS) are defined to demonstrate the efficiency of proposed methodology compared to deterministic approach. In addition, several secondary performance measures such as expected capacity utilization, expected demand fulfilment ratio and capacity loss are calculated under different problem settings. In conclusion, numerical experiments showed that fuzzy stochastic method provides more profit depending upon problem size in compression with deterministic strategy.