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Trust management is an important issue in a grid environment where consumers and service providers are distributed geographically across autonomous administrative domains. In this paper, we propose a reputation-based trust management architecture that supports the choice of service providers (SPs) based on their trust values available on the fly through the intermediaries, brokers. This architecture insists on multiple brokers in each domain. The entities (consumers and the SPs) are distributed across these brokers, with each of these entities being associated with more than one broker. This improves the redundancy of information maintained at the broker sites, thereby improving the reliability. This also eases the network traffic at the broker sites while handling consumer requests and feedbacks. The issues rising out of such an arrangement of multiple brokers, namely the distribution of entities among the brokers and maintenance of consistency of information across the brokers, are addressed well in this paper. Trust values of SPs and consumers are evaluated and updated dynamically after the completion of each transaction. This enables the consumer to receive the response from the broker significantly quicker compared to other reputation-based-trust models where the trust values are computed at the request-time. Trust parameters such as the number of transactions, satisfaction-value, and cost of transaction, criticality of transaction, different weights for direct and indirect transactions and different weights for past and recent transactions are considered for the trust evaluation. This model shows a marked improvement in reduction of the cost-loss to the consumer community and reduction in the waiting time for handling the consumer's requests over other models which operate without trust and with trust computed at the request-time. The impact of broker's feedback on the computation of trust values is also presented.