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Communication networks need to support voice and data calls simultaneously.This results in a queueing system with heterogeneous agents. One class ofagents demand immediate service, would leave the system if not provided. Thesecond class of customers have longer job requirements and can wait for theirturn. We discuss the achievable region of such a two class system, which is theregion of all possible pairs of performance metrics. Blocking probability isthe relevant performance for eager/impatient class while the expected sojourntime is appropriate for the second tolerant class. We obtain the achievableregion, considering static policies that do not depend upon the state of thesecond class. We conjecture a pseudo conservation law, in a fluid limit foreager customers, which relates the blocking probability of eager customers withthe expected sojourn time of the tolerant customers. Using this conjecture weobtain the static achievable region. We validate the pseudo conservation lawusing two example families of static schedulers, both of which achieve all thepoints on the achievable region. Along the way we obtain smooth control(sharing) of resources between voice and data calls. We also consider anexample dynamic policy to establish that the dynamic achievable region isstrictly bigger than the static region, for this heterogeneous queueing system.

Queuing with Heterogeneous Users: Block Probability and Sojourn times