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Abstract

The method of chaining is often used to obtain probability and moment bounds for stochastic processes. We explore the application of the chaining bounds in non-Markovian many-server queues. In these models, we study two-parameter stochastic processes that can be used to describe the service dynamics, in particular, X(t,y) representing the number of jobs in the system at time t that have received an amount of service less than or equal to y (or that have a residual amount of service strictly greater than y). We apply the chaining bounds in two folds: 1) weak convergence of two-parameter stochastic processes and 2) the convergence in distribution of the two-parameter processes to their steady state as t goes to infinity and the interchange of limits. (This is joint work with Yuhang Zhou at Penn State.)