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The Delay/disruption tolerant networks (DTNs) provides a new option for the future network applications, but nothing has been done for the research on how to design and deploy the Web servers which can provide performance guarantee or service differentiation on DTNs. Response delay is a key performance metric for Web servers and proportional delay differentiated service is an important DiffServ model. This paper designs a DTN-enabled Web server supporting differentiated service, and implements proportional delay differentiated service based on an adaptive control approach. Periodically the adaptive controller calculates and adjusts the number of worker threads in Web server for different types of clients according to the pre-specified delay differentiation parameters. Simulation results demonstrate that proportional delay differentiation can be achieved in the DTN-enabled Web server even under dynamic workloads, different workload distributions and varying references.