Grant: Discovery Grants Program - Individual

My objective is to study block-structured Markov chains and various cases of GI/GI/s queues.  These objects are interrelated and complementary to each other. Block-structured Markov chains are characterized by partitioning the state space into subsets called levels, each level consisting of a number of stages, whose transition probabilities form a blocked matrix. I will study block-structured Markov chains where the blocked matrices may be infinite dimensional, and/or level dependent, and/or finite dimensional, but whose sizes may change as the level of the chain changes.    The GI/G/s queueing systems I intend to study are those in which the arriving customers may be of different types; server(s) may take a vacation; the number of available servers may change; blocked customers may retry for service after a random amount of time, or may leave the systems forever without service; and the waiting room capacity may, for different types of customers, be finite or infinite.    The anticipated results of this research will be directly applicable to various real world stochastic models and queueing systems arising in telecommunication networks, wireless communication networks, computer systems and manufacturing systems, and areas such as economics and finance.  The techniques to be developed in this research will provide information on system performance that is essential for system designers seeking out optimal system configurations.  In the longer term, this research will contribute to the theory of Markov processes and the theory of queues and retrial queues. It may also lead to more challenging and practically attractive models, and may provide general techniques useful in other disciplines of stochastic modeling.