Systems of functional equations
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Patterns in random binary search trees
Random Structures & Algorithms
A Tandem Queue with Coupled Processors: Computational Issues
Queueing Systems: Theory and Applications
Multiaccess, Reservations & Queues
Multiaccess, Reservations & Queues
Analytic Combinatorics
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
A tandem queueing model with coupled processors
Operations Research Letters
Exact tail asymptotics in a priority queue--characterizations of the non-preemptive model
Queueing Systems: Theory and Applications
Tail asymptotics for a generalized two-demand queueing model--a kernel method
Queueing Systems: Theory and Applications
Wireless three-hop networks with stealing II: exact solutions through boundary value problems
Queueing Systems: Theory and Applications
First response to letter of G. Fayolle and R. Iasnogorodski
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.