ACM SIGMETRICS Performance Evaluation Review
Series Expansions For Finite-State Markov Chains
Probability in the Engineering and Informational Sciences
Heavily loaded queue coupled to two underloaded queues
Queueing Systems: Theory and Applications
Nonnegativity of solutions to the basic adjoint relationship for some diffusion processes
Queueing Systems: Theory and Applications
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We consider two parallel queues. When both are non-empty, they behave as two independent M/M/1 queues. If one queue is empty the server in the other works at a different rate. We consider the heavy traffic limit, where the system is close to instability. We derive and analyze the heavy traffic diffusion approximation for this model. In particular, we obtain simple integral representations for the joint steady state density of the (scaled) queue lengths. Asymptotic and numerical properties of the solution are studied.