Timed mobile ambients for network protocols

Ambient calculus is a calculus for mobile computing able to express local communications inside hierarchical domains. So far the timing properties have not been considered in the framework of mobile ambients. We add timers to capabilities and ambients, and provide an operational semantics of the new calculus. Certain results are related to the passage of time, and some new behavioural equivalences over timed mobile ambients are defined. Timeout for network communication (TTL) can be naturally modelled by the time constraints over capabilities and ambients. The new formalism can be used to describe network protocols; Simple Network Management Protocol (SNMP) may implement its own strategy for timeout and retransmission in TCP/IP.