The Method of Chaining for Many Server Queues

Thursday, May 17, 2018 - 10:30am - 11:00am
Lind 305
Guodong Pang (The Pennsylvania State University)
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.)